Written By: Michael J. Dickey, P.E., Samantha Justice, P.E., Bryan Wedin, P.E.
When constructing roadways over soft soils and weak subgrades, geocells are one of the most powerful value engineering tools available to the civil engineering and construction industries today. Understandably, some engineers may be apprehensive about using a geosynthetic product for which they have an incomplete technical understanding. So, if you’ve ever wondered how geocells work in load support applications – and the relationship between lateral confinement and hoop stress – you’ve come to the right place.
Generally speaking, geocells can be used to alter the geometry of a soil pressure bulb beneath an applied load through a phenomenon known as the mattress effect. Key to the mattress effect is a physical mechanism unique to geocells known as lateral confinement. When a load is applied to a geocell-reinforced layer, lateral earth pressures develop within the infill material, which is confined laterally by the cell walls against movement, in turn developing upward shear resistance along wall interfaces throughout the interconnected network of cells. In essence, lateral confinement converts horizontal earth pressures into upward resisting shear forces.
When combined with suitable base reinforcement (i.e., an enhanced woven geotextile), it becomes possible to construct over very weak subgrade materials, including those with standard penetration resistance (SPT-N) values less than 2 blows per foot (CBR < 0.5%), where most planar geosynthetic products, such as geogrids, would otherwise fail.
Now, where does hoop stress come into play, and how does it relate to lateral confinement?
Hoop stresses develop within the cell walls as earth pressures propagate radially 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 within 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 within 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:
σH = pnet*(D/2t)
σH = hoop stress
pnet = net pressure = pi – pe
pi = internal pressure
pe = external pressure
D = geocell diameter
t = wall thickness
The internal active earth pressure in a cell directly beneath a point load can be calculated using Boussinesq’s point load stress equation. Concerning external, or “passive”, earth pressures in adjacent cells, Emersleben (2009) investigated the interaction between hoop stresses and passive earth resistance in geocell systems 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.
Not surprisingly, the largest net earth pressures, and largest 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 that would be expected to develop in geocells in response to standard AASHTO load conditions.
Accordingly, the table below summarizes the estimated hoop stresses that would be expected to develop under standard AASHTO load conditions in a 6-inch geocell-reinforced layer overlain by 2 inches of aggregate wearing course. The calculations assume a 9.5-inch diameter geocell infilled with coarse sand having an internal friction angle of 32 degrees.
|AASHTO Load||Wheel Load (lbf)||Tire Pressure (psi)||Estimated Hoop Stress (psi)||Tension in Cell Wall (lb)|
As shown, 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 would not be expected to undergo any permanent deformation or “creep” over time, even when subject to repeat traffic loads over many years.
With regard to strain, 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 lateral confinement. Because of this, the actual strain that develops in the cell wall will be far 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.
This is not to say that hoop stress is not important. 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 designers to develop a preliminary (and very conservative) understanding that tensile forces in the cell wall will remain within the elastic region for the material (with the caveat that many laboratory test methods such as ISO 10319 ignore the effects of confinement, and therefore tend to overestimate strain levels).
In terms of long-term hoop integrity as it pertains to the cell wall (junctions are another matter altogether), dynamic mechanical analysis using a method such as ISO 6721 allows for more accurate characterization of expected material behavior under repeat dynamic loads at reduced strain levels. In general, provided the product is a high-quality HDPE geocell with a flexural storage modulus of at least 116 ksi (800 Mpa) and a 100-year durability rating (ISO 13438), the product can be expected to perform as intended throughout the life of the project.
Emersleben A. et al (2009). Interaction Between Hoop Stresses and Passive Earth Resistance in Single and Multiple Geocell Structures. GIGSA GeoAfrica 2009 Conference, Cape Town 2 – 5 September 2009.