Post on 24-Feb-2022
Diseño de Sistemas de Drenaje
Jorge G. Zornberg, Ph.D., P.E.The University of Texas at Austin, USAPresident, International Geosynthetics Society
Cover systems
VegetationSoil layerGeotextile filter (if needed)Drainage layerGeomembrane liner
Bottom liner system
Protective soil layerGeotextile filter (if needed)Leachate collection layerGeomembrane liner
Geosynthetics in Landfill Applications
Flow Capacity
Flow Capacity (Cont.)
1. Flow capacity at the end of design life …
2. Thickness of liquid layer in service…
Important design considerations :
In service conditions of a drainage layer on a slopesubjected to a uniform rate of liquid supply:
Solutions to governing differential equation are called “mounding equations”
– Liquid Head smaller than prescribed value, e.g. 0.3 m
– Liquid Thickness smaller than drainage layer thickness
Design Criteria for Drainage Systems:
Calculations are needed for the Liquid Head and Liquid Thickness
Head and Thickness
Source: Giroud et al. (2000a)
Geometry of Drainage Layer on Slope
Maximum liquid thickness (or maximum head) as a function of:
• Drainage length, L
• Slope angle, • Liquid supply rate, qh
• Hydraulic conductivity of drainage layer, k
Calculation of the Maximum Liquid Thickness
• Equations are available to calculate tmax if:- The liquid supply rate is uniform and constant- The liquid collection layer is underlain by a
geomembrane liner without defects- The slope of the liquid collection layer is
uniform- There is a drain at the toe of the slope
• The shape of the liquid surface depends on the “Characteristic parameter”, :
Liquid surface
Liner
ttop> 0.25
0.25
~ 0~
xm
tmax
Source: Giroud et al. (2000a)
McEnroe’s Equations (1993)
Comments on McEnroe’s Equations
• Rigorous solution of the differential equation governing the flow of liquid in a drainage layer with uniform liquid supply.
• Used in the HELP Model.• Equations are extremely sensitive to the
number of digits in numerical calculations. More than 15 digits are necessary in some cases.
Giroud’s Equation (1992, 1995)
• Approximate solution (1%)
• Slightly conservative relative to McEnroe’s equations
• Very simple (one simple equation instead of three)
• No numerical problems
• Has been used in numerous landfill designs
Factor j in Giroud’s Equation
Source: Giroud et al. (2000a)
Giroud’s Original Equation (1985):
Giroud’s Modified Equation (1992):
Comparison Giroud vs McEnroe
Source: Giroud et al. (2000a)
Simplified Equation
Simplified Equation
Incorrect Equations:
USEPA Equation (1989), from Moore (1983)
Moore’s equation (1980)
Parameters for Determination of tmax
• Slope, • Drainage length, L
• Hydraulic conductivity, k
• Liquid supply rate, qh
• Hydraulic conductivity, k :
Parameters for Determination of tmax : Hydraulic Conductivity
• Only in the case of geocomposite drains, can use the hydraulic transmissivity, :
Long-Term-In-Soil Hydraulic Transmissivity
Application area RFin RFcr RFcc RFbc
Retaining walls 1.3 – 1.5 1.2 – 1.4 1.1 – 1.5 1 – 1.5
Surface water drains for covers
1.3 - 1.5 1.2 – 1.4 1.0 - 1.2 1.2 – 1.5
Leachate Collection and Removal Systems (LCRS)
1.5 - 2.0 1.4 – 2.0 1.5 - 2.0 1.5 - 2.0
Leachate Detection Systems (LDS)
1.5 - 2.0 1.4 – 2.0 1.5 - 2.0 1.5 - 2.0
Parameters for Determination of tmax
• Slope, • Drainage length, L
• Hydraulic conductivity, k
• Liquid supply rate, qh
• Covers, general case:– Use soil saturated hydraulic conductivity
• Covers, arid climates:– Use HELP
• Base liners, LCRS:– Use HELP
• Base liners, LDS:– Consider conservative scenarios for defects in
primary liner
Parameters for Determination of tmax : Liquid Supply Rate
• General Basis:– Quasi 2-D– Deterministic– Water balance
• Simplifying Assumptions:– Only gravitational forces are responsible for water
flow– ET depth is predefined– Soil moisture content of barrier layers always
remains at field capacity
• Input Parameters:– Weather data– Soil data– Design data
HELP Model
HELP: Typical Landfill Profile
Cover Soil
Precipitation
Runoff
Evapotranspiration
InfiltrationGeocomposite
Geomembrane
Clay Liner
Waste
Geocomposite
Clay Liner
Geomembrane
SandLateral Drainage
Lateral Drainage
Percolation
Leakage
Lateral Drainage
Percolation
LEACHATE COLLECTION LAYER DESIGN
Design Criteria:– Liquid depth smaller than 0.3 m (1 ft)– Liquid thickness smaller than liquid collection layer
thickness
Minimum Prescribed Values:– Thickness 0.3 m (1 ft)– Hydraulic Conductivity 1 x 10-4 m/s (1 x 10-2 cm/s)
(Hydraulic Transmissivity 3 x 10-5 m2/s)– Slope 2%
Special Mounding Equations derived from Giroud’s Equation
• Equations for double slope
• Equations for double layer
• Equations for radial flow
Upstream section
Downstream section
down
up
Double Slope Cover
Upstream section
Downstream section
up
down
Double Slope Bottom Liner
Drain
Soil layer
Drainage layer
Geomembrane liner
Protective soil layer
Leachate collection layer Geomembrane
liner DrainSource: Giroud et al. (2000b)
Ejemplos:Diseño de Sistemas de Drenaje
Jorge G. Zornberg, Ph.D., P.E.The University of Texas at Austin, USAPresident, International Geosynthetics Society
Design Example: Granular Drainage Layer
A liquid collection layer is designed for a landfill cover. The rate of liquid supply is 100 mm in one day. A granular layer is selected. The proposed granular layer has a thickness of 0.30 m and a hydraulic conductivityof 1.0 104 m/s (these values correspond to those prescribed by current regulations). The following geometric characteristics of the liquid collection layer are tentatively considered: a length (measured horizontally) of 30 m and a slope of 2%. Check that the factor of safety (in relation to the thickness of the drainage layer) is greater than 2.5. If this criterion is not satisfied either redesign or consider a geocomposite drainage layer.
Design Example: Drainage Geocomposite
A liquid collection layer is designed for a landfill cover. The rate of liquid supply is 100 mm in one day. A geocomposite drainage layer is selected. A hydraulictransmissivity test was performed on the proposed geocomposite (including the geotextile filters) under stresses and hydraulic gradients consistent with those expected in the field. The stresses were applied for 100 hours before the hydraulic transmissivity was measured. The transmissivity value thus measured was 3.6 103
m2 /s. The proposed geocomposite has a core thicknessof 9 mm under representative field conditions.
The following geometric characteristics of the liquid collection layer are tentatively considered: a length(measured horizontally) of 30 m and a slope of 2%. Check that the factor of safety (in relation to the thickness of the drainage layer) is greater than 2.5, or redesign.
Redesign of Drainage Geocomposite
The liquid collection layer in the previous example is redesigned. The adopted solution is to change the geometry of the liquid collection layer. Specifically, a length (measured horizontally) of 15 m and a slope of 3% are now considered. Check that the factor of safety(in relation to the thickness of the drainage layer) is greater than 2.5, or redesign.
References on Design of Drainage Systems
Giroud, J.P., and Houlihan, M.F. (1995). “Design of Leachate Collection Layers”, Proceedings of the Fifth International Landfill Symposium, Sardinia, Italy, October 1995, Vol. 2, pp. 613-640.
Giroud, J.P., Zornberg, J.G., and Zhao, A. (2000a). “Hydraulic Design of Geosynthetic and Granular Liquid Collection Layers.” Geosynthetics International, Special Issue on Liquid Collection Systems, Vol. 7, Nos. 4-6, pp. 285-380.
Giroud, J.P., Zornberg, J.G., and Beech, J.F. (2000b). “Hydraulic Design of Geosynthetic and Granular Liquid Collection Layers Comprising Two Different Slopes.” Geosynthetics International, Special Issue on Liquid Collection Systems, Vol. 7, Nos. 4-6, pp. 453-489.
Giroud, J.P., Zhao, A., and Bonaparte, R. (2000c). “The Myth of Hydraulic Transmissivity Equivalency Between Geosynthetic and Granular Liquid Collection Layers”, Geosynthetics International, Special Issue on Liquid Collection Layers, Vol. 7, Nos. 4-6, pp. 381-401.
Giroud, J.P., Zhao, A., Tomlinson, H.M., and Zornberg, J.G. (2004). “Liquid Flow Equations for Drainage Systems Composed of Two Layers Including a Geocomposite.” Geosynthetics International, February, Vol. 11, No. 1, pp. 43-58.