Part 1: Allowable stress on geonets
By Dhani Narejo and Sam Allen
Several types of geonets are used in numerous applications worldwide. Examples of the types of geonets include biplanar, triplanar, spiked or profiled, cuspated, tubular, and three-dimensional (3-D) filament meshes (see Figure 1 and Table 1). Common and emerging applications for these materials include roadways, heap leach pads, green roofs, landfills, ponds, slopes, walls, and dams.
Most projects require geonet usage in association with a geotextile on one or both sides, in which case the products are known as drainage geocomposites. The planar drainage performance of geonets and geocomposites is expressed as flow rate or transmissivity, which spans several orders of magnitude when considering all the products available in the marketplace.
The state-of-practice design procedures compare the design transmissivity or flow rate with the allowable transmissivity or flow rate to calculate a drainage factor of safety. The effect of stress is often, but not always, included indirectly in the calculations through the transmissivity value, which is obtained from a test performed at site-specific stress, gradient, and boundary conditions for 100 hours. The creep of a geonet can be accounted for by using a creep reduction factor in the drainage calculations.
Although several papers have been written on geonet creep, including Thornton et al. (2000), Narejo & Allen (2004), Yeo & Hsuan (2007), there has been little discussion in the geosynthetics literature on the allowable stress on geonets. The validity of such a method for many different types and grades of products is challenging.
Narejo (2007) proposed a method for traditional biplanar geonets that was later modified by Narejo & Allen (2010). This three-part series intends to improve the previous work by the authors on this topic by including additional creep data, especially beyond 10,000 hours. The procedure is extended for the first time to materials different from traditional biplanar geonets.
Since some of the data used in the derivations in the second and third articles in this series are obtained from the Stepped Isothermal Method (SIM), a brief comparison of the accelerated and conventional creep methods is presented in this article. The second and third articles in this three-part series also explain the application of the method with several design examples.
The concept of using laboratory creep data to calculate the allowable stress is used currently for geogrids. Similar to geogrids, laboratory creep tests on geonets were performed in isolation without many complicating factors. Lamination to form a geocomposite, soft vs. hard boundaries, hydro-chemical environment, stress inclination, and temperatures can all have an effect on the creep of geonets. Because many such considerations are site-specific, it is hoped that the concept of reduction factors can be used to account for these. The methods presented in this series may be considered to give an approximate value of allowable stress. Although only approximate in nature, it is better than not knowing at all what the stress limits for different types of geonets may be because geonet load capabilities can vary across several orders of magnitude.
Compressive stress/strain behavior and defining rollover
Although there are several types of geonet structures and several grades of products within each structure, compressive stress-strain curves obtained from ASTM D6364 can be used to place all geonets within two groups: those with a rollover and those without it. The term rollover is used in a general sense to denote a layover or a collapse of a geonet’s structure under stress.
Figure 2 shows stress/strain curve from ASTM D6364 for several types of biplanar geonets. The biplanar geonets have two sets of strands crossing each other diagonally to form a mesh. Curves of type III and IV represent a clear rollover of the geonet with a stress-softening after reaching a peak value. The curve of type II shows some rollover but the stress continues to increase with increasing strain. The curve of type I does not show any rollover. Biplanar geonets with type I and type II stress-strain behavior, i.e., a positive stress-strain slope, are defined in this paper series as having a nonrollover structure. The creep data presented later in this series covers all types of biplanar geonets.
Figure 3 shows stress/strain curves for triplanar geonets. Triplanar geonets have three sets of strands: a primary strand in the center with a layer of secondary strand on either side. The initial portion of the stress-strain curve, at strains of less than 12%, represents the compression of secondary strands that have the same general structure as biplanar geonets. The compressibility of the primary strands varies significantly depending on the nature and grade of a triplanar product.
Because there is a positive or zero slope for all three curves, none is called a rollover to differentiate positive or zero post-peak slopes from negative post-peak slopes. For all practical purposes, one may call a type VI curve as showing a rollover because the curve is almost flat after the peak, but for the purposes of this article it is placed in a nonrollover category as was type II biplanar geonet in Figure 2.
Figure 4 shows stress-strain curve of two different spiked geonets that can also be called profiled materials. Spikes or profile can be of many types, such as cones on a geomembrane, T-shaped with or without a geomembrane, and studs with perforated roof at top and bottom. Type VII stress-strain curve indicates an initial straightening of the test specimen requiring some seating load. Above a strain of 10%, the stress-strain curve appears to be linear with no indication of rollover. The second type of the spiked geonet (type VIII) shows a linear stress-strain curve up to a strain of 40% at which a rollover occurs. Only 10% of additional strain—from 40% to 50%—is needed to eliminate the entire structure of the geonet after which there is a sharp uptake in the stress. In practice, this material is used mostly in landfill caps at stresses less than 20 kPa. Therefore, although the curve shows a rollover, the material is placed in a nonrollover category because the rollover in the compression test occurs significantly outside the material’s performance requirements.
Conventional vs. SIM
Conventional and accelerated creep tests were performed in general agreement with ASTM test methods D7406 and D7361, respectively. In addition to these standards, refer to Thornton, et al. (2000), Narejo & Allen (2004), and Narejo (2007) for details of the equipment and procedure.
All creep tests were performed during a period of 10 years from 2002 to 2012 at TRI/Environmental in Austin, Texas. The conventional creep tests were performed in a controlled temperature room at 20° C. The Stepped Isothermal Method (SIM) tests were performed in a temperature control chamber with 7-degree temperature increments from 20° C to 53° C. In all cases, thickness, stress, and temperature were measured with time.
The SIM is attractive because it costs significantly less and a test can be completed within a matter of hours vs. more than a year with the conventional method. However, there has been little comparison of the results from the two methods, especially regarding the effect of a higher temperature as it relates to differences in polymer properties in several types of geonets. Another concern is the effect of higher temperatures on complex structures of several products and whether the methods treat all the structures in the same manner. Therefore, four different geonet structures were tested for creep at 479 kPa according to the two methods. The results of the comparison are summarized in Figure 5.
The top set of curves in Figure 5 is for a biplanar geonet that had stress-strain curves of type II in Figure 2. The figure shows that the creep curves are identical for the two methods. The next set of curves is also for a biplanar geonet but with a stress-strain curve of type III in Figure 2. In this case, SIM predicts a higher creep than the conventional method but both methods predict a creep rollover just before 10,000 hours that is obvious from the change in the slope of the creep curves. The third set of curves in Figure 5 is for a triplanar geonet with stress-strain behavior of type V in Figure 3. At the end of 10,000 hours, SIM predicts a 5% lower retained thickness than the conventional method. The last set of curves in Figure 5 is for a profiled geonet of the type VII in Figure 4. Here again SIM results in a slightly higher creep than the conventional method.
This section is not a comprehensive comparison of the two methods for creep evaluation of geonets. The limited data set presented here shows SIM to give the same or slightly conservative creep results although the difference could also be attributed to possible differences in the test specimens. In this three-part series, SIM is used together with the conventional method to obtain creep rollover time for conventional biplanar geonets with a rollover and creep strain rate for products with a nonrollover stress/strain behavior. The methods presented in this series, to the extent they are affected by the data from SIM, could be slightly conservative as compared to a similar approach based entirely on conventional creep tests.
Summary and conclusions
Compressive strength of a geonet depends on the type of the core and the grade as well as the quality of the specific product. A broad range of products is available to satisfy both the load and the flow rate requirements of projects. The rollover is defined as a collapse of a geonet’s structure in a short-term or long-term compression test and is not limited to biplanar geonets. Not all types of biplanar geonets exhibit a rollover, as can be seen from the data presented in this series. Procedures for calculating the allowable stress on geonets can be obtained based on relationship among stress, strain, and time derived from laboratory creep tests. These relationships, to be presented in second and third articles in this series, are useful in obtaining an estimate of the load carrying capacity of geonets.
Dhani Narejo, Ph.D., P.E., is president of Narejo Inc., an independent consulting firm based in Conroe, Texas.
Sam Allen is vice president at TRI/Environmental Inc. in Austin, Texas.
Both authors are members of Geosynthetics magazine’s Editorial Advisory Committee.
Allen, S. (2011). “Accelerated flow testing of geosynthetic drains,” Geosynthetics, Vol. 29, No. 3, pp. 10–16.
ASTM D6364, “Standard Test Method for Determining Short Term Compression Behavior of Geosynthetics,” ASTM International, 100 Barr Harbor Drive, P.O. Box C700, West Conshohocken, Pa., USA.
ASTM D7361, “Standard Test Method for Accelerated Compressive Creep of Geosynthetic Materials Based on Time Temperature Superposition Using the Stepped Isothermal Method,” ASTM International, 100 Barr Harbor Drive, P.O. Box C700, West Conshohocken, Pa., USA.
ASTM D7406, “Standard Test Method for Time Dependent (Creep) Deformation under Constant Pressure for Geosynthetic Drainage Products,” ASTM International, 100 Barr Harbor Drive, P.O. Box C700, West Conshohocken, Pa., USA.
Narejo, D. and Allen, S. (2004). “Using the stepped isothermal method for geonet creep evaluation,” Proceedings of EuroGeo3 conference, Munich, Germany, pp. 539–544.
Narejo, D. (2007). “Design strength of geonet geocomposites,” Proceedings of Geosynthetics 2007 conference, January 16-19, Washington, D.C.
Narejo, D. and Allen, S. (2010). “Effect of sustained loading on structural stability of biplanar geonets,” Proceedings of 9th International Conference on Geosynthetics, May 23-27, Guarujá, Brazil.
Thornton, J., Allen, S. and Siebken, J. (2000). “Long-term compression creep of high density polyethylene geonet,” Proceedings of EuroGeo2 conference, Bologna, Italy, pp. 869–875.
Yeo, S.-S and Hsuan, Y.G. (2007). “Short- and long-term compressive behavior of high-density polyethylene geonet and geocomposite under inclined conditions,” Geosynthetics International, Vol. 14, No. 3, pp. 154–164.