landfilldesign.com
Unit Gradient Method - Design Calculator

 

Problem Statement

The transmissivity of a drainage geocomposite must be great enough to carry all of the infiltrating flow from the soil layer(s) above. If the drainage geocomposite can not carry all the infiltrating water (very long slope, or very permeable cover soil,...); swales can be placed as shown in the above figure. The three conditions for stability are:
  1. The interface shear strength of all interfaces is adequate
  2. Pore water pressures do not build up and reduce the contact stress between the geomembrane and the soil. The Seepage Force Stability Calculator can be used to determine the factor of safety of a landfill cover with consideration of seepage forces
  3. Landfill gas pressures beneath the liner are vented properly.The Landfill Gas Pressure Relief Calculator can be used to determine the gas transmissivity of the relief layer. The Landfill Gas Stability Calculator can be used to verify the factor of safety of a landfill cover subject to landfill gas pressure underneath a geomembrane liner.
This webpage determines the ultimate transmissivity sufficient to transmit all incoming flow within the thickness of the geocomposite; i.e. maximum head < geonet thickness; therefore seepage forces in the cover soil will be zero.

With Darcy's law:

Inflow of water in the geocomposite

Outflow of water from the geocomposite at the toe of the slope

Inflow equals outflow (Factor of Safety = 1)

This results in a required transmissivity of the geocomposite of:

Which results in the ultimate transmissivity after multiplying by the Total Serviceability Factor (TSF)

Required Data

Symbol Name Dimensions
Lh Drainage pipe spacing or length of slope measured horizontally Length
kveg Permeability of the vegetative supporting soil Length/Time
S The liner's slope, S = tan b -
FSslope Minimum factor of safety against sliding, for
soil/geocomposite or geocomposite/geomembrane interfaces 		-

FSd Overall factor of safety for drainage
RFin Intrusion Reduction Factor
RFcr Creep Reduction Factor
RFcc Chemical Clogging Reduction Factor
RFbc Biological Clogging Reduction Factor

 

Input Values
Note: If you do not wish to perform calculations for 3 cases, please leave default data as is.

Case 1 Case 2 Case 3
S % % %
Lh m m m
kveg cm/sec cm/sec cm/sec
FSslope
 
Reduction Factors and Safety Factor
  Case 1 Case 2 Case 3 Surface Water Drains
RFin [1] 1.0 - 1.2
RFcr [2] Calculate RFCR
RFcc [3] 1.0 - 1.2
RFbc [3] 1.2 - 3.5
FSd [4] 2.0 - 10.0


[1] Intrusion reduction factor from 100 hour to design life. Giroud et. al (2000)
[2] Creep reduction factor from 100 hour to design life (for instance, 30 years). RFCR is determined from 10,000 hour compressive creep test, extrapolated to design life, GRI-GC8 (2001). RFCR is product and normal load specific.
[3] GRI-GC8
[4] FS value = 2-3. Giroud, et. al (2000)
    FS value > 10 for filtration and drainage. Koerner (2001)
[5] Note: The calculated transmissivity is corresponding to the case where the seating time is 100 hours and the boundary conditions due to adjacent materials are simulated in the hydraulic transmissivity test.

 
References

"GRI-GC8, Determination of the Allowable Flow Rate of a Drainage Geocomposite". Geosynthetics Research Institute, 2001.

"Beyond a factor-of-safety value, i.e., the probability of failure". GRI Newsletter/Report, Vol. 15, no. 3.

"Designing with Geosynthetics". R.M. Koerner, Prentice Hall Publishing Co., Englewood Cliffs, NJ, 1998.

"Hydraulic Design of Geosynthetic and Granular Liquid Collection Layers". J. P. Giroud, J. G. Zornberg and A. Zhao, Geosynthetics International, Vol. 7, Nos 4-5.

"Lateral Drainage Design update - part 2". G. N. Richardson, J.P. Giroud and A. Zhao, Geotechnical Fabrics Report, March, 2002

Copyright 2001 Advanced Geotech Systems.  All rights reserved.