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Design of Lateral Drainage Layers Comprising Two Different Slopes - Design Calculator

 

Problem Statement
Lateral drainage layers used in landfills are often comprised of two sections with two different slopes. For instance, in a landfill cover, there is a flat slope typical of 3-8% as an upstream, and a steep slope typical of 4:1 or 3:1 as downstream. In a landfill liner system, however, the upstream is a steep slope and the downstream is a flat slope. Geonet composites can be used for both steep slopes and flat slopes. For liner systems, granular drain is also used at the downstream section. This calculator determines the maximum liquid depth over the liner and required transmissivity for two slopes without an intermediate drainage system.

When an intermediate drainage system is present to separate the two drainage layers, the single slope design calculator should be used.

 

Problem Solution

Case 1 (a & b): Geocomposite drains are used for both upstream and downstream sections

Maximum Liquid Depth
Upstream section
Downstream section
Required Transmissivity
Upstream section
Downstream section
Ultimate Transmissivity
Upstream section
Downstream section

 Case 2: Geocomposite drains at the upstream and granular drain at downstream

 

Maximum Liquid Depth
Upstream section
Downstream section
where
    
and
     
Required Transmissivity
Upstream section
Downstream section
Ultimate Transmissivity
Upstream section
Downstream section

 Case 3: Granular drains at the upstream and geocomposite drain at downstream

 

Maximum Liquid Depth
Upstream section
where
    
and
     
Downstream section
Required Transmissivity
Upstream section
Downstream section
Ultimate Transmissivity
Upstream section
Downstream section

where:

Symbol

 Description

Unit
kup The hydraulic conductivity of the liquid collection material in the upstream section m/s
kdown The hydraulic conductivity of the liquid collection material in the downstream section m/s
Lup The length of the liquid collection layer in the upstream section m
Ldown The length of the liquid collection layer in the downstream section m
q h Impingement rate m/s
bup Slope for the upstream section degrees
bdown Slope for the downstream section degrees
FS d Overall factor of safety for drainage -
RF in Intrusion Reduction Factor -
RFcr Creep Reduction Factor -
RFcc Chemical Clogging Reduction Factor -
RFbc Biological Clogging Reduction Factor -

 

Input Values
GC up/GC down GC up/Granular down Granular up/GC down
 
q h m/s m/s m/s
L up m m m
L down m m m
k up m/s m/s m/s
k down m/s m/s m/s
b up degrees degrees degrees
b down degrees degrees degrees
Factor GC up/GC down GC up/Granular down Granular up/GC down
 
 SurfaceWater Drains Leachate Collection and Removal Leachate Detection Systems
RFin 1.0 - 1.2 1.0 - 1.2 1.0 - 1.2
RFcr Calculate RFCR
RFcc 1.0 - 1.2 1.5 - 2.0 1.1 - 1.5
RFbc 1.5 - 3.5 1.1 - 1.3 1.1 - 1.3
FS 2.0 - 10.0 2.0 - 10.0 2.0 - 10.0

Note:  The reduction factor values given correspond to the case where the seating time exceeds 100 hours and the boundary conditions due to adjacent materials are simulated in the hydraulic transmissivity test.

 
References

"Hydraulic Design of Geosynthetic and Granular Liquid Collection Layers Comprising Two Different Slopes". Giroud, J.P., Zornberg, J.G., Beech, J.F., Geosynthetics International, Vol. 7, No. 5-6, 2000.

"Hydraulic Design of Geosynthetic and Granular Liquid Collection Layers". Giroud, J.P., Zhao, A., Zornberg, J.G., Geosynthetics International, Vol. 7, No 5-6, 2000.

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

Copyright 2001 Advanced Geotech Systems.  All rights reserved.