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.