Written By: Samantha Justice, P.E., Bryan Wedin, P.E.

Geocells provide one of the most powerful solutions available to engineers and contractors when designing and constructing roadways over soft and weak subgrades. With a successful track record of over 40 years, geocells have proven effective in load support applications over challenging conditions. If you’ve ever wondered how geocells work in load support applications – and the relationship between lateral confinement, hoop stress and wall tension – you’ve come to the right place.

Geocells are used to alter vertical stresses beneath an applied cyclical load. When a vertical, cyclical load is applied over geocells, active earth pressures develop in the loaded cell. These pressures arise due to the friction between the infill material and the cell wall. This friction pushes back against the passive earth pressure in the adjacent cells, helping to support the load. Refer to Figure 1. The balance of active and passive earth pressures activates the hoop stress in the cell walls, which increases the stiffness and bearing capacity of infill material. The infill material is confined within the individual cells with no chance of displacement, or lateral or vertical spreading and the result is increased stiffness. In effect, geocells behave more like three-dimensional structures or a semi-rigid slab by increasing the load distribution angle and spreading the vertical stresses over a larger area which is commonly referred to as the mattress effect.

Figure 1

An enhanced woven geotextile separation layer is typically provided under the geocell system and works in conjunction to provide additional load distribution along with filtration, separation, and controlled drainage. With the enhanced woven geotextile, it is possible to construct over extremely weak subgrades with standard penetration resistance (SPT-N) values less than 2 blows per foot (CBR < 0.5%), where planar geosynthetics, such as geogrids, would otherwise fail.

How Does Hoop Stress and Wall Tension Relate to Lateral Confinement?

Hoop stresses develop within the cell walls as earth pressures increase in response to an applied load at ground surface. In other words, the same earth pressures responsible for developing interface friction between the geocell and the infill material also result in hoop stresses with the cell walls. Although not perfectly cylindrical, geocells can be envisioned to behave similarly to an interconnected network of pressurized cylinders, wherein hoop stresses are a function of the net pressure that develops due to the internal and external pressures acting in and around each cell.
In this manner, radial pressures that develop within each cell are resisted by those that develop in the adjacent cells, and hoop stresses may be estimated using the classic equation for hoop stress for a pressurized thin-wall cylindrical vessel:

σ_H = p_net*(D/2t)

Where,

σ_H = hoop stress

p_net = net pressure = p_i – p_e

p_i = internal pressure

p_e = external pressure

D = geocell diameter

t = wall thickness

The active earth pressure in a loaded cell below a cyclical load can be calculated using the Boussinesq stress equation. The interaction between hoop stresses and passive earth resistance in geocell systems was investigated by Emersleben (2009) and observed that lateral pressures in adjacent cells decrease exponentially with increasing distance from the actively loaded, or “source” cell(s) – in effect, defining a pressure gradient. Based on Emersleben’s findings, it is possible to evaluate the net earth pressure that develops between the interior and the exterior of a cell wall, using the thickness of the cell wall as the distance between two points along the defined pressure gradient line.  Refer to Figure 2.

Lateral Pressure vs Distance

Figure 2

The largest net earth pressures, and hoop stresses, occur in cells directly beneath the perimeter of the load footprint—the wheel contact area in the case of vehicle loads. Based on this, it is possible to estimate the maximum hoop stresses expected to develop in geocells in response to standard AASHTO load conditions.

Table 1 summarizes the estimated hoop stress and cell wall tensions developed under standard AASHTO load ratings for a 6-inch geocell-reinforced layer with a 2-inch wear surface. The calculated values assume a nominal 9.5-inch diameter geocell infilled with a granular material having an internal friction angle of 32 degrees and unit weight of 120 lbs/ft³.

Hoop Stress and Cell Wall Tension

Table 1

The corresponding tensile forces that develop under working load conditions are relatively modest due to the lateral confinement effect of the adjacent cells. When compared to the typical yield strength for most high-quality HDPE geocells, the above-referenced tensile forces are well within the elastic region for the material and any permanent deformation or “creep” over time is not expected, even when subject to cyclical traffic loads. Due to hoop stresses and earth pressures surrounding the loaded cells, there is no ability for the material to have any appreciable sustained deformation, and therefore, creep is not an issue.

The elastic response of the geocell-reinforced layer will ultimately be governed by the elastic properties of the infill material, and provided that suitable granular infill is used, the development of any significant strain in the cell walls will be heavily constrained by the effects of confinement of the granular material by the cell walls. The actual strain that develops in the cell wall will be significantly less than the amount of strain represented on a typical stress-strain curve generated from laboratory tests such as ISO 10319 or ASTM D4595 where samples are subjected to tensile forces in an unconfined state.

Development of hoop stress is essential for the proper engagement of the lateral confinement mechanism. Moreover, the ability to estimate hoop stresses under specific project circumstances can be useful as it allows engineers to develop a preliminary (and very conservative) understanding that tensile forces in the cell wall will remain within the elastic range for the material. It should be noted that many laboratory test methods such as ISO 10319 ignore the effects of confinement, and therefore, tend to overestimate strain levels that are outside of practical design conditions. Researchers who have completed laboratory and field test on geocells under applied loadings show that the strain in geocell walls is on the order of 0.2%. Evaluating material strength beyond reasonable strains is not relevant for sub grade reinforcement and the focus should be on strains less than 1.0%.

In general, provided the geocell is manufactured with a high-quality HDPE with a flexural storage modulus of at least 116 ksi (800 Mpa) and a 100-year durability rating (ISO 13438), the geocell can be expected to perform as intended throughout the service life of the project.