Calculo de Drenaje Con Geotextiles

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


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


Girouds Original Equation (1985):

Girouds Modified Equation (1992):


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Comparison Giroud vs McEnroe


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.

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Calculo de Drenaje Con Geotextiles