### By Dhani Narejo and Sam Allen

## Introduction

This article focuses on biplanar geonets to the extent of the possible tendency for the two sets of integrally joined ribs to roll over on one another while load is applied. The significance of such a rollover is a reduced transmissivity value as compared to that obtained from 100-hour performance transmissivity tests.

One measure of a geonet’s performance is its ability to resist compression in a short-term compression test for example, according to ASTM D6364. *Rollover* is a term that has been used in the industry to differentiate high-strength and low-strength geonets. The first article in this series (June/July 2014 *Geosynthetics*, pp. 36–41) discussed rollover and defined it for the purpose of the methodology presented in this article.

It is assumed in this article that the term *rollover* is applicable only if the post-peak slope of a compression stress-strain curve is zero or negative. If the post-peak slope is positive or there is no peak at all, the material’s structure is assumed to be of a non-rollover type.

Rollover can occur in many different types of geonet structures, but most geonet structures can be made to be of a non-rollover type by changing the die design, polymer properties, and process conditions. Geonets with a rollover type curve in a standard compression test also show a rollover in a creep test. Geonets with a non-rollover structure do not show a rollover in a creep test. *Creep rollover* refers to noticeable abrupt change in strain rate during a creep test.

A separate method, based on allowable strain, and applicable to many other types of geonets, including biplanar geonets of non-rollover structure, will be presented in part 3 of this series (*Geosynthetics*, October/November 2014).

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
---|---|---|---|---|---|---|---|---|

Sample # | Strength (kPa) | Mass (g/m^{2}) |
Thickness (mm) | Test Stress (kPa) | Test Type | Time to Layover (hours) | Stress-Strain Curve* | Structure |

A1 | 606.7 | 873.9 | 6.0 | 359.1 | Conv | 6 | III, IV | biplanar |

A2 | 1013.5 | 873.9 | 6.4 | 478.8 | Conv | 7,000 | III, IV | biplanar |

A3 | 961.0 | 916.4 | 6.1 | 384.4 | SIM | 1×10^{7} |
III, IV | biplanar |

A4 | 1013.5 | 873.9 | 6.4 | 538.6 | Conv | 0.6 | III, IV | biplanar |

B5 | 1330.7 | 1010.6 | 6.9 | 598.5 | Conv | 785 | III, IV | biplanar |

B6 | 1330.7 | 1010.6 | 6.9 | 718.2 | Conv | 200 | III, IV | biplanar |

B7 | 1330.7 | 1010.6 | 6.9 | 897.7 | Conv | 1 | III, IV | biplanar |

B8 | 1330.7 | 1010.6 | 6.9 | 897.7 | Conv | 3.5 | III, IV | biplanar |

B9 | 1084.3 | 1147.4 | 7.1 | 478.8 | Conv | 50 | III, IV | biplanar |

B10 | 868.7 | 1093.6 | 6.5 | 478.8 | Conv | 772 | III, IV | biplanar |

B11 | 828.1 | 1019.5 | 6.7 | 248.4 | SIM | 39,810 | III, IV | biplanar |

C12 | 1378.5 | 1196.2 | 7.4 | 718.2 | SIM | 10,000 | III, IV | biplanar |

C13 | 1378.5 | 1303.6 | 7.6 | 1077.3 | SIM | 0.1 | III, IV | biplanar |

C14 | 1762.1 | 1372.0 | 7.8 | 718.2 | Conv | 9,000 | III, IV | biplanar |

C15 | 1762.1 | 1372.0 | 7.8 | 1077.3 | Conv | 1,000 | III, IV | biplanar |

C16 | 1644.4 | 1523.3 | 7.9 | 493.4 | SIM | 315,360 | III, IV | biplanar |

C17 | 1644.4 | 1523.3 | 7.9 | 657.8 | SIM | 32 | III, IV | biplanar |

C18 | 1700.0 | 1530.1 | 8.0 | 544.0 | SIM | 65,700 | III, IV | biplanar |

C19 | 1680.0 | 1535.0 | 8.1 | 1125.6 | Conv | 1 | III, IV | biplanar |

C20 | 1771.9 | 1537.9 | 8.2 | 574.6 | SIM | 8×10^{5} |
III, IV | biplanar |

C21 | 1771.9 | 1537.9 | 8.2 | 861.8 | SIM | 40 | III, IV | biplanar |

C22 | 1771.9 | 1537.9 | 8.2 | 1197.0 | SIM | 1 | III, IV | biplanar |

* See Figure 1 (above) or refer to Part 1 in this series: June/July 2014 Geosynthetics, pp. 36–41 |

## Derivation of the method

A total of 22 creep rollover tests were performed during a 10-year period, 2002–2012, for biplanar geonets with rollover structure. A summary of these tests is presented in **Table 1**, wherein each entry is a single test.

Column 1 in **Table 1** gives material category and sample number. A, B, and C are the geonet categories with increasingly higher compression strength (column 2) and mass per unit area (column 3). The thickness and test stress are in columns 4 and 5. Conventional method or stepped isothermal method (SIM) to perform the creep test is in column 6. Creep rollover time is in column 7. Columns 8 and 9 give the type of stress-strain curve and general structure of the geonet.

The creep test stress (column 5 in **Table 1**) when divided by the strength (column 2 in **Table 1**) results in a normalized pressure. The latter was plotted against creep rollover time given in column 7 of **Table 1**.

The resulting relationship between normalized pressure and rollover time is presented in **Figure 2**. The scatter in the data in **Figure 2** is obvious and almost two orders of magnitude difference in time can occur in rollover time with a small change in stress. For example, at a stress/strength ratio of 0.48–0.49, rollover time was 32 hours in one test and 10,000 hours in another.

Scatter in compression strength of geonets can be high and values can vary by as much as 60% across the roll width. The scatter worsens as one includes many different samples, production lines, and test procedures into one figure, as is the case in **Figure 2**. The empirical relationship for the best-fit line shown in the figure is re-written here as follows:

Where y = stress/strength and x = time (hours). Substituting S for strength (kPa), σ for stress (kPa), and t for time (hours), the above relationship becomes:

Re-arranging the terms in the equation, one obtains:

Equation 3 expresses the relationship between stress, strength, and time for biplanar geonets with stress-strain curve of a rollover type. The majority of products used for drainage in waste containment systems are of this type. To apply the equation in field for design purpose, it must be modified to account for several differences between field and laboratory conditions. Equation 3 can be re-written as:

Where p_{allow} = allowable stress (kPa), RF_{B} = reduction factor for boundary, and RF_{T} = reduction factor for temperature. The RFB term accounts for differences in boundaries that can be of soft and hard types. Since Equation 4 is based on the data at 20°C, the RF_{T} term accounts for higher temperatures in some types of projects. A factor of safety against a creep rollover can be obtained as:

Where p_{design} is the field overburden stress in kPa and p_{allow} is the allowable stress on a geonet in kPa. The denominator term in Equation 5 can be obtained from the following equation:

Where γ = overburden density in kN/m^{3} and h is the overburden height in m.

## Critique of the method

**Figure 2** shows that overburden stress on geonets with rollover must be kept to a small percentage of their rollover strength. However, the underlying assumption in deriving the method was that a small—4in.×4in.—laboratory creep test specimen is representative of the field conditions involving large installations.

Additional research on the effect of boundary conditions, test procedures, and environmental aspects is needed to validate the method. The method also assumes that all biplanar geonets with a rollover structure can be placed in the same category. Even within conventional biplanar geonets, there can be significant variation in quality and performance.

Lastly, the method combines conventional and SIM data to establish a trend with a significant scatter. Additional tests from other researchers with a different product set are needed to corroborate the recommendations in this article. The data used to derive the method had R² value of 0.73. Additional tests are needed to increase R² to 0.9 or higher.

The method presented in this article is not meant to be used as an alternative to product-specific creep tests. However, the trends from this article can be used to help set up creep tests for the intended duration. For example, a 10,000-hour creep test should not be set at 60% of compression strength because the material will layover before the intended time. Creep reduction factors are needed for a drainage design in addition to ensuring that a layover does not occur during a project’s design life. This article does not discuss or cover creep reduction factors as these are known to be material specific.