### By Dhani Narejo and Sam Allen

## Introduction

The first article in this three-part series presented compressive stress-strain behavior of several different geonet structures. The collapse, or rollover, does not occur for many types of geonets.

In the absence of a rollover, the compression of geonets is non-linear in most cases with the compression rate being higher at increasingly higher stress. The short-term compressive stress-strain curve of non-rollover materials does not have a zero or negative slope at any point on the stress-strain curve.

Consequently, compressive creep tests for non-rollover materials result in an approximately linear curve of strain vs. time on a semi-log scale. As such, allowable stress for materials with no rollover cannot be based on the same procedure that was presented in Part 2 of this series. This article presents a method that can be used for any geonet structure that does not roll over.

## Derivation of the method

For geonets with no rollover, thickness retained (or strain) vs. log time plot is approximately linear. This was confirmed by 22 creep tests, summarized in **Table 1**, that the authors performed on geonets of different types where strain was found to be approximately linear against log time.

Biplanar geonets of stress-strain curves of types I and II (**Figure 1**) did not develop a creep rollover even at a relatively high stress. Therefore, these geonets are placed under this section as opposed to biplanar geonets of types III and IV that were covered in Part 2 (Geosynthetics, Vol. 32 No. 4, pp.48-51).

The creep rate is the slope of the creep curves at any point and average creep rate is the total creep strain divided by the total time. The creep rate plotted in Figure 2 is based on a time of 200,000 hours. This required extrapolating the conventional 10,000-hour creep curves by a little more than one log cycle.

The relationship between creep rate and stress is of exponential nature and can be expressed as:

y = Ae^{Bx} (1)

Where y = average strain per year or average creep rate, x = stress (kPa), and A, B = material-specific curve fitting constants. Equation 1 can be re-arranged to calculate stress instead of creep rate as:

x = C.ln(y) + D (2)

Where C and D = material-specific constants. A and B for Equation 1, and C and D for Equation 2 are summarized in **Table 2** for the materials in **Table 1**. These constants can vary depending on the type of the material and the stress range and must be obtained by manufacturers for their specific products. For a rough approximation, an average value of the constants is also provided in the table.

These average values represent materials of non-rollover type used currently for applications at a higher end of stress (480 kPa and higher). Material D was not included in the average because it is meant to be used only for low-stress applications such as green roofs and landfill caps. Substituting Ïƒ for stress, Îµ for strain and t for time in Equations 1 and 2:

(3)

(4)

Then allowable stress, pallow, can be obtained from Equation 4 as:

(5)

Where, ε = strain (ratio), t = time (years), σ = stress (kPa), RFB = reduction factor for boundary conditions, and

RFT = reduction factor for temperature.

## Summary and conclusions

The primary types of geonets available for use with drainage geocomposites can be described as biplanar, triplanar, and spiked. Each of these general categories includes many sub-categories and product types to match project requirements in a range of applications.

The stress-strain behavior of some geonets can reach a peak value after which there is a plateau or a negative slope. This type of stress-strain behavior is manifested as a creep rollover in compressive creep tests. No creep rollover occurs when compressive stress-strain curve has a positive slope for the entire stress range tested. Creep rollover is not desirable in the field because it can lead to a sudden change in the structure, and therefore in the in-plane porosity, of geonets. Excessive compressive creep is also undesirable in geonets because it can gradually close a geonet structure and eliminate all in-plane flow.

Conventional and stepped isothermal method (SIM) compressive creep tests were performed on several types of geonets. The data shows the SIM to be equivalent to, or slightly conservative, than the conventional method. The creep data was used to derive two types of empirical methods to determine allowable stress in the field. For geonets with rollover, the method (presented in Part 2 of this series) calculates the allowable stress to prevent a rollover. For geonets with no rollover, the method calculates allowable stress for a design strain and time.

Sample # | Mass (g/m^{2}) |
Thickness (mm) | Test Stress (kPa) | Test Type | Duration (hours)1 | Creep Reduction Factor | Stress-Strain Curve | Structure |
---|---|---|---|---|---|---|---|---|

D1 | 1801.6 | 9.3 | 24 | SIM | 133,788 | 1.06 | VIII | Spiked |

D2 | 1869.9 | 9.4 | 48 | SIM | 133,787 | 1.10 | VIII | Spiked |

D3 | 1957.8 | 9.1 | 239 | SIM | 133,810 | 1.21 | VIII | Spiked |

E4 | 2094.6^{2} |
6.0 | 239 | CON | 10076 | 1.09 | VII | Spiked |

E5 | 2094.6^{2} |
6.1 | 479 | CON | 10099 | 1.19 | VII | Spiked |

E6 | 2094.6^{2} |
6.0 | 479 | SIM | 298,9131 | 1.41 | VII | Spiked |

E7 | 2094.6^{2} |
6.1 | 958 | CON | 10099 | 1.68 | VII | Spiked |

F8 | 1617.2 | 8.7 | 239 | CON | 10562 | 1.21 | II | Biplanar |

F9 | 1617.2 | 8.6 | 479 | CON | 10557 | 1.27 | II | Biplanar |

F10 | 1617.2 | 8.3 | 479 | SIM | 255,3134 | 1.24 | II | Biplanar |

F11 | 1617.2 | 8.2 | 958 | CON | 10562 | 1.71 | II | Biplanar |

G12 | 2211.7 | 8.5 | 239 | SIM | 238,753 | 1.15 | I | Biplanar |

G13 | 2211.7 | 8.4 | 479 | SIM | 59,957 | 1.3 | I | Biplanar |

G14 | 2211.7 | 8.4 | 718 | SIM | 77,334 | 1.39 | I | Biplanar |

G15 | 2211.7 | 8.4 | 958 | SIM | 59,957 | 1.45 | I | Biplanar |

G16 | 2211.7 | 8.4 | 1197 | SIM | 59,955 | 1.53 | I | Biplanar |

G17 | 2152.8 | 8.2 | 718 | CON | 10,000 | 1.28 | I | Biplanar |

G18 | 2152.8 | 8.2 | 1197 | CON | 10,000 | 1.67 | I | Biplanar |

H19 | 1200.0 | 8.1 | 239 | CON | 10535 | 1.14 | V | Triplanar |

H20 | 1455.0 | 9.1 | 479 | CON | 10579 | 1.18 | V | Triplanar |

H21 | 1184.0 | 7.8 | 479 | SIM | 346,5404 | 1.49 | V | Triplanar |

H22 | 1455.0 | 9.2 | 958 | CON | 10579 | 1.64 | V | Triplanar |