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8/13/2019 Calculo de Drenaje Con Geotextiles
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DiseodeSistemasdeDrenajeJorge G. Zornberg, Ph.D., P.E.The University of Texas at Austin, USA
President, International Geosynthetics Society
Coversystems
Vegetation
Soil layer
Geotextile filter (if needed)
Drainage layer
Geomembrane liner
Bottom linersystem
Protective soil layer
Geotextile filter (if needed)
Leachate collection layer
Geomembrane liner
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Geosynthetics in Landfill Applications
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Flow Capacity
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Flow Capacity (Cont.)
1. Flow capacity at the end of design life
2. Thickness of liquid layer in service
Important design considerations :
In service condi tions of a drainage layer on a slope
subjected to a uniform rate of liquid supply:
Solut ions to governing dif ferential equation are
called mounding equations
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Liquid Head smaller than prescribedvalue, e.g. 0.3 m
Liquid Thickness smaller than drainagelayer thickness
Design Criteria for DrainageSystems:
Calculations are needed for the Liquid Head andLiquid Thickness
Head and Thickness
Source: Giroud et al. (2000a)
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Geometry of Drainage Layer onSlope
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 MaximumLiquid Thickness
Equations are available to calculate tmax if:- The liquid supply rate is uniform and constant
- The liquid collection layer is underlain by ageomembrane 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 onthe Characteristic parameter, :
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Liquid surface
Liner
ttop> 0.25
0.25
~ 0~
xm
tmax
Source: Giroud et al. (2000a)
McEnroes Equations (1993)
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Comments on McEnroesEquations
Rigorous solution of the differentialequation governing the flow of liquid in a
drainage layer with uniform liquid supply. Used in the HELP Model.
Equations are extremely sensitive to thenumber of digits in numerical calculations.More than 15 digits are necessary in somecases.
Girouds Equation (1992, 1995)
Approximate solution (1%)
Slightly conservative relative to McEnroes equations
Very simple (one simple equation instead of three)
No numerical problems
Has been used in numerous landfill designs
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Factor j in Girouds Equation
Source: Giroud et al. (2000a)
Girouds Original Equation (1985):
Girouds Modified Equation (1992):
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Comparison Giroud vs McEnroe
Source: Giroud et al. (2000a)
Simplif ied Equation
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Simplif ied Equation
Incorrect Equations:
USEPA Equation (1989), from Moore (1983)
Moores equation (1980)
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Parameters forDetermination of tmax
Slope, Drainage length, L
Hydraulic conductivity, k
Liquid supply rate, qh
Hydraulic conductivity, k :
Parameters for Determination oftmax : Hydraulic Conductivity
Only in the case of geocomposite drains,
can use the hydraulic transmissivity, :
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Long-Term-In-Soil HydraulicTransmissivity
Appl ication area RFin RFcr RFcc RFbcRetaining walls 1.3 1.5 1.2 1.4 1.1 1.5 1 1.5
Surface water drains for
covers1.3 - 1.5 1.2 1.4 1.0 - 1.2 1.2 1.5
Leachate Collectionand 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 forDetermination of tmax
Slope,
Drainage length, L
Hydraulic conductivity, k Liquid supply rate, qh
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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 inprimary liner
Parameters for Determination oftmax : 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 alwaysremains at field capacity
Input Parameters: Weather data
Soil data
Design data
HELP Model
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HELP: Typical Landfil l Profile
Cover Soil
Precipitation
Runoff
Evapotranspiration
Infiltration
GeocompositeGeomembrane
Clay Liner
Waste
Geocomposite
Clay Liner
Geomembrane
SandLateral
Drainage
Lateral
Drainage
Percolation
Leakage
Lateral Drainage
Percolation
LEACHATE COLLECTIONLAYER 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%
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Special Mounding Equationsderived from Girouds Equation
Equations for double slope
Equations for double layer
Equations for radial flow
Upstream section
Downstream section
down
up
Double SlopeCover
Upstream section
Downstream section
up
down
Double SlopeBottom Liner
Drain
Soil layer
Drainage layer
Geomembrane liner
Protective
soil layer
Leachate collection
layer Geomembrane
liner DrainSource: Giroud et al. (2000b)
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Ejemplos:
DiseodeSistemasdeDrenajeJorge G. Zornberg, Ph.D., P.E.The University of Texas at Austin, USA
President, International Geosynthetics Society
Design Example: Granular DrainageLayer
A liquid collection layer is designed for a landfill cover.The rate of liquid supply is 100 mm in one day. Agranular layer is selected. The proposed granular layerhas a thickness of 0.30 m and a hydraulic conductivityof 1.0 104 m/s (these values correspond to thoseprescribed by current regulations). The following
geometric characteristics of the liquid collection layerare tentatively considered: a length (measuredhorizontally) of 30 m and a slope of 2%. Check that thefactor of safety (in relation to the thickness of thedrainage layer) is greater than 2.5. If this criterion isnot satisfied either redesign or consider ageocomposite drainage layer.
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Design Example: DrainageGeocomposite
A liquid collection layer is designed for a landfill cover. Therate of liquid supply is 100 mm in one day. Ageocomposite drainage layer is selected. A hydraulic
transmissivity test was performed on the proposedgeocomposite (including the geotextile filters) understresses and hydraulic gradients consistent with thoseexpected in the field. The stresses were applied for 100hours 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 thicknessof the drainage layer) is greater than 2.5, or redesign.
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Redesign of Drainage Geocomposite
The liquid collection layer in the previous example isredesigned. The adopted solution is to change thegeometry of the liquid collection layer. Specifically, alength (measured horizontally) of 15 m and a slope of3% are now considered. Check that the factor of safety(in relation to the thickness of the drainage layer) isgreater than 2.5, or redesign.
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References on Design ofDrainage 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.