Geocells for Unpaved Roads: Analysis of Design Methods from the Literature

Abstract

Most forest roads are unpaved, connecting rural and forest areas and enabling access for firefighting and commercial purposes. Low traffic levels lead to reduced functional demands, while rapid development of deformations results in frequent maintenance. Using geocells as reinforcements reduces deformations, minimizing maintenance needs. Herein, geocell-reinforced soil design methods were collected and categorized based on their result: increase in confining pressure; bearing capacity; height of the base layer. The goal was to compare methods reported in the literature, from a user perspective and within each category, using a base scenario. The methods were analysed to better understand their differences and application conditions. Methods that estimate the increase in confining pressure refer to static or cyclic loading, leading to results that are not directly comparable; often, the reinforcement contribution is represented by an apparent cohesion, with no physical meaning and misleading. Methods that estimate the increase in bearing capacity due to geocell consider its contribution differently (lateral resistance, vertical stress dispersion, and membrane effects) and distinct combinations. For geocell reinforcement, the membrane effect can be neglected. Methods that estimate the height of the base layer can be used directly for an expedite design of unpaved roads. When geocell reinforcement is adopted, the minimum height of the base layer should coincide with that of the geocell. Thus, while current methods contribute and support the design of unpaved roads, further work is essential to develop methods that are of simple and of expedite application for forest engineers, adaptable to local conditions and requirements.

Introduction

The introduction of geosynthetics in structural layers for increasing the bearing capacity in unpaved and paved roads have been subject of study for over 40 years [1]. Geocells are one of many types of geosynthetics, but one of the few that are three-dimensional (3D). This characteristic provides confinement of the infill soil, increasing the bearing capacity, which is of relevant importance for roads [1,2,3]. The advantages of using geocells in roads include: reducing construction time; reducing quantities of good quality borrow materials needed; lowering the requirements for the borrow material, allowing the use of local soils; increasing intervals between maintenance operations and rehabilitation works on the road; increasing sustainability, and decreasing pollution and the carbon footprint, for example associated with transporting borrow materials to the road construction site [1, 4,5,6].

Existing studies on geocells include different approaches, namely: experimental studies, such as monotonic [7, 8] and cyclic [9, 10] triaxial tests; analytical studies, namely using equations to quantify the contribution of geocells based on increased confining pressure, load carrying capacity and failure stresses and strains; numerical studies, adopting an equivalent composite approach or discretising the different materials, and two-dimensional (2D) or three-dimensional (3D) numerical models [3]. 2D numerical models that include geocells have many simplifications, as they cannot capture the true 3D nature of the geocells and their mobilisation mechanisms. In most cases, a geocell is represented by a composite material with properties similar to those of a soil and a Mohr–Coulomb model; examples in [11,12,13,14]. Alternatively, 3D numerical models can represent the response of geocells more realistically. Examples of 3D models of structures including geocells are presented in [15,16,17]. Nevertheless, most practitioners do not have access to commercial software that enables carrying out 3D analysis. Thus, numerical simulations using software should be used to complement and verify designs resulting from analytical methods.

This paper includes an analytical study on the design of geocells for unpaved roads. Methods for quantifying the contribution of geocells were compiled and grouped. To facilitate understanding and comparison of methods and their associated variables and parameters, the notation adopted was homogenised. A general base scenario was defined, to enable comparison between groups of design methods. A parametric analysis was carried out to better understand the influence of relevant parameters on the outputs of each design method. The main goal of this paper is to provide actual, simple, and systematised information to assist practitioners in the design of geocell reinforced unpaved roads. Usually, the investment on unpaved roads, at different project stages (including design, construction, and maintenance) is quite low. Making available information in a straightforward way, that practitioners with limited experience on geocells can use, will contribute to more realistic and sound designs.

Geocells in the Design of Unpaved Roads

Geocells in Unpaved Roads

Unpaved roads are often characterised by having low traffic volumes. Thus, investment in the design and construction phases is low, resulting in rapid degradation of the structure and a consequent need for frequent maintenance operations [18]. Usually, unpaved roads consist of three layers: subgrade; base layer; surface layer (Fig. 1). As the traffic level is often low, frequently the pavement structure is simplified, resulting in only two layers (subgrade and base layer); the latter functions as a surface layer. The base layer may consist of a local soil, an aggregate, or a mixture of these two materials, depending on the traffic level [19, 20] and availability of materials.

Fig. 1

Typical structure of an unpaved road; includes typical load dispersion within the base layer (adapted from [21])

Often, the design assumes requirements that need to be met during construction, including adequate compaction of the material layers, and the materials used must comply with minimum requirements [20]. In the literature there are examples of using geosynthetic reinforcements to decrease the number of maintenance operations necessary to ensure serviceability of the road [4,5,6]. Reinforcement with geosynthetics, particularly with geocells, is a long-term, viable, and economical solution, avoiding multiple maintenance throughout the useful life of a road [4,5,6]. Usually, geocells are introduced into the base layer. Figure 2 illustrates common cross sections of unpaved roads with geocells, including three-layer and two-layer structures. The height of the geocell layer can coincide with the base layer or be smaller; often, the infill soil is that of the base layer.

Fig. 2

Layers of the pavement structure with geocell in the base layer: a three layers and height of the base layer equal to the height of the geocell; b two layers (no surface layer) and the height of geocell smaller than the base layer

Types of Design Methods

In the literature, different design methods for geosynthetics and, in particular for geocells, can be found. These methods can be grouped according to the approach adopted. Some authors quantify the influence of the geocell as an increase in confining pressure (Sect. Increase in Confining Pressure), while others quantify it as an increase in bearing capacity (Sect. Bearing Capacity); other methods allow estimating the height of the base layer directly with and without reinforcement (Sect.Height of the Base Layer). Table 1 presents the design methods identified in the literature review, grouped according to the approach adopted. These formulations have been based on: monotonic triaxial tests [7, 8]; cyclic triaxial tests [9, 10]; large-scale cubical tests with cyclic load [10]; analytical methods [22,23,24,25,26,27]. Some design methods focus on the case of unpaved roads, such as Giroud et al. [28, 29], Presto [23] and Pokharel et al. [1]. Indraratna et al. [10] developed a method based on railways. Zhang et al. [24, 25] developed a method based on reinforced road embankment. The methods by Giroud et al. [28, 29] and Pokharel et al. [1], developed for unpaved roads, have as major output the required height for the base layer, considering its reinforcement with a geogrid or geotextile, for Giroud et al. [28, 29], and with geocells, for Pokharel et al. [1]).

Table 1 Design methods with geocells, from the literature, grouped according to the approach adopted

In the following sections, the different methods are described in detail; the notation adopted was changed relatively to the original publications, to enable direct comparison between methods.

Overview of Existing Design Methods for Geocells

Initial Considerations

The beneficial effect of geocells in roads is often attributed to their ability to increase the confining pressure of the infill soil (Sect. Increase in Confining Pressure) or to the improved bearing capacity of the pavement structure (Sect. bearing capacity). Other methods do not account for the reinforcement explicitly and give direct outputs for the design of unpaved roads (Sect. Height of the Base Layer).

General Characteristics of Geocells

Geocells are one of the few types of geosynthetics with a 3D structure (Fig. 3): a honeycomb shape, characterised by an initial diameter of the cell pocket d₀, and height h_g. The honeycomb structure is filled with soil or other material, which is confined within that structure.

Fig. 3

Geocell reinforcement: a plan-view; b 3D view

Polypropylene (PP) and polyethylene (PE) are the most common constituent polymers in geosynthetics. Different grades of PE can be distinguished: low-density polyethylene (LDPE); medium-density polyethylene (MDPE); high-density polyethylene (HDPE) [22, 30]. One of the advantages of using PP is that its density is lower than that of HDPE. However, PP has high sensitivity to oxidation, environmental exposure, and high temperatures [31]. Geocells are constituted by polyethylene (PE), polypropylene (PP) and novel polymeric alloy (NPA) [1, 3, 22, 30]. Table 2 presents key characteristics of PP, PE, and NPA.

Table 2 Comparative summary of key characteristics of polymers used in geocells [22, 30, 32]

Increase in Confining Pressure

Due to its honeycomb-shaped geometry, a geocell can limit lateral movements of soil particles in its pockets, creating an increased confinement effect [9]. During loading, the geocell exerts an additional confining force on soil particles, preventing their dispersion [9, 10]. Table 3 summarises equations from the literature to calculate the increase in confining pressure (Δσ₃) due to geocells. The relevant characteristics of the geocell and the geocell-soil combination are presented in Table 4, while other relevant quantities are summarised in Table 5.

Table 3 Equations from the literature for the increase of confining stress due to a geocell; see Tables 4 and 5 for the meaning of the different quantities

Table 4 Characteristics of the geocell relevant for quantifying the increase in confining pressure due to a geocell, in Table 3

Table 5 Parameters needed for the application of the methods that quantify the increase in confining pressure due to a geocell, in Table 3

According to Bathurst and Karpurapu [7], there are several proposals to estimate the increasing in confining stress (Δσ₃) caused by a membrane using data from triaxial tests, particularly using the Elastic Membrane Theory proposed by Henkel and Gilbert [33]. Bathurst and Karpurapu [7] carried out monotonic triaxial tests to assess the behaviour of the geocell-soil composite material. These authors studied different infill materials, such as silica sand and crushed stone. The results obtained allowed estimating the increase in apparent cohesion (cʹ, Fig. 4) of the geocell-soil composite material relatively to the unreinforced soil. Figure 4 illustrates conceptually the stress state of the unreinforced soil and of the soil reinforced with geocell. To describe the effect of the reinforcement as an additional lateral or confining pressure, this method analyses the geocell-reinforced soil as a homogenous material (a soil) with the same fundamental shear strength. Bathurst and Karpurapu [7] used Eq. (1) (Table 3), proposed by Henkel and Gilbert [33], to calculate the increase in confining pressure (Δσ₃).

Fig. 4

Mohr circle construction for calculation of equivalent cohesion for geocell-soil composites, based on an increase in confining pressure (adapted from [34])

In the literature, the increase in confining pressure (Δσ₃) is a function of modulus of the geocell, M, and its diameter, d, and other parameters that depend on the proposal for quantifying Δσ₃ analysed. Rajagopal et al. [8] studied the influence of the confinement provided by geocells on the behaviour of granular soils, namely their stiffness and strength. The authors present a simple methodology for estimating the apparent cohesion (cʹ, Fig. 4) based on the increase in confining pressure (Δσ₃) considering a membrane effect (Eq. 2).

According to Anjos et al. [34], the apparent cohesion should not be used to quantify the shear strength of reinforced soil, because using a cohesion intercept, for both reinforced and unreinforced soil, that has no physical significance is misleading and ought to be avoided.

Yang and Han [9] used a mechanistic-empirical method combined with the results obtained from triaxial cyclic tests (repeated load tests). The increase in confining pressure (Δσ₃) was estimated by Yang and Han [9] considering the geocell tensile stiffness, M_T, and the permanent deformation behaviour of the geosynthetic-reinforced unbound granular material, resulting in Eq. (3). Indraratna et al. [10] performed large-scale cubical triaxial tests with cyclic loading. The authors used sub-ballast as the infill soil for the geocell and the study was designed for railways. The increase in confining pressure (Δσ₃) was estimated by assuming a constant ratio between the radial, ε₃, and circumferential, ε_c, strains considering a profile of deflection, resulting in Eq. (4).

Bearing Capacity

When loaded, reinforcements, namely geocells, cause different effects on soil, such as lateral resistance effect (confinement effect), Fig. 5a, vertical stress dispersion effect, Fig. 5b, and membrane effect, Fig. 5c. When the soil is loaded, the confinement effect is originated, inducing horizontal stresses between the infill soil and the geocell wall, redistributing the vertical load on the subgrade, thus creating the vertical stress dispersion effect. This effect reduces the vertical stress transmitted to the subgrade. The membrane effect is generated through the imposed load, originating an additional tensile force (T) on the geocell. This force improves the bearing capacity of the reinforced solution (p_r) relative to the unreinforced soil (p_u) and reduces the pressure on the subgrade soil [23, 24].

Fig. 5

Geocell effects (adapted from [24]): a lateral resistance effect (confinement effect); b vertical stress dispersion effect; c membrane effect

Table 6 presents equations for the bearing capacity of the reinforced soil (p_r), the mechanisms considered on each case, and the relevant loading conditions from different studies. The approach adopted is similar, and the bearing capacity of the soil reinforced with geocell (p_r) is obtained as the sum of the bearing capacity of the unreinforced soil (p_u), and the contribution of the geocell reinforcement (Δp_r). The proposals in the literature refer to different loading conditions (drained and undrained); and the influence of the geocell is accounted for differently. Koerner [22] and Presto [23] provided equations for the calculation of the bearing capacity of the unreinforced soil (p_u): Eq. (5) (without depth factors, d) and Eq. (6) (without shape and depth factors, s and d), respectively. Zhang et al. [24, 25], Avesani et al. [26] and Sitharam and Hegde [27] did not present equations for p_u. For those cases, herein it was assumed that p_u was calculated according to [35], Eqs. (5) and (6), as well as the bearing capacity factors (N_c, N_q, N_γ, N_cu), shape factors (s_c, s_q, s_γ, s_cu) and the depths factors (d_c, d_q, d_γ, d_cu). Equation (5) and Eq. (6) refer, respectively, to the bearing capacity of the unreinforced soil (p_u) for drained and undrained loading conditions.

Table 6 Bearing capacity equations considering the effect of the geocell reinforcement; see Tables 7, 8, and 9 for meaning of the different quantities

$${p}_{u}=c^{\prime}{N}_{c}{s}_{c}{d}_{c}+q^{\prime}{N}_{q}{s}_{q}{d}_{q}+0.5 {N}_{\gamma }{s}_{\gamma }{d}_{\gamma }{B}_{p}\gamma ^{\prime}$$

(5)

$${p}_{u}={N}_{cu}{s}_{cu}{d}_{cu}{c}_{u}$$

(6)

The characteristics of the geocell, the infill soil and the load are described in Tables 7, 8 and 9, respectively.

Table 7 Characteristics of the geocell relevant for estimating the bearing capacity, in Table 6

Table 8 Characteristics of the infill soil relevant for estimating the bearing capacity, in Table 6

Table 9 Characteristics of the load relevant for estimate the bearing capacity in Table 6

In Eq. (7) and Eq. (11) K_a is given by Eq. (12).

$${K}_{a}=ta{n}^{2}\left(45-{\phi }_{IF}^{\prime}/2\right)$$

(12)

Height of the Base Layer

In the literature there are methods that can directly estimate the height of the base layer of unpaved roads reinforced with geosynthetics, which are the cases of the methods proposed by Giroud et al. [28, 29] and Pokharel et al. [1]. These methods consider different types of geosynthetics: the method by Giroud et al. [28, 29] refers to geogrids and geotextiles, and the one by Pokharel et al. [1] is applied to geocells.

Giroud et al. [28, 29] developed a design method for reinforcing unpaved roads using geogrids, which also includes geotextiles. At the time, this method was a step change, as it was more accurate than previous methods. The method by Giroud et al. [28, 29] allows estimating the height of the base layer, considering different factors (Table 10), such as the tire radius (calculated using tire pressure and axle load [28]), load and pressure, Eq. (13), characteristics of the foundation soil, the infill soil and the geosynthetic reinforcement. The parameters of Eq. (13) are presented in Table 10.

Table 10 Relevant characteristics for estimating the height of the base layer used in [28, 29] and Pokharel et al. [1] methods

$$P=p\times \pi \times {r}^{2}$$

(13)

The Giroud et al. [28, 29] method was initially formulated based on laboratory cyclic plate load tests. However, as these tests do not correspond to real field conditions, later the method was calibrated using field data [28, 29]. When using the method by Giroud et al. [28, 29], it is necessary for the designer to have a critical notion of the number of passages.

The method by Giroud et al. [28, 29] includes two equations, one for estimating the height of the base layer without reinforcement, h_u (Eq. (14), which corresponds to Eq. (15) with J = 0 mN/º) and another one to estimate the height of the base layer (h_r) for the solution reinforced with a geogrid or a geotextile, Eq. (15). These equations were calibrated by the authors, using field data from Giroud et al. [29].

$${h}_{u}=\frac{0.868+0.661\times {\left(\frac{r}{h}\right)}^{1.5}\times {\text{log}}N}{1+0.204\times \left({\text{min}}\left(\frac{3.48 CB{R}_{BL}^{0.3}}{CB{R}_{SG}}, 5.0\right)-1\right)}\times \left[\sqrt{\frac{\frac{P}{\pi \times {r}^{2}}}{m\times {N}_{c}\times CB{R}_{SG}\times {f}_{C}}}-1\right]\times r$$

(14)

$${h}_{r}=\frac{0.868+(0.661-1.006\times {J}^{2})\times {\left(\frac{r}{h}\right)}^{1.5}\times {\text{log}}N}{1+0.204\times \left({\text{min}}\left(\frac{3.48 CB{R}_{BL}^{0.3}}{CB{R}_{SG}}, 5.0\right)-1\right)}\times \left[\sqrt{\frac{\frac{P}{\pi \times {r}^{2}}}{m\times {N}_{c}\times CB{R}_{SG}\times {f}_{C}}}-1\right]\times r$$

(15)

Herein, m is the bearing capacity mobilization coefficient, Eq. (16).

$$m=\left(\frac{s}{{f}_{s}}\right)\times \left\{1-\upxi \times \left[-\upomega \times {\left(\frac{r}{h}\right)}^{n}\right]\right\}$$

(16)

In the study of Giroud et al. [28, 29], an acceptable rut depth of 75 mm was considered, corresponding to the serviceability failure. If there is a base layer, the deflection at the interface between the base and the subgrade layers will be smaller than 75 mm. Thus, the corresponding value for the bearing capacity mobilization coefficient (m, Eq. 16) will be lower than 1 (and equal to 1 if there is no base layer). In addition, it is necessary to define a minimum height of the base layer [28, 29]. For an acceptable rut depth of 75 mm, the minimum height of the base layer is 100 mm.

Equation (15) can be written considering the undrained shear strength of the subgrade soil, c_u,SF, (in kPa), as this quantity can be related with the CBR value of the subgrade, CBR_SB, Eq. (17), where f_c (factor between undrained shear strength and CBR of subgrade soil) is equal to 30 [28, 29]; this equation is only applicable for values of CBR_SG less than 5.

$${c}_{u,SG}={f}_{c}\times CB{R}_{SG}$$

(17)

The method by Pokharel et al. [1] is based on the method by Giroud et al. [28, 29] but it was formulated specifically for the application of geocells. Laboratory cyclic plate load tests and full-scale moving wheel tests were used to calibrate the method. The latter were carried out on existing roads and the already constructed road was assumed to be the subgrade, adding the geocell placed on top of the road with a generous layer of infill soil, resulting in the base layer and a surface layer. Equation (18) is used to estimate the height of the base layer (h_r) with geocell reinforcement. To estimate the height of the unreinforced base layer (h_u), Eq. (14) proposed by Giroud et al. [28, 29]. was applied. The Pokharel et al. [1] method was also calibrated by using laboratory cyclic plate loading tests and a full-scale moving-wheel tests, considering a weak subgrade, a NPA geocell and an acceptable rut depth of 75 mm.

$${h}_{r}=\frac{\left(0.868+0.52\times {\left(\frac{r}{h}\right)}^\frac{3}{2}\times {\text{log}}N\right)}{1+0.204\times \left({\text{min}}\left(\frac{3.48 CB{R}_{BL}^{0.3}}{CB{R}_{SG}}, 5.0\right)-1\right)}\times \left(\sqrt{\frac{P}{\pi \times {r}^{2}\times m\times 5.14\times {c}_{u,SG}}}-1\right)\times r$$

(18)

Methodology

Initial Considerations

In this paper, methods for the design of unpaved roads with geocells were compiled, grouped according to their output (Sect. “Overview of Existing Design Methods for Geocells”), and analysed by comparing their results. A base scenario was defined, to compare the design methods within each group (described in Sect. “Base Scenario”). To better understand how key design parameters influence the design outputs, a parametric analysis was also carried out (summarised in Sect. “Parametric Analysis”).

Base Scenario

For comparing the design methods identified in the literature, a base scenario for each group of methods was defined (Tables 11, 12, 13). A three-layered cross section was chosen, Fig. 2a, with the height of the geocell coinciding with that of the base layer (Fig. 6). The estimates of the height of the base layer did not consider the contribution of the surface layer for the overall strength. Thus, a surface layer with a height of 50 mm [36] was considered to avoid exposing the geocell directly to the stresses and strains due to the traffic. The variety of methods and input parameters of each method created an additional challenge, as some methods use specific parameters, not always available or simple to quantify. Because of all the differences between methods, it was impossible to define a single base scenario that allowed direct comparison between all methods.

Table 11 Parameters of the base scenario for the methods that estimate the increase in confining pressure

Table 12 Parameters of the base scenario for the methods that estimate the bearing capacity

Table 13 Parameters of the base scenario for the methods that estimate the height of the base layer that correspond to the application of the Giroud et al. [28, 29] method

Fig. 6

Chosen section for the base scenario

To define each base scenario the following approach was adopted. First, common parameters were identified, their values compared, and particular values were chosen (included in Tables 11 and 12). Some parameters were assumed equal. For example, for the methods with the increase in confining pressure, the membrane modulus (M), the mobilized geocell modulus (M_m), the secant modulus of the geosynthetics (M_s), and the geocell tensile stiffness (M_T) were assumed to be the same (Table 11). For the bearing capacity methods, the angle of dispersion due to the geocell reinforcement (θ_c) and the horizontal angle of the tensile force T (α) were assumed to be the same, Fig. 6 and Table 12.

Second, method specific parameters were taken from the original source. For methods that estimate the increasing confining pressure, the data is summarised in Table 11, from Yang and Han [9] and Indraratna et al. [10], as the latter is based on the former. In the method by Rajagopal et al. [8] two types of geocell diameter are identified: d_f, diameter of the cell pocket at an axial strain of ε_a; d₀, initial diameter of the cell pocket. For the base scenario considered herein, d₀ was 0.15 m and d_f was obtained using Eq. (21) [8]. For the Indraratna et al. [10] method, it was necessary to assume the value of the volumetric strain to calculate the radial strain: ${\varepsilon }_{vol}={\varepsilon }_{1}+2{\varepsilon }_{3}$.The data relevant for the methods that estimate bearing capacity are summarised in Table 12. Lastly, for the methods that directly estimate the required base layer height, the data from Giroud et al. [28, 29] and Pokharel et al. [1] were considered (summarised in Table 13).

For the methods that estimate bearing capacity (p_r), additional data was needed. The subgrade soil was assumed to be a clay soil, with c_u,SG = 10 kPa. The base was formed by a geocell filled with soil: geocell of diameter d = 0.15 m; for the unit weight of the infill soil (γ) and angle of internal friction of infill soil ($\phi$'_IF) to be placed within the geocell pockets, values of 16 kN/m³ and 20º, respectively, were considered. For the loading, the conditions defined by Giroud et al. [28, 29] were assumed: acting load, p_act, of 550 kPa and radius (r) of the equivalent circular contact area of the tire with the top of the base layer equal to 0.152 m. The value of B_p was adjusted to reflect the assumptions of the different methods regarding the plan configuration of the loaded area, while keeping the equivalent contact area of the tire constant. Thus, a width of 0.304 m (circular load area) and 0.270 m (rectangular load area) were considered. To estimate the value of the tensile force of the geocell (T), a correlation between the tensile modulus of the geocell (E_g), and the tensile strain of the geocell material (ε) was used, resulting in Eq. (19).

$$T={E}_{g}\times \varepsilon \times {h}_{g}$$

(19)

For the vertical stress dispersion effect, an angle of dispersion of the load due to the geocell reinforcement, θ_c, of 30° was adopted. For comparable conditions, the stress redistribution effect (e) defined by [26], was calculated to be the same as that by [26], as $\frac{{B}_{p} }{{B}_{p}+2{h}_{g}tan{\theta }_{c}}$.

Table 12 presents the parameters, values, units, and their corresponding source selected for the base scenario, for the methods that estimate the bearing capacity (p_r).

For the methods that estimate directly the required base layer height (h_r), the data provided by Giroud et al. [28, 29] and Pokharel et al. [1] were considered (Table 13), with exception of the subgrade parameters (c_u,SG and CBR_SG). For the case of the unreinforced solution, Eq. (14) by Giroud et al. [28, 29] was used; for the solution reinforced with geocells the data by Pokharel et al. [1] was adopted for the base scenario.

Parametric Analysis

To better understand the importance of the different quantities on the output from the design methods analysed, a parametric analysis was carried out. Again, each group of methods was considered separately.

For the methods that quantify an increase in confining pressure, the parameters analysed were: the modulus of the membrane, M, the secant modulus of the geosynthetics, M_S, the geocell tensile stiffness, M_T and the mobilized geocell modulus, M_m; original diameter of the triaxial specimen, d and the initial diameter of the cell pocket, d₀; circumferential strain, ε_c; dilation angle, ψ; limit number of passes/cycles, N_Limit; the Poisson’s ratio of geocell, υ_g.

For methods considering the increase in bearing capacity due to geocell reinforcement, the parameters studied were: the acting load, p_act; the angle of internal friction of the infill soil, $\phi$′_IF and the interface friction angle between the infill soil and the geocell wall, δ; the angle of dispersion of the load due to the geocell reinforcement, θ_c; the undrained shear strength of the subgrade, c_u,SG; the angle of internal friction of the unreinforced soil, $\phi$'_SG; the effective cohesion of the unreinforced soil, c' _SG.

Lastly, for the methods that directly estimate the height of the base layer, the following quantities were included in the parametric study: the undrained shear strength of the subgrade soil, c_u,SG; the California Bearing Ratio of the subgrade soil, CBR_SG; the axle load, P; the number of the passes of axle, N.

Results and Discussion

Increase in Confining Pressure

Base Scenario

Table 14 summarises the results for the increase in confining stress, Δσ₃, obtained for the base scenario defined (Table 11). The results range between ~ 22 kPa and ~ 75 kPa. A reference value for the initial horizontal effective stress inside the geocell, σ′_h0, that corresponds to the at-rest effective stress at mid-height of the geocell, can be considered. For the parameters adopted in the base scenario (d = 0.15 mm, ϕ′_IF = 20°, γ = 16 kN/m³), σ′_h0 is ~ 0.79 kPa. Thus, the increase in confining pressure Δσ₃ obtained corresponds, respectively, to 18 and to 62 times the value of σ′_h0. This illustrates how important the confining effect provided by the geocell is to the overall shear strength of the base layer.

Table 14 Results from the application of the base scenario to estimate the increase in confining pressure

All methods (summarised in Table 3) rely on a ratio between a modulus for the geocell and its diameter (Table 4). As the same value was adopted for these parameters, they will influence the results in a similar way.

Methods referring to the same type of loading (static and cyclic) were compared directly. The methods proposed by Bathurst and Karpurapu [7] and Rajagopal et al. [8], applicable to static loading, lead to very similar estimates of the increase in confining pressure (~ 75 and ~ 71 kPa, respectively), using Eqs. (1) and (2) from Table 3. Equation (2), presented by Rajagopal et al. [8], considers the influence of the axial strain (${\upvarepsilon }_{{\text{a}}}$) on the diameter of the cell pocket (d₀), by defining d_f, the diameter of the cell pocket at an axial strain ${\upvarepsilon }_{{\text{a}}}$. Thus, in these two methods, the circumferential strain, ${\upvarepsilon }_{{\text{c}}}$, of the geocell is different—Eq. (20) for Bathurst and Karpurapu [7], and Eq. (21) for Rajagopal et al. [8].

$${\varepsilon }_{c}=\frac{1-\sqrt{1-{\varepsilon }_{a}}}{1-{\varepsilon }_{a}}$$

(20)

$${\varepsilon }_{c}=\frac{{d}_{f}-{d}_{0}}{{d}_{0}}$$

(21)

The estimate for Δσ₃ obtained from the method by Rajagopal et al. [8] seems more reasonable, as it allows for a more realistic value of the geocell pocket diameter to be considered (d_f ~ 0.154 m for ${\upvarepsilon }_{{\text{a}}}=5\mathrm{\%}$), and it is more conservative. The proposal by Rajagopal et al. [8] leads to a value for Δσ₃ which is 5% smaller than that of Bathurst and Karpurapu [7].

Two methods estimate the increase in confining stress under cyclic loading due to geocells: Yang and Han [9] and Indraratna et al. [10]. The difference in values for Δσ₃ is clear, as these methods result in ~ 22 and ~ 46 kPa, respectively. The increase in confining stress is 18 and 38 times larger than the reference value for the initial horizontal effective stress inside the geocell, σ′_h0. Although both methods refer to cyclic loading, they are inherently different, starting from distinct data and base hypothesis, and thus making use of different parameters. The method by Yang and Han [9] (Eq. 3) was based on repeated load triaxial tests and (among other parameters) depends on the resilient modulus for two different load stages (M_r1 and M_r2, which are calculated through an iterative process, Table 4); the method by Indraratna et al. [10] is based on the hoop tension theory (Eq. 4). The increase in confining pressure Δσ₃ from Yang and Han [9] is nearly half that from Indraratna et al. [10]. These different bases limit direct comparison between the two methods.

When comparing the methods for static and cyclic loading, a key trend emerged: the effect of cyclic loading significantly reduces the beneficial confining effect attributed to the geocell, reducing the increase in confining pressure 35–70% (depending on the methods compared). This points out the relevance of considering a realistic type of loading in the design of unpaved roads reinforced with geocells.

A parametric analysis was carried out to understand how some parameters influence the increase in confining pressure.

Parametric Analysis

The equations of the methods that estimate the increase in confining pressure have two parameters in common, modulus of the membrane (M) and diameter (d), even if they are labelled slightly different (Table 4). Varying these two parameters (M and d) influences the increase in confining pressure obtained from the different methods in the same way (Fig. 7a, and b, respectively): stiffer geocells lead to higher beneficial effect, higher Δσ₃; geocells with larger pockets are less efficient in confining the infill soil.

Fig. 7

Summary of results for the parametric analysis of the methods that estimate the increase in confining pressure, Δσ₃, considering the effect of: a diameter of the geocell (all methods); b membrane modulus (all methods); c circumferential strain, methods by Bathurst and Karpurapu [7] and Rajagopal et al. [8]

The methods for static loading suggested by Bathurst and Karpurapu [7] and Rajagopal et al. [8] have similar equations for estimating the increase in confining pressure; the difference lies in the determination of the circumferential strain (Eqs. 20 and 21, respectively). Therefore, the circumferential strain was varied to understand its effect on the increase on confining pressure. Figure 7c shows that the effect of the circumferential strain is practically the same in both methods. The differences become more important as the circumferential strain increases, particularly for ε_c > 3.6%. As stated before, the method by Rajagopal et al. [8] is more conservative and more realistic.

The methods for cyclic loading, by Yang and Han [9] and by Indraratna et al. [10], were not compared directly, as they are very different, both in terms of data and parameters considered. The parametric analysis was done separately. For the Yang and Han [9] method the influence of the dilation angle (ψ) and the limit number of passes/cycles (N_limit) was studied. Figure 8a and b (with different scales) shows that increasing the dilation angle (ψ) of the infill soil has little influence on the increase in confining pressure (Δσ₃). Figure 8c indicates that as the limit number of passes/cycles (N_limit) increases, so does the increase in confining pressure, approaching an asymptotic value, Fig. 8d, which for the case analysed corresponds to ~ 23 kPa. Thus, the influence of the geocell leads to an improved benefit that increases with the number of passes up to a limit.

Fig. 8

a dilation angle, Yang and Han [9] method; b—a detail of the effect of the dilation angle, Yang and Han [9] method; c limit number of passes/cycles, Yang and Han [9] method; d detail of the effect of the limit number of passes/cycles

For the Indraratna et al. [10] method the influence of the Poisson’s ratio of geocell (υ_g) was analysed. The Poisson’s ratio of geocell (υ_g) was varied between 0.2 and 0.4; Fig. 9a and b (with different scales) shows that increasing the Poisson’s ratio results in higher confining pressure and thus, higher benefit from the geocell.

Fig. 9

a Poisson’s ratio of geocell, Indraratna et al. [10] method with Δσ; b detail of the effect of the Poisson’s ratio of geocell, Indraratna et al. [10] method

Bearing Capacity

The bearing capacity methods include two types of formulations (Table 6): loading under undrained conditions (short-term response) and drained conditions (long-term response). For the latter, two methods were used: Koerner [22] and Zhang et al. [24, 25]. For the short-term response, all methods presented in Table 6 were used.

Base Scenario

Undrained Conditions

The case for unpaved roads with a weak and compressible subgrade is often considered the most critical in design, particularly its short-term response. The base scenario defined (Sect. “Methodology”) corresponds to an extreme situation, with an undrained shear strength for the subgrade soil of c_u,SB = 10 kPa. Table 15 summarises the results obtained for the bearing capacity in such case.

Table 15 Results of the bearing capacity for the base scenario, undrained conditions (short-term response)

The bearing capacity of the unreinforced soil, p_u, was the same for all methods considered, as similar conditions and parameters were defined (application of the traffic load at the top of the subgrade layer, without any base layer).

The inclusion of a geocell reinforcement significantly increased the short-term bearing capacity, as the contribution of the geocell reinforcement to the bearing capacity, Δp_r, is ~ 2 to ~ 7 times the bearing capacity of the unreinforced soil, p_u.

The differences between methods lay on how the contribution of the geocell was considered, namely the effects accounted for and their combination (Tables 6 and 15). Most methods (exception for the method by Zhang et al. [24, 25]) consider a term for the lateral resistance (or confinement) effect. The formulations by Koerner [22] and Sitharam and Hegde [27] are the same and are based on frictional resistance mobilised on the geocell wall. These formulations assume the worst-case scenario, in which only two walls of the geocell contribute to the bearing capacity (represented by the factor 2 in Eqs. 7 and 11). However, that may not be realistic. The formulations by Presto [23] and by Avesani et al. [26] try to address it by applying a factor h_g/d, representing the area of influence of the geocell pocket. Most methods assume that the infill soil is at an active state, due to the horizontal displacement of the geocell wall associated with the placement of the infill soil. The method by Avesani et al. [26] considers the at-rest earth pressure coefficient, but reduces the frictional resistance mobilised by applying a factor representing the stress distribution effect (e), while also including a factor of 4 (instead of 2, as the other methods). For the base scenario analysed and an angle of dispersion θ_c = 30°, the stress distribution effect is ~ 0.6; the contribution of the lateral resistance effect is very similar for all relevant methods, except for Avesani et al. [26], which is ~ 1.6 times larger that of the other methods. This suggest that some caution must be taken when using this method.

The vertical stress dispersion effect is considered in the methods by Zhang et al. [24, 25], Avesani et al. [26] and Sitharam and Hegde [27], by applying a vertical stress dispersion factor to the acting load. For the base scenario analysed, the stress redistribution factor was the same for the methods by Avesani et al. [26] and by Sitharam and Hegde [27], leading to a bearing capacity increment of ~ 215 kPa. The corresponding estimate from the Zhang et al. [24, 25] method is less optimistic (~ 200 kPa); the different value is due to the shape of the loaded area defined by these authors (circular, rather than rectangular as defined by [26] and [27]).

The method by Zhang et al. [24, 25] is the only one that includes the membrane effect for geocell reinforcement. For the base scenario analysed, the contribution of this effect is minimal (~ 0.5 kPa). It must be pointed out that, in their proposal, Sitharam and Hegde [27] include the membrane effect, but only for planar reinforcements (rather than 3D reinforcements, such as geocells).

For the base scenario analysed, the most conservative methods are those by Koerner [22] and Presto [23], while the more optimistic results were obtained using the method by Avesani et al. [26], ~ 3.3 times higher than that by Koerner [22].

Drained Conditions

For the long-term response, corresponding to drained conditions, two different scenarios were analysed. On the one hand, the water table (WT) was assumed below the area of influence of the traffic (i, no WT); and on the other hand, the worst-case scenario of the water table at the road surface (ii, WT). The bearing capacity of the unreinforced soil, p_u, for scenarios i (no WT) and ii (WT) was 4.94 kPa and 3.04 kPa, respectively. As the positions of the water table considered only influence the bearing capacity of the unreinforced soil, in the following only scenario i (no WT) was discussed (Table 16).

Table 16 Results of the contribution of the geocell reinforcement, Δp_r, for drained conditions, for scenario i

The bearing capacity of the unreinforced soil is very low; these values (smaller than the short-term bearing capacity) can be ascribed to the zero effective cohesion assigned to the subgrade soil. For example, assuming a cohesion of 3 kPa leads to a significant increase of the bearing capacity of the unreinforced soil, resulting in 67.49 kPa and 65.59 kPa, for scenarios i and ii, respectively. The influence of this parameter is further discussed in the parametric analysis below.

The two methods analysed, Koerner [22] and Zhang et al. [24, 25], lead to very different estimates of the contribution of the reinforcement to the bearing capacity: ~ 127 kPa and ~ 205 kPa, respectively. That contribution represents 26–41 times the bearing capacity of the unreinforced soil (cʹ = 0 kPa) and is not influenced by the presence of the water table. As before, these two methods account for the geocell differently, as the effects and their combination are distinct.

A parametric analysis was carried out to understand the influence of relevant quantities on the estimates of the bearing capacity for both undrained and drained conditions.

Parametric Analysis

The bearing capacity methods were formulated to either undrained or drained conditions (Table 6). Although not always explicitly described in the original methods, these proposals assume that the infill material, to be placed in the geocell pockets, is purely frictional. Thus, the contribution of the geocell reinforcement, Δp_r, is not influenced by the loading conditions. This is particularly evident for the methods by Zhang et al. [24, 25] and Koerner [22], which allow analysis for both conditions (Tables 15 and 16). Consequently, only the bearing capacity of the unreinforced soil is affected by the type of loading conditions. Nevertheless, in the following subsections, the type of loading conditions is considered, to distinguish between the conditions of applicability of the methods studied.

Undrained Conditions

For methods that estimate the bearing capacity in undrained conditions, the parameters analysed were: acting load (p_act); angle of internal friction of infill soil ($\phi$'_IF); interface friction angle between the infill soil and the geocell wall (δ); angle of dispersion of the load due to the geocell reinforcement (θ_c); horizontal angle of the tensile force T (α); undrained shear strength of the subgrade (c_u,SG), namely its impact on the improvement factor due to the geocell (Δp_r/p_r). Each parameter was varied, while the remaining data was the same of the relevant base scenario (Table 12). The results are summarised in Fig. 10.

Fig. 10

a Variation of the p_act vs Δp_r; b variation of $\phi$'_IF and δ vs Δp_r (Koerner [22] method); c variation of $\phi$'_IF and δ vs Δp_r (Presto [23] method); d variation of $\phi$'_IF and δ vs Δp_r (Avesani et al. [26] method); e variation of $\phi$'_IF and δ vs Δp_r (Sitharam and Hegde [27] method); f variation of θ_c and α vs Δp_r (Zhang et al. [24, 25], Avesani et al. [26] and Sitharam and Hegde [27] methods)

The acting load, which often is taken as the tire pressure transmitted to the unpaved road surface, was varied between 20 and 550 kPa. The bearing capacity increment increases (almost linearly) with the acting load (p_act) for all the methods analysed (Fig. 10a); the response obtained using Koerner [22] and Presto [23] methods are nearly identical.

The angle of internal friction of infill soil ($\phi$'_IF) was varied between 20° and 40°; the interface friction angle between the infill soil and the geocell wall (δ) was varied proportionally, considering the angle δ equal to: one third of $\phi$'_IF (1/3 $\phi$'_IF); two thirds of $\phi$'_IF (2/3 $\phi$'_IF); equal to $\phi$'_IF (3/3 $\phi$'_IF). The results exhibit a trend that is very similar for all methods that rely on these quantities: Koerner [22], Presto [23], Avesani et al. [26] and Sitharam and Hegde [27], summarised in Fig. 10b–e, respectively. The increment in bearing capacity due to the geocell, Δp_r, increases parabolically with $\phi$'_IF. For example, for the method by Koerner [22], the highest Δp_r was obtained for an angle of internal friction of infill soil ($\phi$'_IF) of 26.4°, 27.7° and 30.5°, respectively for δ of 1/3 $\phi$'_IF, 2/3 $\phi$'_IF and 3/3 $\phi$'_IF. This indicates that, for the methods analysed herein, there is no gain in increasing the requirements for the shear strength of the infill soil beyond those limits. Increasing the shear strength of the infill soil-geocell interface results in higher benefit from the geocell, as expected.

The angle of dispersion of the load due to the geocell reinforcement (θ_c) and the horizontal angle of the tensile force T (α), Table 6, intervene in the methods by Zhang et al. [24, 25], Avesani et al. [26] (in parameter e) and Sitharam and Hegde [27]. Herein these angles were assumed to be the same (Fig. 6) and were varied between 25° and 45° (Fig. 10f). The increment in bearing capacity due to the geocell, Δp_r, increases linearly with these angles. A higher value of the angle of dispersion, θ_c, means that the geocell has a more important contribution in reducing the stress transmitted to the subgrade by further mobilising the vertical stress dispersion effect; consequently, a higher Δp_r is expected. Similarly, a larger value of the horizontal angle of the tensile force T (α) means that the membrane effect of the geocell is more important, with a larger vertical component to support the acting load. The methods led to different estimates of Δp_r: the method by Avesani et al. [26] was the most optimistic, followed by the method by Sitharam and Hegde [27]; the Zhang et al. [24, 25] method was the most conservative.

As mentioned before, the undrained shear strength of the subgrade (c_u,SG) does not influence the contribution of the reinforcement to the bearing capacity of the reinforced soil, and it only affects the bearing capacity of the unreinforced soil (p_u). These two quantities are directly proportional. The undrained shear strength c_u,SG was varied between 5 and 120 kPa (Fig. 11). If the subgrade has higher strength, the need for reinforcement decreases and, thus, the corresponding benefit decreases as well (from 6.5 to 0.3, for the method by Zhang et al. [24, 25]).

Fig. 11

Variation of bearing capacity of unreinforced soil and of the reinforcement benefit vs undrained shear strength, c_u,SG, of the subgrade for the Zhang et al. [24, 25] method

Drained Conditions

For methods that estimate the bearing capacity in drained conditions, the parameters analysed were: the angle of internal friction of infill soil ($\phi$'_IF); the interface friction angle between the infill soil and the geocell wall (δ); the angle of internal friction of the subgrade ($\phi \mathrm{^{\prime}}$_SG); and the effective cohesion of the unreinforced soil (c´).

As for the previous section, the angle of internal friction of infill soil ($\phi$'_IF) was varied between 20° and 40°; the interface friction angle between the infill soil and the geocell wall (δ) was varied proportionally, considering the angle δ equal to: one third of $\phi$'_IF (1/3 $\phi$'_IF); two thirds of $\phi$'_IF (2/3 $\phi$'_IF); equal to $\phi$'_IF (3/3 $\phi$'_IF). As the bearing capacity increment Δp_r does not depend on the loading conditions, the same results and trends discussed for the method by Koerner [22] applies (Fig. 10b).

The angle of internal friction of the subgrade ($\phi \mathrm{^{\prime}}$_SG) was varied between 20° and 40°. This parameter only influences the bearing capacity of the unreinforced soil (Fig. 12). As the shear strength of the subgrade increases, the need for reinforcement decreases, as well as the corresponding improvement, represented as Δp_r/p_u that decreases from 40.5 to 1.4 for the method by Zhang et al. [24, 25] (Fig. 12a).

Fig. 12

Variation of bearing capacity of unreinforced soil and of the reinforcement benefit for the Zhang et al. [23, 24] method vs: a the angle of internal friction of the subgrade, $\phi \mathrm{^{\prime}}$_SG; b cohesion of the subgrade, c´_SG

Similarly, the effective cohesion of the subgrade soil (c$\mathrm{^{\prime}}$_SG) only influences the bearing capacity of the unreinforced soil and was varied between 0 and 130 kPa. A similar trend as described for $\phi \mathrm{^{\prime}}$_SG was observed (Fig. 12b), with improvement ranging between 40.5 and 0.2 for the Zhang et al. [24, 25] method. The use of this shear strength parameter (c$\mathrm{^{\prime}}$_SG) must be avoided, as it is flawed by the inclusion of an effective cohesive intercept that has no physical meaning for most natural soils, as there is no cementation.

Height of the Base Layer

Base Scenario

Table 17 summarises the results obtained for the methods that directly estimate the height of the base layer using the base scenario data included in Table 13. The height of the base layer without reinforcement is ~ 0.94 m (based on Giroud et al. [28, 29]). The inclusion of geocell reinforcement, with height coinciding with that of the base layer, leads to a reduction of 27% of that height: h_r ~ 0.69 m (Pokharel et al. [1]). This leads to saving in aggregate/soil that would be used in the construction of the base layer.

Table 17 Result of the base layer height value without (h_u) and with reinforcement (h_r)

Parametric Analysis

A parametric analysis was carried out, varying the following parameters: undrained shear strength of the subgrade soil (c_u,SG); California Bearing Ratio of the subgrade (CBR_SG); tire load (P); number of axle passes (N).

The methods by Giroud et al. [28, 29] and Pokharel et al. [1] are applicable to the short-term response (undrained conditions), as the shear strength of the subgrade is represented by its undrained shear strength. Figure 13a represents the variation of the height of the base layer as the undrained resistance of the foundation soil increases from 10 to 100 kPa. As for other methods before, increasing the undrained shear strength of the subgrade soil (c_u,SG), the smaller the benefit from the reinforcement, and, consequently, the smaller the height of the base layer with geocell (ranging between 0.69 and 0.10 m). It is important to note that the parameters were only varied until the height of the base layer reached the minimum value required by the Giroud et al. [28, 29] method, which is 0.10 m. For geocell reinforcement, the minimum height of the base layer defined by Giroud et al. [28, 29] needs to be adjusted. Such height must coincide with the height of the geocell, h_g. For c_u,SG of 10 kPa the height of the base layer is reduced in ~ 27%, while for 100 kPa that reduction is ~ 72%.

Fig. 13

Parametric analysis results: a effect of c_u,SF on the height of the base layer; b effect of CBR_SG on the height of the base layer; c effect of P on the height of the base layer; d effect of N on the height of the base layer

Alternatively, the strength of the subgrade can be represented by a CBR_SG value. The range of CBR_SG values considered refers to the conditions of applicability of Eq. (17), CBR_SG between 0.33 and 5 (corresponding to c_u,SG of 10 and 150 kPa). A large CBR_SG value represents a stiffer subgrade and, thus, the height of the base layer can be reduced (Fig. 13b).

The tire load, P, was varied between 40 and 150 kN. The greater the tire load, the larger is the height of the base layer (Fig. 13c) and the trend observed for h_u and h_r is similar. The variation between these two quantities, with reinforcement and without geocell, is never less than 27%, which means that the use of geocell is beneficial.

The number of axle passes, N, was varied between 5000 and 20,000. Figure 13d shows that such increase results in an increased height of the base layer, although not very significant; for the reinforced solution, that height varied between 0.69 and 0.70 m.

Finaly, in Fig. 13 it is notable that the introduction of a geocell leads to a significant reduction of the height of the base layer, highlighting the benefit of reinforcing the soil.

Conclusions

This paper focuses on the design of geocells for unpaved roads; methods for quantifying the contribution of geocells were compiled based on how they consider that effect: increase in confining pressure (Δσ₃); bearing capacity (p_r); height of the base layer (h_r). A general base scenario was defined, to enable comparison between groups of design methods. A parametric analysis was carried out to better understand the influence of relevant parameters on the outputs of each design method. The main conclusions from this study are as follows:

• Design methods available in the literature are presented in a systematised way, with homogenised notation. The critical analysis of design methods relevant for the use of geocells for unpaved roads will help forest engineers in adopting this type of solution when designing or rehabilitating forest roads.

• The methods that estimate the increase in confining pressure (Δσ₃) are applicable to either static or cyclic loading; these approaches are different, and their results are not directly comparable. Stiffer geocells with smaller pockets lead to higher benefit. Often, these methods make use of an apparent cohesion to represent the contribution of the reinforcement, analysing the geocell-reinforced soil as a homogenous material (a soil) with the same fundamental shear strength. Such approach should be avoided, as a cohesive intercept has no physical meaning and may be misleading. This strategy is often used when modelling geocell reinforced soil in 2D and must be avoided.

• The methods that estimate the increase in bearing capacity (Δp_r) due to geocell reinforcement consider the contribution of the geocell differently (lateral resistance effect, vertical stress dispersion effect and membrane effect, and distinct combinations). For geocell reinforcement, the membrane effect is small and can be neglected. The beneficial effect of the geocell is higher for weaker subgrades, particularly weak and compressible soils. Most methods assume that the infill soil is purely frictional (for drained conditions), reducing their applicability to materials with a different response. The geocell benefit associated with the shear strength of the infill soil is limited, as there are values of its angle of friction that maximise the increase in bearing capacity due to the geocell. The ability of the geocell to disperse the load is key to maximise its benefit; thus, the design should seek a realistic estimate of this effect.

• The methods that estimate the height of the base layer of the reinforced soil (h_r) can be used directly for an expedite design of unpaved roads. When a geocell reinforcement is adopted, a minimum height for the base layer must be defined (coinciding with that of the geocell). A realistic estimate of the number of passes of vehicles is key for the design, which may prove difficult to quantify for unpaved roads with very low traffic. As these methods can rely on CBR values to define the subgrade, they do not require extensive site investigation. Nevertheless, the relation between the CBR value and the undrained shear strength of the subgrade should be adapted to the site conditions.

The main goal of this paper is to provide actual, simple, and systematised information to assist practitioners in the design of geocell reinforced unpaved roads. Usually, the investment on unpaved roads, at different project stages (including design, construction, and maintenance) is quite low. Making available information in a straightforward way, that practitioners with limited experience on geocells, such as forest engineers, can use will contribute to more realistic and sound designs. Furthermore, consistently adopting geocell reinforcements will contribute to reducing quantities of good quality borrow materials needed for the base layer of unpaved roads, as well as lowering the requirements for the borrow material, allowing the use of local soils. This way, sustainable development goals (SGD), as defined by the United Nations [37] will be addressed, particularly, SDG11, Sustainable cities and communities and SDG12, Responsible consumption and production.

Thus, while current methods contribute and support the design of unpaved roads, further work is essential to develop methods that are of simple and of expedite application for forest engineers, adaptable to local conditions and requirements. These methods are very important to enable quick decision-making, reducing project timelines and associated costs, both during construction and operation. Additionally, the implementation of geocell-reinforced solutions contributes to sustainable and resilient unpaved roads, supporting increased traffic loads, reducing the maintenance operations, and extending the overall lifespan of infrastructure.