Leachate Collection Systems - Hochschule Ostwestfalen-Lippe · 1 Introduction Lining of landfill...

STANDORT HÖXTER FACHGEBIET ABFALLWIRTSCHAFT UND DEPONIETECHNIK

Leachate Collection Systems

Hans-Günter Ramke, Höxter

Contribution to the

1st Middle European Conference on Landfill Technology

organised by the Technical Committee 6.1 – Geotechnics of Landfills – of the German Geotechnical Society (DGGT)

and the Hungarian National Committee of the ISSMGE

Hungarian Academy of Sciences, Budapest, 06-08 February 2008

Chairmen:

K. J. Witt, H.-G. Ramke, G. Telekes, E. Imre

Address of the Author

Professor Dr.-Ing. Hans-Günter Ramke

University of Applied Sciences Ostwestfalen-Lippe, Campus Hoexter An der Wilhelmshöhe 44, D-37671 Hoexter

Phone ++49/5271/687-130, e-mail [email protected]

This publication can be cited as follows: RAMKE, H.-G., 2008: Leachate Collection Systems in: TELEKES, G., IMRE, E.; WITT, K. J.; RAMKE, H.-G. (EDTS.), 2009: Proceedings of the 1st Middle European Conference on Landfill Technology February 6-8, 2008, Budapest, Hungary Szent István University, Budapest, Hungary


Leachate Collection Systems Hans-Günter Ramke Faculty of Environmental Engineering, Campus Höxter, University of Applied Sciences Ostwestfalen-Lippe

Keywords: leachate collection systems, drainage, incrustations, hydraulic calculation

ABSTRACT: Leachate collection systems in bottom liner systems of landfills are of essential importance within the whole concept of landfill lining. Without sufficient leachate collection the long-term efficiency of the liner system is problematic, and the stability of the waste body cannot be ensured. Leachate collection systems consist of a drainage layer, the drainage pipes, shafts, and collection pipes. The Directive on the Landfilling of Waste of the European Union defines minimum standards for leachate collection systems, but a suitable design requires the consideration of many details, which are compiled in the Technical Recommendations “Geotechnics of Landfills” of the German Geotechnical Society. Incrustation processes are the most urgent problem for long-term functionality of leachate collection systems. The explanation of incrustation processes and proposals for mitigation measures are a first focus. A second focus is the hydraulic calculation of leachate collection systems. Beginning with the derivation of basic equations analytical and numerical solutions are shown, and practical examples will be demonstrated. Finally some detailed design recommendations are given.

1 Introduction Lining of landfill bottoms requires a leachate collection system

- to collect leachate - to discharge it at defined points out of the dumping area - to avoid an accumulation of leachate above the bottom liner.

The accumulation of leachate needs to be controlled in a landfill for four reasons:

- to prevent liquid levels rising to such an extent that they can spill over and cause uncontrolled pollution to ditches, drains, watercourses, etc.

- to increase the efficiency of the liners by reduction of the hydraulic head of leachate above the liner - to reduce the intensity of leaching of waste - to ensure the stability of the waste body in the case of above ground landfills.

A leachate collection system basically consists of a drainage layer of inert material with high permeability, of drainage pipes which have to collect the leachate and to discharge it out of the dumping area, of collection and inspection shafts, and of collection pipes. There are differing national regulations and a number of guidance documents available on leachate drainage system design. The objective of this paper is to explain the state-of-the-art of leachate collection systems for engineering purposes. Beginning with a brief overview of requirements on leachate collection systems and of design features a first focus will be laid on the clogging of leachate collection systems (incrustation process). This mechanism is the most urgent problem for the long-life functionality of leachate collection systems. A second focus is the explanation of methods of hydraulic calculation of drainage systems. Due to the fact that the hydraulic calculation for both leachate collection systems in bottom liner systems and in drainage systems of landfill capping systems is more or less identical both systems will be covered. Finally some more detailed recommendations for the design of leachate collection system will be given. The paper is mainly based on the Technical Recommendation “Design Principles for Leachate Collection Systems in Bottom Liner Systems” of the Technical Committee Geotechnics of Landfills of the German Geotechnical Society (GDA E 2-14, 1997) and a comprehensive compilation of RAMKE, 1998.


2 General Principles of Design

2.1 General Requirements For general guidance a leachate collection system should (see GERMAN GEOTECHNICAL SOCIETY, 1993):

- be able to drain down leachate within the landfill such that the saturated thickness of leachate above the bottom liner is less than any specified level

- be strong enough to withstand physical damage due to the loading imposed by the waste, and any

compaction equipment working over the system - be able to accommodate the predicted settlement at the base of the landfill under the applied loads

and foundation conditions - be resistant to microbiological and chemical attacks in the corrosive environment of the landfill - be able to function in spite of unavoidable incrustation processes during and after the operational life of

the landfill - be capable of inspection and maintenance until such time as the system is no Ionger required to

function - incorporate a suitable level of "redundancy" in the design to take account of failure of parts of the

system and provide alternative drainage routes to collection points. Leachate volume and properties can be assessed as follows:

- Leachate Volume The drainage system should be designed to collect the expected volumes of leachate generated. This

will vary during the life of the site and can be estimated using a water balance calculation. Details are given in Chapter 4.2.1.

- Leachate Quality Materials selected for use in the drainage system should be resistant to and compatible with the

expected "worst case" leachate quality. It should be borne in mind that leachate quality depends on waste composition and degradation process and therefore may vary with time and age.

- Temperature The drainage system should be capable of withstanding the elevated temperatures which can occur at

the base of a landfill (between 15° and 40°C may be expected at the bottom of landfills for municipal solid waste).

- Leachate Viscosity The viscosity of the leachate depends on its temperature and composition. In particular the organic

content (COD) significantly influences the viscosity of high-strength leachates. However, in general, the influence of viscosity can be disregarded in hydraulic calculations for the drainage system (RAMKE, 1991).

2.2 Legal Requirements The Landfill Directive of the European Union distinguishes between landfills for non-hazardous waste and hazardous waste, but requires in both cases a drainage layer with a thickness of at minimum 50 cm. Furthermore the directive states:

“In addition to the geological barrier described above a leachate collection and sealing system must be added in accordance with the following principles so as to ensure that leachate accumulation at the base of the landfills is kept to a minimum. Member states may set general or specific requirements for inert waste landfills and for the characteristics of the above mentioned technical means.”

The German directives on landfilling of waste have defined the requirements much more in detail.


Leachate collection systems in bottom liner systems of landfills for construction and demolition waste, for municipal solid waste and for hazardous waste have to fulfil these requirements:

- Drainage layer: - thickness: ≥ 30 cm - hydraulic conductivity ≥ 1·10-3 m/s - material, grain size gravel 16 - 32 mm - Drainage pipes: - inside diameter ≥ 300 mm - length unspecified - drain spacing ≤ 30 m - Slopes: - cross slope ≥ 3 % - longitudinal slope ≥ 1 %

The drain spacing of 30 m is valid for a roof-like shaped landfill bottom. In landfills on sloping planes the drain spacing should not exceed 15 m. In both cases the maximum drainage length is limited to 15 m. For drainage pipes a technical standard defines minimum requirements (DIN 19667, 1991).

2.3 Design Features In order to satisfy the general requirements, it is suggested that the following features should offer minimum guidance for design purposes (according to GERMAN GEOTECHNICAL SOCIETY, 1993):

- A leachate collection system should extend over the entire base of a landfill and, if below ground, should extend up its sloping side walls.

- The drainage layer consisting of granular materials should be at least 300 mm thick and should have a

hydraulic conductivity of at least 1·10-3 m/s. - The bottom liner has to be profiled to have sufficient gradient to promote efficient drainage to the

drainage pipes. The drainage pipes should have sufficient longitudinal slope to reduce sedimentation. Due regard should be given to potential settlement of the landfill base. Minimum values for slopes

range from less than 1 % to 3 %, depending on the topographical and hydrogeological setting of the landfill and the design objectives.

- The granular material of the drainage layer should be prewashed to remove fines. Limestone or other

calcareous materials should not be used. - A network of perforated drainage pipes should be laid within the drainage layer with continuous

gradients towards the leachate collection point(s) and should be capable of being inspected and maintained.

- Leachate removal from a common collection point should be capable of continuous and automatic

functioning. Gravity drainage and discharge is much better than pumping. - The system should be inspected regularly and cleaned out accordingly. - The construction documentations should be retained.

Figure 2.1 shows an example of a leachate collection system that satisfies the current German requirements for landfills for municipal solid waste. Although the specific details may not be relevant in all cases, depending on national regulations and/or site specific conditions, they indicate the general principles and considerations for leachate drainage system design.


Figure 2.1: Plan View and Cross Section of a Leachate Collection System


3 Clogging in Leachate Collection Systems

3.1 Overview Two main reasons of failure of leachate collection systems or of their parts can be distinguished:

- mechanical damages, especially of the drainage pipes - clogging of the drainage layer and in the drainage pipes.

Mechanical damages, e.g. fractures of bending resistant drainage pipes or plastic buckling of flexible drainage pipes, can be prevented by careful design and material selection. But the formation of consolidated, insoluble incrustations in drainage pipes and drainage layers (clogging), in particular in leachate collection systems of landfills for municipal solid waste, represents the most important problem facing the long-term effective functioning of landfill drainage systems in bottom liner systems. Incrustation material can be removed from the drainage pipes by regular flushing and if necessary by milling, but cannot be removed from the pipe casing or from the drainage layer. The focus of this chapter therefore will be a description of the incrustation processes, of their mechanisms and causes, and of recommendations for construction and operation. A survey of sanitary landfills in Germany at the end of the 1980’s showed that such incrustation occurs at most landfill sites. Observed impairment ranges from local areas of incrustation to extensive consolidation and can result in partial up to extensive loss of functional capability of the leachate collection system. The cause behind the sometimes very extensive incrustation process was largely unknown (see RAMKE, 1987), until extensive field investigations and laboratory experiments were carried out by two institutes of the Technical University of Braunschweig (Leichtweiß-lnstitute of Water Research and Institute of Microbiology), on behalf of the Federal Environment Agency (UMWELTBUNDESAMT) and the Ministry of Research and Technology (BMFT). The main observations and results of these investigations will be summarised in the following chapters, because these investigations resulted in a comprehensive understanding of the incrustation process. The results of this project were published by RAMKE/BRUNE, 1990 and BRUNE ET AL., 1991. The microbiological investigations were described in detail by BRUNE, 1991. All the photos in the following were published in RAMKE/BRUNE, 1990. The scanning-electron-microscope photos were taken by BRUNE.

3.2 Field Investigations on Clogging Processes Within the framework of the above mentioned research programme field investigations were conducted at a total of 10 sanitary landfills. The programme of investigation, which owing to the nature of things could only be completely implemented in some cases, consisted of the following steps:

- chemical and microbiological analyses of leachate - determination of composition of gases in the drainage pipes - temperature measurements in the drainage pipes - camera inspection and sampling of material flushed out of the pipes - experiments on microbial biofilm formation in drainage pipes - excavation of the drainage system - chemical and microbial analyses of incrustation materials.

The objective of the study was to obtain information about the physicochemical and microbiological milieu conditions in the drainage system. Further emphasis was placed on the investigation of the incrustation material. Methods and results are described in detail by RAMKE/BRUNE, 1990. The field investigations showed that varying degrees of incrustation took place in the drainage systems of nearly all the landfills investigated. In the drainage pipes the degree of incrustation ranged from thin layers on the pipe wall to a significant reduction in pipe cross section. The material which was flushed out of the pipes (see Figure 3.1) was generally hard, black, pulverisable and homogenous. Testing with acid showed sulphide and carbonate as chemical components. Generally, incrustations in the pipes could be removed by flushing or, in some cases, by milling. Incrustation of the drainage layer, particularly in the casing of the pipe, can in extreme cases lead to a complete loss of permeability (see Figure 3.2), although a certain residue permeability usually remains. The structure of the incrusted drainage material ranged from grains of gravel, covered with a thin layer of fine material, to complete filling of the pores between the gravel grains forming a structure like that of concrete. Macroscopically the fine material corresponded to that of the pipe deposits. Although drainage gravel covered with just a layer of sludge was found, usually it was consolidated to a hard mass which could extend over an area of several meters diameter.


Silting of the drainage layer by fine particles being washed out of the overlying refuse was seldom observed in the course of the excavations. The transition from the lowest layer of refuse to the drainage layer was usually sharply defined on the landfills for municipal solid waste investigated. Only in cases of intensive water flow might a degree of silting be assumed.

Figure 3.1: Incrustation material flushed out of a drainage pipe

Figure 3.2: Detail of drainage material with incrustation of the pipe casing The main constituents of the incrustation material are calcium and iron combined with carbonate and sulphur (mainly in the form of sulphide). The composition of some typical samples of incrustation material is presented in Figure 3.3.


Typical for the material flushed out of the drains is the small amount of insoluble residue after dissolving in aqua regia. The insoluble residue left from the encrusted drainage gravel is considerably greater, no doubt on account of the incomplete separation of incrustation material and drainage material. The composition of the incrustation materials ranges from those consisting primarily of calcium carbonate to others with a high iron and sulphur content. Generally a significant amount of organic material is found in all the deposits (loss on ignition or organic carbon).

Figure 3.3: Composition of selected incrustation material from landfills

The fine structure of a typical piece of incrustation material is shown at increasing magnification in Figure 3.4 (RAMKE/BRUNE, 1990). The example shown, from drainage pipe incrustations at the landfill Altwarmbüchen - Hannover, was photographed in the scanning electron microscope. The particles of material, which had been flushed out of the drain, are a 3-dimensional network of tightly packed aggregates of bacteria. The aggregates, with a diameter of about 10 µm, are covered to varying degrees with inorganic precipitates. The network of bacterial aggregates encloses at least an equal volume of pore space, the individual pores of which have a similar diameter to those of the aggregates.

Medium magnification High magnification

Figure 3.4: Typical structure of incrustation material in landfill drainage systems

- progressive magnification in scanning electron microscope


The deposits formed on the bacteria have a diameter well under 1 µm and appear as pimples on the cell surface. At a more advanced stage of incrustation the precipitates enclose the whole aggregate of bacteria. On a single piece of flushing material incrustations at various stages of development can be seen. In general these structures could be observed on flushing material from all the investigated sites as well as on the encrusted drainage material. According to the EDX-analyses (Energy Dispersive X-ray Analysis) which were carried out in conjunction with the SEM examination (Scanning Electron Microscope), the principle elements contained in the deposits precipitated by the bacteria were sulphur, calcium and iron. Although their proportions varied, they always formed the bulk of the elements present, whether in the pipe deposits or in the incrustation material from the drainage gravel. Figure 3.5 shows a typical EDX-analysis of flushing material in conjunction with the SEM. The peak for silicon indicates a small amount of fine sand grains being mixed in with the material.

Scanning electron microscope photo

Spot analysis

Figure 3.5: EDX-Analyses of incrustation material (Landfill Altwarmbüchen, Drain AI/3, 1988)

The results of the field investigations concerning the causes of the incrustation process and the connexion with the type of landfill operation can be summarized as follows:

- Physicochemical analyses of the leachate and gases in the drainage pipes, as well as the colour and

chemical composition of the deposits, show that milieu conditions in the drainage system are determined by the anaerobic microbial processes in the landfill.

- Microscopic examination of the incrustation material, of the microflora in the drainage system and of

the experimentally exposed pieces of glass and gravel provided evidence for the metabolic activity of anaerobic bacteria being the cause of the incrustations.


- Purely physicochemical causes for the incrustations, such as a reduction in temperature or an altered partial pressure of carbon dioxide, cannot be ruled out, but considering the proven role of microbiological processes, the part they play can only be of minor significance.

- The main components of the incrustation material are the cations of calcium and iron, combined with

carbonate and sulphur (mainly in the form of its sulphide). - Of all the landfill sites investigated the one being most rapidly filled with waste was also the one with

the highest concentrations of organic and inorganic substances in its leachate and with the most rapid formation of incrustations. It was here that the greatest annual amounts of drain deposits were repeatedly formed.

- Once a landfill has reached the stable methane phase with its lightly loaded leachate incrustation

hardly occurs. - The landfill with the aerobic pre-treatment of the refuse (rotting process) was found to have a very low

intensity of incrustation formation. - Excavation of a sewage sludge deposit revealed that over large areas the drainage system had

become more or less impermeable due to massive incrustations. - Limestone gravel is absolutely unsuitable as drainage layer material. It decomposes under the milieu

conditions prevalent on the bottom of a sanitary landfill.

3.3 Laboratory Investigations on Clogging Processes In addition to the investigations on the landfill sites laboratory experiments were conducted by RAMKE/BRUNE, 1990 with the objective of simulating the incrustation process. It was intended to isolate the influence of individual factors on the incrustation process and to analyze the course of its development in time. The experimental apparatus is illustrated in Figure 3.6. The experiments were performed in closed plastic columns with a diameter of up to 200 mm and a height of approx. 1 m. Drainage material was placed on a sieve plate in the column to a height of 30 cm, on top of which was placed a further 15 cm layer of refuse compost. Leachate, supplied by a peristaltic pump, was fed onto the column from above and permeated the unsaturated layers of compost and drainage material before passing through the sieve plate.

Figure 3.6: Column for simulation of incrustation processes under anaerobic conditions


Apart from the geometrical similarity the laboratory simulation of the incrustation process also needed to reproduce the physicochemical and microbiological conditions on the bottom of a sanitary landfill. This was ensured by the use of leachate from two operating landfills, and a temperature of 30 °C in the room the columns were placed. Both measures initiated the microbial degradation process of organic leachate constituents. As a consequence of the microbial degradation process an intensive anaerobic biocenosis developed, and landfill gas was generated. A comparison of input and output leachate composition showed that not only the physico-chemical conditions but the degradation processes are of particular importance for the simulation of the incrustation processes. Next to the reduction of the organic constituents a significant reduction of iron and calcium was observed, the main components of incrustation materials. The experiments are described in detail by RAMKE/BRUNE, 1990 and BRUNE ET AL., 1991. After developing the method for simulating the incrustation process in columns the influence of leachate quality on the incrustation process and the influence of grain size distribution of drainage material on the longevity of the drainage layer were tested in 12 columns. Figure 3.7 shows a comparison of the inflow and outflow of two highly loaded columns. The concentrations of COD and Calcium significantly decreased during passing the columns. Organic compounds were decomposed; inorganic compounds like calcium were precipitated.

Figure 3.7: Laboratory experiments for simulating incrustation processes – curves of in- and outflow levels of columns with highly loaded leachate

1000

10000

100000

0 100 200 300 400 500Time [days]

InflowOutflow - C 2Outflow - C 7

COD [mg O2/l]

10

100

1000

10000

0 100 200 300 400 500Time [days]

InflowOutflow - C 2Outflow - C 7

Calcium [mg/l]


The laboratory investigations experiments led to the following results:

- Incrustations were not formed in significant amounts by the lightly loaded leachate of the stable methane phase of decomposition.

- By the use of highly loaded leachate incrustation was extensive and corresponded to that observed at

sanitary landfills. - The incrustation material from the columns corresponded to that from the landfill sites not only in its

chemical composition, but also in its microscopic structure. - Independent of the degree of incrustation, the incrustation material always had a similar structure. - At the end of the experiment the permeability of coarse drainage material, especially gravel of grain

size 16 - 32 mm, was hardly affected, while that of finer drainage material, e.g. gravel of grain size 8-16 mm, showed a significant reduction in pore volume.

- Fine and well graded drainage material (2 – 4 mm and 1- 32 mm respectively) suffered almost a

complete loss of permeability. - By the use of highly loaded leachate, the geotextiles placed between compost and the drainage layer

largely lost their permeability.

From the above the following conclusions can be drawn:

- In respect to incrustation formation highly loaded leachate is far more problematical than lightly loaded leachate.

- Under similar conditions coarse drainage materials retain their permeability far longer than finer

drainage materials or the investigated geotextiles. - Since sanitary landfills, at least initially, always produce highly loaded leachate, drainage materials

whose permeability can be seriously affected by incrustation processes are unsuitable.

3.4 Causes of the Incrustation Process The results of the microbiological investigations can be summarized as follows (see RAMKE/BRUNE, 1990): Anaerobic bacteria are responsible for the formation of incrustations in drainage pipes and drainage layer material. This conclusion is based on the following observations:

- Anaerobic microorganisms are present in high concentrations in landfill leachate and readily colonize the surfaces of the drainage system.

- Analysis of the fine structure of the incrustation material shows it to consist of a network of aggregates

of bacteria with deposits of precipitated inorganic material on their surfaces. - On-growth experiments in which glass surfaces and gravel were exposed in the drainage pipes of two

sanitary landfills showed on microscopic examination that the incrustation process is only initiated on the bacterial cells and the slime fibrils which they excrete.

Further precipitation centres around these seeds of incrustation until the whole biofilm becomes filled

with inorganic precipitations. The aggregates of bacteria and the deposited inorganic material can accumulate to the degree already indicated.

- Chemical analysis of the incrustation material shows that its inorganic components consist of calcium,

iron, magnesium and manganese combined with carbonate and sulphur.


Precipitation of the incrustation material is essentially caused by two processes (see Figure 3.8):

- Bacteriogenesis of sulphidic deposits Iron reducing bacteria solubilise Fe(lll) by reducing it to Fe(II), while sulphate reducing bacteria reduce

sulphate, for example gypsum, to sulphide. This bioreduction of sulphate causes the milieu in the vicinity of the sulphate reducing bacteria to

become more alkaline, which results in sulphur precipitating as its insoluble metal sulphide. - Bacteriogenesis of carbonates Before calcium carbonate can be precipitated calcium must first be mobilized from the refuse material.

This is achieved by fermentative organisms producing organic acids which lower the pH of the leachate and thus mobilize the calcium.

Precipitation of calcium carbonate onto the surface of the methane and sulphate reducing bacteria

probably results from their metabolic consumption of hydrogen ions causing a local elevation of pH and consequently disturbing the balance between carbonate and hydrogen carbonate.

Figure 3.8: Schematic representation of processes leading to formation of incrustation material on bacteria

The formation of deposits in the drainage systems of sanitary landfills can thus be considered to take place in two stages:

- Fermentative bacteria together with iron and manganese reducing bacteria give rise to a process of mobilization, whereby a part of the organic component of the refuse is converted into volatile fatty acids (VFA) being dissolved in the leachate.

This leads to a lowering of pH-value and thus causing the increasing dissolution of parts of the

inorganic components of the refuse. In the second stage, the precipitation process, predominantly methane and sulphate reducing bacteria

in the drainage system, through their specific metabolism, cause the formation of insoluble sulphides and carbonates from metal ions dissolved in the leachate.

This is the essential process which leads to incrustations being formed.

Consequently, incrustations can only arise when the landfill leachate contains both easily degradable organic substances (as nutrients for the incrustation forming bacteria) and inorganic ions (calcium, iron, sulphate, hydrogen carbonate etc.) in solution.


3.5 Recommendations for Construction and Operation of Sanitary Landfills The main consequences to be derived from these investigations for site construction and operation of landfills for municipal solid waste are as follows:

1. Incrustation of sanitary landfill drainage systems cannot be completely prevented, but can be greatly reduced by appropriate methods of landfill operation.

2. The material of the drainage layer should be chosen as coarse as possible, in order to provide a

sufficient proportion of pore space and pore diameter (nothing can be said, however, about the filter stability of materials with a grain size greater than 16 - 32 mm).

3. Decisive for the effective life of the drainage system will be to limit the severity of incrustation through

measures involving waste management and landfill operation, thus producing unfavourable conditions for the incrustation forming bacteria.

4. Intensity and duration of the acidic phase of biodegradation needs to be reduced. This can be

achieved either by operational methods which result in a predominantly aerobic degradation of the organic refuse, such as

- mechanical-biological pre-treatment of municipal waste - slower filling of the landfill or by methods of waste management, e.g. - separate collection of organic waste and - subsequent composting.

5. The supply of inorganic incrustation forming substances such as iron and calcium needs to be

reduced. The separate dumping of construction and demolition waste would probably be to good effect.

6. According to the present state of knowledge, it is particularly critical when leachate with a high

incrustation potential (heavily loaded with easily degradable organic substances and a high iron and calcium concentration) coincides with a microflora in the stable methane phase.

For this reason it should be avoided to establish a stable methane phase in the lower waste layers

when in the following the site must filled quickly and an intensive acidic fermentation has to be expected.


4 Hydraulic Calculation of Drainage Systems

4.1 Introduction The hydraulic design of drainage systems both in bottom liner systems and in landfill capping systems requires the determination of the following elements:

- hydraulic conductivity of the material of the drainage layer - thickness of the drainage layer - slope of the drainage layer - drainage length or distance between drains.

The hydraulic calculation of drainage pipes, collection pipes, and detention reservoirs can be done with standard methods of civil engineering and is not covered here. The design criterion of drainage systems is the saturated thickness above the liner. It results from general requirements on the efficiency of drainage systems:

- Drainage systems in bottom liner systems: The saturated zone above the liner should/must not extend into the waste. - Drainage systems in landfill capping systems The saturated zone above the liner should not exceed its thickness.

In both cases the efficiency of the whole liner system is directly determined by the hydraulic pressure of leachate or rainfall percolation above the liner. In addition questions of leaching of waste (bottom) and slope stability (landfills on sloping bottoms and landfill capping systems) have to be considered. Flow of water in a drainage layer can be described like flow of fluids in porous media. In particular the methods of calculating groundwater flow can be used, but the general assumptions and methods have to be adapted to these particular systems. Hydraulic calculations of water flow in a sloping drainage layer normally can be performed in one dimension, using the following assumptions:

- unconfined flow, assuming the drainage layer as a phreatic aquifer - small saturated thickness compared to length of the layer (DUPUIT-assumptions) - homogeneous properties of drainage material - uniform leakage rates - parallel flow.

In some cases two-dimensional calculations in horizontal or vertical planes might be necessary. These particular problems will be touched on at the end of this chapter. Beginning with a brief overview of leachate and rainfall percolation rates the basic equations of flow in sloping drainage layers will be derived, then numerical and analytical solutions will be presented, and finally some examples will be given.

4.2 Leachate and Rainfall Percolation Rates

4.2.1 Leachate Rates at Landfill Bottom

Three cases are to distinguish for determination of leachate rates at landfill bottom: - begin of landfill operation – no cover with waste - operating state of landfill – uncovered surface of waste - end of landfill operation – landfill after restoration.

At the beginning of landfill operation the landfill has no or nearly no storage capacity due the low thickness of waste. Precipitation enters the drainage system directly. Intensity and frequency of precipitation can be estimated accordingly the methodology of urban hydrology. Rainfalls with typical design intensities are short, and the resulting height of leachate in the drainage layer does not exceed some centimetres. Therefore a hydraulic calculation of the drainage layer seems not to be necessary, but other elements of the leachate collection system like drainpipes, collection pipes, and detention reservoirs have to be designed for this loading condition. After landfill restoration leachate generation decreases, compared to the operating state of landfills with uncovered waste. Landfill covers with earth and plants reduce leachate generation caused by precipitation significantly,


liners in landfill capping systems totally. Other components of leachate generation like consolidation, biochemical processes, and reduction of storage capacity by decay processes are of less importance. The operating state of landfills with uncovered waste is relevant to the hydraulic design of bottom leachate collection systems. Long-term tests with lysimeters and the analysis of daily weather and discharge data of five landfills led to the classification of landfills into three groups of discharge behaviour (RAMKE, 1991):

I. landfills with free storage capacity II. landfills with a saturated landfill body III. landfills with leachate recirculation

Leachate discharge of landfills with saturated landfill body and open waste surface is decisive for design purposes. The following rounded leachate discharge rates, derived for Germany, might be useful under the same climatic circumstances for landfills for municipal waste in Middle Europe:

- average leachate rate (67 % - value): 1 mm/d - high leachate rate (99 % - value): 10 mm/d

Hydraulic calculations can be performed with a leachate discharge rate of 10 mm/d, because this value covers most of the cases of practical interest. Using this value for steady state calculations longer periods of higher discharges are covered, too.

4.2.2 Rainfall Percolation Rates in Landfill Capping Systems

The rainfall percolation rate below the restoration layer on top of the drainage layer in a landfill capping system depends next to the climatic conditions and the geometry on three factors:

- plant cover - type of soil of restoration layer - thickness of restoration layer.

Each project requires particular hydrologic calculations, e.g. with the HELP-Model (Hydrologic Evaluation of Landfill Performance), to determine the local percolation rates. The design rate depends on the requirements of slope stability and the resulting acceptable percolation rate. RAMKE, 2002 has calculated exemplary the percolation rate for different types of restoration layers under the climatic conditions of Hamburg, Germany (precipitation: 800 mm) with the HELP-model 3.07D for a period of 10 years with embedded weather data. The standardized conditions of calculation were:

- plant cover: good stand of grass - restoration layer: thickness 1 m - drainage layer: 30 cm, k = 1·10-2 m/s, slope 5 % - liner: geomembranes, no percolation

The resulting daily drainage discharge rates – under these conditions nearly equivalent to the percolation rate – were arranged in ascending order and shown as duration curve of percolation rates. Table 4.1 gives the percolation rates for different frequencies of days with lower percolation rates in dependence on the type of soil.

Table 4.1: Percolation rates for different types of soil of restoration layer (example for Hamburg, Germany)

Frequency of days with lower percolation rates Type of Soil of Restoration Layer

Actual Evapotranspiration [mm/year] 99.00 % 99.73 %

Percolation rates [mm/d] Sand 430 4.8 7.0

Loamy Sand 487 6.3 9.4 Silt 504 6.2 9.9

Clayey Loam 496 4.6 6.4 A comparison of these data with data of lysimeters, test fields and landfills has proven the range and height of the percolation rates (RAMKE, 2002). For the purpose of pre-designs a percolation rate of 10 mm/d is recommended, based on these considerations (GDA, E 2-20, 2003).


4.3 Basic Equations Some efforts were performed in the last two to three decades to describe the flow in a sloping drainage layer. The approaches range from rough calculations over accurate derivations up to highly sophisticated solutions and approximations. A systematic overview is given by RAMKE, 1991. Recent publications will be mentioned in the Chapters 4.5 and 4.7. For the derivation of the basic equation describing the flow in soils above a sloping impermeable bottom or in sloping drainage layers two different assumptions are possible:

- the streamlines are parallel to the slope (first assumption of BOUSSINESQ or extended DUPUIT-FORCHHEIMER assumption) - the streamlines are horizontal (second assumption of BOUSSINESQ or DUPUIT-FORCHHEIMER assumption).

For slopes less than app. 10 % the differences between both solutions can be neglected, but for drainage layers which are components of landfill capping systems and have a lower hydraulic conductivity these differences should be considered. The basic equations shall be developed for steady state conditions under the assumptions made in Chapter 4.1. In addition to these assumptions an impervious liner will be supposed. Therefore no leakage through the liner has to be considered. The assumptions of parallel flow in a homogenous medium will lead to one-dimensional differential equations, which must be solved for the particular boundary conditions. The derivations of the basic equations as well as their solution require an analysis of the shape of the water table, the determination of the zenith of the water table and the definition of the boundary conditions. Figure 4.1 describes the general options of boundary conditions and resulting water table shapes.

Figure 4.1: Shape of water table and boundary conditions

Case 1: Discharge in sloping drainage layer between two drains: zenith between the drains.

Case 2: Discharge on a roof-like shaped bottom liner: zenith at the end of the drainage area (horizontal tangent).

Case 3: Discharge in sloping drainage layer between two drains and/or discharge on a roof-like shaped bottom liner: saturated thickness at the end of drainage area about zero


The basic equations will be developed for the cases 2 and 3. In both cases the inflow into the drainage area over the right border is equal to zero. For the left boundary a boundary condition of the first kind (predefined hydraulic head) is assumed, which means here a predetermined water level in a drain or trench. Case 1 is a special case of case 2. The shape of the water table can be calculated from the left and from the right border, the location of point of zenith must be found by iterations (see e.g. RAMKE, 1991). The definitions for the derivation of the basic equation according to the first assumption of BOUSSINESQ are given by Figure 4.2. The streamlines in the drainage layer are parallel to the bottom of the drainage layer – the liner; the equipotential lines are perpendicular to the slope. For the derivation of the equation a coordinate system parallel and rectangular to the slope is used.

Figure 4.2: Definition sketch for derivation of the drainage formula on a sloping liner according to the first approximation of BOUSSINESQ

In any cross section along the drainage length must be a balance of inflow and outflow under steady state conditions. For the inflow we receive:

( )( )α⋅′Δ−−⋅= cosx'xlvq xnin (4.1) The factor “cos α” results from the conversion of the sloping x’-axis into the horizontal length. The term “Δx’” considers the portion of the water table on the shift against the x-direction: α⋅′=′Δ tanax (4.2) Details are explained in the supplement to Figure 4.2. The discharge is calculated according to DARCY’s law:

xhkaikaqout ′∂∂

⋅⋅′=⋅⋅′= (4.3)

The hydraulic gradient is calculated with the normal definition of the hydraulic potential, which consists of the elevation and the pressure head:


α⋅′+α⋅′=

+=cosasinxh

azh (4.4)

This relationship considers that the lines of equipotential are perpendicular to the sloping liner. Equating the input and output leads to the first basic equation:

( ) ( )( )α⋅α⋅′−′−⋅=

′∂α⋅′+α⋅′∂

⋅⋅′ costanaxlvx

cosasinxka xn (4.5)

After rearranging the equation and dividing by cos α we receive:

( )

αα

−α⋅′

α⋅′+α⋅′−⋅=

′∂′∂

cossin

cosasinacosxl

kv

xa xn (4.6)

with h = hydraulic potential, piezometric head [m] a’ = saturated thickness rectangular to the liner [m] z = elevation head above datum plane [m] x’ = axis parallel to the sloping drainage layer [m] i = hydraulic gradient [-] lx = horizontal drainage length [m] vn = leakage rate, (rainfall) percolation rate [m/s] k = hydraulic conductivity [m/s] qin = input flow into a cross section [m3/(m·s)] qout = output flow out of a cross section [m3/(m·s)] α = angle of slope [°] Equation 4.6 is the first one, often used equation for the description of groundwater flow on an impermeable sloping bottom with groundwater recharge. Figure 4.3 shows the definition scheme for the derivation of the basic equation on base of the second assumption of BOUSSINESQ. Streamlines are horizontal, the equipotential lines are vertical.

Figure 4.3: Definition sketch for derivation of the drainage formula on a sloping liner according to the second approximation of BOUSSINESQ


The condition of continuity requires at any cross section again the equity of discharge for inflow and outflow under steady state conditions.

( )

( )xhktanxhikaq

vxlq

out

nxin

∂∂⋅⋅α⋅−=⋅⋅=

⋅−= (4.7)

We receive:

( ) ( )xhktanxhikavxl nx ∂∂⋅⋅α⋅−=⋅⋅=⋅− (4.8)

Rearranging the variables leads to the second basic equation:

)tanxh(

)xl(kv

xh xn

α⋅−−

⋅=∂∂

(4.9)

with h = hydraulic potential, piezometric head [m] a = saturated thickness above the liner [m] z = elevation head above datum plane [m] x = horizontal axis [m] i = hydraulic gradient [-] lx = horizontal drainage length [m] vn = leakage rate, (rainfall) percolation rate [m/s] k = hydraulic conductivity [m/s] qin = input flow into a cross section [m3/(m·s)] qout = output flow out of a cross section [m3/(m·s)] α = angle of slope [°] In case of α = 0 (horizontal layer) both equations become identical. An analytical solution of these equations is possible, but only some solutions are useful in practice. These solutions will be shown in chapter 4.5 for determination of the maximum saturated thickness above the liner. For the calculation of the course of the water table numerical solutions will be demonstrated, because the analytical solutions are not explicit .

4.4 Numerical Solutions Both equations can be solved numerically as initial value problem. An often used approximation is the RUNGE-KUTTA method. RAMKE, 1991 has described its use for this problem in detail. The specification of the RUNGE-KUTTA method is as follows:

( ) ( ) ( )( )( )( )( )3004

2003

1002

001

432100

kh,xxfxk2/kh,2/xxfxk2/kh,2/xxfxk

h,xfxk

kk2k2k61xhxxh

+Δ+⋅Δ=

+Δ+⋅Δ=

+Δ+⋅Δ=

⋅Δ=

+++⋅+=Δ+

(4.11)


with h(x0) = value of the function at x0 h(x0+Δx) = new value of the function at “x0+Δx” Δx = increment in x-direction k1,2,3,4 = interim values The RUNGE-KUTTA method can be implemented easily in an EXCEL-spreadsheet. Figure 4.4 gives an example (screenshot).

Figure 4.4: Example of an EXCEL-Spreadsheet for numerical calculation of the saturated thickness in a sloping

layer with the RUNGE-KUTTA Method An increment of less than 1 cm is recommended, when leachate recharge is quite low and the hydraulic conductivity is comparative high. The initial value – the height of the water table in the drain or trench – must be adapted to the parameter set. For drainage layers consisting of coarse gravel with a very high hydraulic conductivity an initial value – predetermined water level – of 1 cm is recommended by practical considerations (see RAMKE, 1991). A lower hydraulic conductivity might require a higher initial value in order to avoid a “numerical backwater”, caused by a predefined head too low for the resulting saturated thickness. The optimum can be found by iterations. When the average height of saturated thickness, calculated over the whole drainage length, becomes a minimum the optimal initial value has been chosen. The results of both calculations can be compared directly, if the location of the water table is converted from one system of coordinates into the other point by point. Figure 4.5 shows the necessary relations between the two sets of coordinates. For the conversion from the x’a’-system into the xh-system it can be set:

( ) ( )

( ) α+α⋅Δ−=α+α⋅=+=α⋅α⋅−=α⋅′Δ−=

cos/'asin'x'xcos/'atanxazhcostan'a'xcosx'xx

(4.12)


Figure 4.5: Definition sketch for conversion of coordinates from an inclined to a CARTESIAN system The applicability of the different solutions shall be tested with a set of parameters perhaps typical for drainage systems in landfill capping systems:

- percolation rate vn: 10 mm/d = 1.16·10-7 m/s - hydraulic conductivity k: 10-4 m/s (instead of 10-3 m/s) - horizontal drainage length lx: 30 m

The hydraulic conductivity was chosen to 10-4 m/s instead of 10-3 m/s (which is required in German standards) for better demonstration of differences between the two approximations. The calculations were performed for slope inclinations between 10 % and 33 %. Figure 4.6 shows the saturated thickness in dependence of the distance to the drain. The results of the calculation with the first approximation of Boussinesq were converted from the “x’a’-system” into the “xh(a)-system”. For the lower slope inclination of 10% the maximum of the saturated thickness is about 29 cm, the zenith is in a distance of approximately 5 m to the drain. Both curves are nearly identical. The difference in the maximum of saturated thickness is just 3 mm.

Figure 4.6: Saturated thickness in dependence of distance to drain – Comparison of the BOUSSINESQ-Approximations (k =10-4 m/s, vn = 10 mm/d)

0,00

0,05

0,10

0,15

0,20

0,25

0,30

0,35

0,0 5,0 10,0 15,0 20,0 25,0 30,0

Saturated Thickness [m]

Distance to Drain [m]

tan a = 0,33

1. Approximation

2. Approximation

1. Approximation

2. Approximation

tan a = 0,10


The curves of saturated thickness at a slope inclination of 33 % are shaped differently compared to the shapes at the lower inclination. The maximum saturated thickness is - as a matter of course – reduced to 10 – 11 cm, the zenith is located much closer to the drain (about 1.50 m). The difference between the two approximations is approximately 1 cm, the saturated thickness calculated with the 1. approximation of BOUSSINESQ is the higher one. This is due to the reduced height of the profile of flow when assuming flow to be parallel to the slope. This comparison demonstrates the general appraisement, that there is no relevant difference in the calculations for slopes below 10 %. But even in case of a slope of 33 % and a low hydraulic conductivity 10-4 m/s the difference is in a range with seems to be of low importance compared to the other influences like parameter variability etc. The shape of the water table shall be demonstrated for a bottom liner system using again typical standard parameters:

- leakage rate vn: 10 mm/d = 1.16·10-7 m/s - horizontal drainage length lx: 15 m (roof-like shaped landfill bottom) - cross slope tan α: 3 %

The hydraulic conductivity k was varied between k = 10-2 down to 10-5 m/s. The resulting courses of the water tables in the drainage layers are shown by Fig. 4.7. The saturated thickness is nearly zero at the end of the drainage area in the two examples with higher hydraulic conductivity. In the other two examples there is a horizontal gradient in a distance of 15 m to the drain. The maximum saturated thickness varies between some millimetres up to 1.32 m. The standard system with a hydraulic conductivity of k = 10-3 m/s has a maximum saturated thickness of 4.7 cm and an average saturated thickness of 2.9 cm. A hydraulic dimensioning of a drainage system in a bottom liner system can be omitted, if the standard parameters are kept and the leakage rate of 10 mm/d is not exceeded.

Figure 4.7: Course of water table in a sloping drainage layer in dependence of distance to drain for different hydraulic conductivities (standard leachate collection system at the bottom, vn = 10 mm/d)

4.5 Analytical Solutions Analytical solutions of the basic equations 4.6 and 4.9 are possible, but the resulting formulas do not allow a direct calculation of the height of the water table (eq. 4.9) or of the saturated thickness (eq. 4.6) in dependence of the distance to the drain (x or x’) for given parameters (explicit analytical solution). Only implicit analytical solutions are possible (see MCBEAN ET AL., 1982; MCENROE, 1989, RAMKE, 1991). The relation between h and x or a’ and x’ has to be determined iteratively in this case, and the iteration scheme often shows a difficult convergence behaviour (RAMKE, 1991). Therefore the use of these solutions for the calculation of the course of the water table or the saturated thickness is not very recommendable compared to the

0,00

0,20

0,40

0,60

0,80

1,00

1,20

1,40

1,60

1,80

2,00

0,0 3,0 6,0 9,0 12,0 15,0

Height of Water Table [m]

Distance to Drain [m]

k = 1·10-2 m/s

k = 1·10-5 m/s

k = 1·10-4 m/s

k = 1·10-3 m/s


easiness of the implementation of the RUNGE-KUTTA scheme. But explicit equations for the calculation of the maximum saturated thickness are available. Unfortunately an often quoted formula of MOORE, 1980, for the calculation of the maximum saturated thickness, mentioned in papers of the US EPA, does not work properly. Also a number of approximations were developed, but either the have a limited range of application or they are difficult in use, too. As explicit solutions the approaches of MCENROE, 1993 and GIROUD/HOULIHAN, 1995 and the formulas of SCHMID, 1993, and of LESAFFRE, 1987 for the determination of the maximum saturated thickness should be mentioned. The set of equation of SCHMID, 1993 was developed for the boundary cases 2 and 3 (see Figure 4.1), that means either a horizontal gradient at the end of the drainage area or a saturated thickness about zero. The solution of SCHMID, 1993 complies with the solution of MCENROE, 1993.

Figure 4.8: Definition sketch for the approach of SCHMID, 1993

SCHMID’s set of equations was developed by solving the implicit formula for the condition ∂a’/∂x’ = 0 (gradient parallel to the x’-axis, maximum of saturated thickness). Figure 4.8 explains the particular definitions for the approach of SCHMID, 1993. Three cases of parameter combinations have to be distinguished:

( )

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛

Δ

α−

Δ⋅α⋅

⋅−α⋅⋅

Δ

α⋅⋅=

>α−⋅=Δ

tanarctgtank

v2tankarctgtanexplkv'a

:0tank/v4:ACase

n2

'xn

max

2n

(4.13)

( )

)Numbers'Eurlere(e1l

kv'a

:0tank/v4:BCase

'xn

max

2n

=⋅⋅=

=α−⋅=Δ (4.14)

( )

( )( )

Δ−⋅

α

Δ−−α

Δ−+α⋅

Δ−+α⋅α⋅+⋅−

Δ−−α⋅α⋅+⋅−⋅⋅=

<α−⋅=Δ

2tan

n

n'x

nmax

2n

tantan

tantankv2tantankv2l

kv'a

:0tank/v4:CCase

(4.15)


with a’max = maximum saturated thickness rectangular to the liner [m] lx’ = length of slope parallel to the bottom [m] vn = leakage rate, (rainfall) percolation rate [m/s] k = hydraulic conductivity [m/s] α = angle of slope [°] LESAFFRE, 1987 has developed a very elegant approximation for case 1 (and virtual for case 3) of Figure 4.1, discharge in a sloping drainage layer between two drains on an impermeable liner (see Figure 4.9):

( )2/1

22

nnmax'

's tan1vk

vk4

al

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛α⋅⎟⎟

⎠

⎞⎜⎜⎝

⎛−+

⋅= (4.16)

with a’max = maximum saturated thickness rectangular to the liner [m] ls’ = drain spacing parallel to the slope [m] vn = leakage rate, (rainfall) percolation rate [m/s] k = hydraulic conductivity [m/s] α = angle of slope [°]

Figure 4.9: Definition sketch for the approach of LESAFFRE, 1987 Figure 4.10 summarises a comparison of the two analytical and a numerical solution according to the second approximation of BOUSSINESQ using the RUNGE-KUTTA method. The diagram shows the maximum saturated thickness in dependence of the slope inclination. The calculations were performed with a length of the drainage area of 15 m, a hydraulic conductivity of k = 1·10-4 m/s and a leakage rate of 10 mm/d. It can be seen that there is an excellent correlation between the numerical solution and the analytical solution of SCHMID between a slope inclination from 0 to 10 %. Above the latter value the differences between the solutions according to the first and the second approximation of BOUSSINESQ become noticeable because of the reasons mentioned above. The solution of LESAFFRE is in conformity with the other two solutions above a slope inclination of 7.5 %. This is due to the fact that LESAFFRE considers an uphill drain, which is also dewatering the slope when the drainage layer is partly saturated at the top, too. When the drainage layer near to the uphill drain is nearly unsaturated the uphill drain has no influence, and case 3 of Figure 4.1 is calculated.


Figure 4.10: Maximum saturated thickness in a sloping drainage layer in dependence slope inclination (drainage length 15 m, k = 1·10-4 m/s, vn = 10 mm/d)

This example demonstrates at first the good applicability of the solutions presented here. At second it is shown that it can be necessary also to calculate the shape of the water and not only the maximum of saturated thickness.

4.6 Examples The saturated thickness in leachate collection systems at landfill bottom is calculated with the RUNGE-KUTTA method for varying cross slopes and hydraulic conductivities (Figures 4.11 and 4.12). In both figures the maximum and the average saturated thickness is shown. The standard parameters used in the calculations were

- drain spacing 30 m (drainage length 15 m in each part of a roof-like shaped bottom) - cross slope 3 % - hydraulic conductivity k = 1·10-3

m/s - leachate rate 10 mm/d

Figure 4.11 confirms the necessity of a sufficient cross slope in the bottom drainage system. A reduction of the slope from 3 % to 1 % increases the saturated thickness two to three times and significantly reduces the efficiency of the whole system. But more than the cross slope the long term behaviour of the hydraulic conductivity is of importance. As shown in Figure 4.12 a loss of hydraulic conductivity in the drainage layer from k = 1·10-3 m/s down to k = 1·10-4 m/s – e.g. by clogging – will lead to a maximum saturated thickness of 30 cm instead of 4.7 cm. An extensive loss of hydraulic conductivity would result in an unacceptable height of leachate above the liner in a range of more than 1 m (k = 1·10-5 m/s). This relation testifies the necessity of a thickness of 30 cm of the drainage layer. Such a thickness seems not to be necessary by hydraulic reasons if the hydraulic conductivity is in a range of k = 1·10-3 m/s and the leachate rate is approximately 10 mm/d, but in particular clogging processes can reduce the hydraulic conductivity significantly. Coarse drainage material like gravel 16 – 32 mm has a hydraulic conductivity considerable higher than k = 1·10-3 m/s, which is often the value of the hydraulic conductivity to be kept long-term. But only the combination of the use of such a coarse drainage material (in leachate collection systems), which is comparatively resistant to clogging effects and might ensure an acceptable long-term value of hydraulic conductivity, and the additional inherent safety factor, resulting from the thickness of the drainage layer and the maximum saturated thickness under “design conditions”, can ensure the long-term function of the leachate collection system.


Figure 4.11: Saturated thickness in a drainage layer in dependence of the cross slope (drainage length 15 m, k = 1·10-3 m/s, vn = 10 mm/d)

Figure 4.12: Saturated thickness in a drainage layer in dependence of the hydraulic conductivity (drainage length 15 m, cross slope 3 %, vn = 10 mm/d)

When the hydraulic conductivity is increased to k = 1·10-2 m/s and more, which is more applicable for coarse drainage material, the average saturated thickness is lower than 3 mm. This height is much lower than the diameter of a single grain of coarse drainage material. DARCY’s law, which bases on the assumption of a homogenous porous medium, is not longer applicable under these circumstances. The flow of leachate with a rate of 10 mm/d in such a drainage layer with coarse drainage material can rather be compared with a flow of a thin film of leachate between grain particles. RAMKE, 1991 has shown, that the assumption of DARCIAN flow is justified for hydraulic conductivities equal and lower than k = 1·10-3 m/s, not for higher hydraulic conductivities. But due to the fact, that the application of the equations based on DARCY’s law results in an overestimation of the saturated thickness in coarse drainage material, it seems to be reasonable to use these equations for purposes of comparison.


Two further examples demonstrate the development of the saturated thickness in dependence of the slope inclination and the length of the slope for drainage systems in landfill capping systems. The examples were calculated with a hydraulic conductivity of k = 1·10-3 and 1·10-4 m/s, the rainfall percolation rate was assumed with 5 and 10 mm/d, which covers the range of higher percolation rates. The calculations were performed with the approaches of LESAFFRE and SCHMID. The results are documented in the Figures 4.13 and 4.14. The coordinate system used for the figures is parallel and perpendicular to the slope.

Figure 4.13: Maximum saturated thickness in a drainage layer in dependence of the slope inclination (length of the slope 50 m, k = 1·10-3 and 1·10-4 m/s)

Figure 4.14: Maximum saturated thickness in a drainage layer in dependence of length of the slope (slope inclination 5 %, k = 1·10-3 and 1·10-4 m/s)

0,001

0,010

0,100

1,000

5,0 10,0 15,0 20,0 25,0 30,0 35,0 40,0 45,0 50,0

Length of Slope Parallel to Bottom [m]

Lesaffre, 5 mm/d, 1E-3 m/s Lesaffre, 10 mm/d, 1E-3 m/s


Schmid, 5 mm/d, 1E-3 m/s Schmid,10 mm/d, 1E-3 m/s

Schmid, 5 mm/d, 1E-4 m/s Schmid, 10 mm/d, 1E-4 m/s

Maximum Saturated Thickness a' [ ]

0,00

0,10

0,20

0,30

0,40

0,50

0,60

0,70

0,80

0,90

1,00

0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40Slope Inclination [-]



Schmid, 5 mm/d, 1E-3 m/s Schmid,10 mm/d, 1E-3 m/s

Schmid, 5 mm/d, 1E-4 m/s Schmid, 10 mm/d, 1E-4 m/s

Maximum Saturated Thickness a' [ ]


Figure 4.13 shows the influence of slope inclination on the saturated thickness in a drainage layer with a length of 50 m. The maximum saturated thickness in a “standard system” with a hydraulic conductivity of k = 1·10-3 m/s and a slope inclination of 5 % does not exceed much more than 10 cm, if the percolation rate amounts 10 mm/d. This is much less than the often required thickness of the drainage layer of 30 cm. If the hydraulic conductivity is reduced to k = 1·10-4 m/s it needs a minimum slope inclination of 18 % to ensure that the saturated thickness caused by this percolation rate does not exceed 30 cm. Furthermore Figure 4.13 demonstrates the influence of the drain at the hillside on the saturated thickness. If both calculations show the same result, there is no flow towards the hillside drain. For a hydraulic conductivity of k = 1·10-3 m/s there is no hillside drain necessary even if the slope inclination is just 2 percent. But if the conductivity is limited to k = 1·10-4 m/s flow occurs to the downhill and the uphill drains up to a slope of 6 %. The influence of the length of the slope or the drain spacing is shown by Figure 4.14 (uniform slope inclination 5 %). The maximum saturated thickness does not exceed 10 cm at a length of the slope of 50 m, if the hydraulic conductivity is k = 1·10-3 m/s (vn = 10 mm/d). For a conductivity of k = 1·10-4 m/s the drainage area is limited to 20 m for a percolation rate of 10 mm/d and a allowable maximum saturated thickness of 30 cm.

4.7 Additional Numerical Solutions In most cases of practical importance the hydraulic calculation of drainage systems in bottom liner systems or in landfill capping systems can be performed under the assumption of parallel flow and steady state conditions. This allows the use of the one-dimensional differential equation for the calculation of the saturated thickness in sloping drainage layers presented above. The numerical solution of both the equation according to the first and to the second approximation of BOUSSINESQ is also an excellent base for considering some important influences:

- change of hydraulic conductivity in the direction of flow (drainage pipe gravel casing) - non-DARCIAN flow in coarse drainage material - protective layers (sand) below drainage layers - permeable liners below the drainage layer.

The last case is of special importance for calculations of the efficiency of systems with mineral liners. RAMKE, 1991 has demonstrated the necessary extensions of the basic equations for the issues above and their numerical solutions. Two dimensional calculations in a horizontal plane with methods like finite difference discretization (FID) or finite elements (FEM) can become necessary under the following conditions:

- calculation of the saturated thickness at the toe of the bottom dam in systems with larger longitudinal slope or long drain spacings

- calculation of the consequences of spatial incrustation processes - simulation of preferential flow of leachate - leachate collection systems with trenches of split gravel (see Chapter 5.2).

A two-dimensional hydraulic calculation in a vertical plan with FID or FEM might be of interest in order

- to investigate the influence of incrustations of the drainage material in direct neighbourhood of the drains

- to review the applicability of analytical and one-dimensional numerical solutions, in particular for slopes with high inclinations.

RAMKE, 1991 has tested to the applicability of horizontal and vertical FID-methods for these purposes and exemplarily performed a couple of calculations for the above mentioned problems. The calculation of unsteady flow in drainage systems is of particular importance for drainage layers in landfill capping systems. In particular during the construction period rainfalls of high intensity are an important loading condition for hydraulic calculation due to the missing earth cover of the drainage layer. A steady state assumption for these precipitations of high intensity will result in an overestimate of the saturated thickness, but neglecting this loading condition might result in slope failures. A more realistic calculation has to consider the length of time of the precipitation events next to their intensity. This requires an unsteady state or transient calculation.


Direct analytical solutions of the equations of transient saturated flow in sloping drainage layers are not possible. Some approximations were developed, and ZIMMER ET AL., 1997 present a semi-analytical solution. Considering the general availability of convenient computer programmes for groundwater modelling it seems to be better to use a numerical model. RAMKE, 2002 has shown the influence of an intensive rainfall period (30 mm in three days) on the saturated thickness in a slightly sloping drainage layer (slope inclination 5 %) using a finite difference scheme for the one-dimensional unsteady differential equation. The advantages of an unsteady calculation of this loading case became obvious.

5 Recommendations on Design and Materials

5.1 Standard Design

5.1.1 Introduction

The following is an example of design considerations based on satisfying the current German regulations for municipal solid waste landfills. They relate to above ground landfills with gravity drainage and external leachate collection. Although the specific details may not be relevant to other situations, depending on national regulations and/or site specific conditions, they indicate the general principles and considerations for leachate drainage system design. The proposals in this chapter are to a great extent identical with the design considerations “Leachate Drainage Systems”, first published by the GERMAN GEOTECHNICAL SOCIETY, 1993 in an English version of parts of the Technical Recommendations on Geotechnics of Landfill Design.

5.1.2 Profile and Geometry

The surface of the bottom liner system has to be profiled with longitudinal and cross gradients so as to ensure gravity drainage. Therefore, it is necessary to install drainage pipes at the lowest points of the roof-like shaped bottom liner system. The drainage pipes should be constructed in such a manner that:

- they are rectilinear to landfill edges - they discharge to collection and inspection shafts placed outside of the waste body - they can be permanently inspected, maintained and cleaned.

Pipe joints at the landfill base which cannot be cleaned or inspected must be avoided. The drainage system should satisfy the following criteria, unless it can be proven otherwise:

- maximum drain spacing: ≤ 30 m - maximum length of drainage pipes: ≤ 400 m - longitudinal slope: ≥ 1% (corresponding to the slope of the drainage pipes) - cross slope: ≥ 3 %

The minimum slopes must be kept after fading away of settlements and deformations under the applied loading from the waste body etc. If appropriate, raised profiles should be incorporated, corresponding to the results of settlement and deformation calculations.

5.1.3 Protective Layer

Geomembranes in bottom liner systems will be exposed to mechanical stress due to loading by the waste body and also thermal, chemical and biochemical effects during the construction phase, the operating phase and the post closure period. In particular, the grain size and shape of the drainage material should not damage the geomembrane. Therefore it is necessary to construct a durable and effective protective layer between the geomembrane and the drainage layer.


The protective layer can comprise geotextiles, mineral materials (sand and/or fine gravel) or a combination thereof. The permeability of the protective layer must not be considered as a drainage function. If a mineral protective layer is used, its filter stability (TERZAGHI filter rule) with the drainage layer must be proved. If appropriate a geotextile with a separation function must be chosen. In hydraulic terms, for a gravity system, the thickness of the protective layer can influence the saturated thickness of leachate above the bottom liner. Therefore the protective layer should only be as thick as necessary to provide adequate protection of the geomembrane. Carbonates or calcium cemented materials should not be used. A maximum of 20 % CaCO3 by weight is allowed (calcareous materials can release calcium and carbonates, which could precipitate out and affect the drainage system). The selected materials must be capable of withstanding all mechanical stresses and the physical/chemical and biochemical influences. The quality of material has to be proved. The adequacy of any geotextiles or sand layer, as appropriate, has to be proved in term of its protective function.

5.1.4 Drainage Layer

The following criteria need to be satisfied:

- thickness of drainage layer 0.3 m - gravel or stone (double split) grain size 16 - 32 mm.

In selecting the grading of the drainage blanket, it is the susceptibility to incrustation which is of primary consideration, rather than the "filter stability". German experience to date suggests that there is minimal transport of coarse material in leachate from sites receiving municipal wastes like domestic, commercial and construction waste, and drained sewage sludge. It is important to maintain a permeability value of k greater than 1·10-3 m/s in the drainage layer under operating conditions. Therefore, coarse grained material should be chosen. A material grading which provides high porosity with large pore spaces should be used. The selected materials (gravel or stone) must be solid and have a round surface. A maximum of 0.5 % elutriatable components and a maximum of 20 % grains by weight with a ratio of length: thickness > 3: 1 is allowed. In the case of coarse grained gravel the amount of crushed particles should not exceed 1.0 %. The material qualities have to be proved and should meet the requirements according to Chapter 5.1.3.

5.1.5 Drainage Pipes

Leachate collected and accumulated within the drainage layer is collected in drainage pipes and discharged from the waste body. The drainage pipes are to be installed in the lowest points of the bottom liner system. All drainage pipes should be capable of being inspected, maintained and cleaned. It is recommended that the internal diameter should be 250 mm or greater, although smaller diameters may be acceptable depending on the proposed inspection and cleaning methods/equipment. To encourage leachate access, the maximum possible percentage open area and opening dimensions should be chosen, commensurate with the grain size of the drainage materials. Considering the load requirements of pipes, hole diameters should not be less than 12 mm, wide slots are to prefer. To avoid peak stresses, oblong holes are recommended. It must be ensured that the drainage pipes do not damage the bottom liner system, particularly the geomembrane, under loaded conditions. Vertical penetration of the bottom liner system (e. g. through pipe tunnels) is not acceptable. Horizontal penetrations (e.g. through bottom dams) have to be capable for inspection.


The pipe material chosen must be suitable to withstand all chemical and biochemical attacks by organic or inorganic leachate components. In addition, the expected post-closure physical, chemical and biochemical stresses have to be considered. In the last two decades of modern landfill technology PE-HD pipes have become the standard. The suitability of the drainage pipes, primarily their stability properties, temperature and deformation behaviour, have to be proved.

5.1.6 Inspection and Cleaning Shafts

Where man-access is required, in principle, leachate inspection and cleaning shafts should be located outside the waste body. They must be resistant to leachate and completely waterproof. The shaft cover should be sufficiently large to allow adequate ventilation. Furthermore, comprehensive measurement and examination of the drainage pipes should be possible from the shafts. Therefore, the inner diameter of the shafts should be at least 1.5 m and the manhole should have a diameter of at least I.0 m. No stirrups or similar aids should be placed in the shaft (danger of corrosion and consequently danger of falling). In the case of purpose-designed, non-vented shafts the whole pipe system must be sealed to avoid gas and odour emissions. Furthermore, the outlets of the drainage pipes have to be designed to prevent all gas emissions and the intrusion of air into the drainage system (e.g. by use of siphons). The shafts can be made of reinforced concrete (especially designed for resistance against leachate and landfill gas), synthetic materials or a combination thereof (concrete with a synthetic inliner). Where leachate monitoring/pumping shafts are located within the waste body, special consideration must be given to their structural stability, particularly in terms of deformation of the surrounding waste body, and excessive foundation loading on the bottom liner caused by negative skin friction.

5.2 Alternative Design with Secondary Drains To increase the effectiveness of the drainage system, in addition to the drainage layer, secondary high permeability stone drains can be installed on a herringbone pattern, feeding into the drainage pipes (see Figure 5.1). The secondary drains may be designed as trenches within the linear system profile. Under such circumstances, special consideration needs to be given to the practicality of installing and ensuring the quality of the geomembrane. The following dimensions and parameters are recommended for the secondary drains (see also Figure 5.1):

- width of the secondary stone drain 2.5 m - height > 1.0 m - drain spacing 15 – 20 m - angle of drainage pipes to secondary drains according to the slope line

(example: cross slope 1 %, longitudinal slope 3 %, α = 18,5 %) - drainage material: coarse-grained material, e. g. 32-150 mm.

The secondary drainage material must have a significant higher long-term hydraulic conductivity under operating conditions than the drainage layer (k > 10-2 m/s). This system is of special interest in case of no or low availability of coarse drainage material, especially washed gravel (RAMKE, 2005). In this case the combination of a drainage layer, consisting of coarse sand/fine gravel, and trenches of split gravel/stones, can improve the efficiency and the life span of the leachate collection system significantly.


Figure 5.1: Leachate Collection System with Secondary Drains

References BRUNE, M., 1991: Ursachen für die Bildung fester und schlammiger Sedimente in Entwässerungssystemen von

Hausmülldeponien, Dissertation, Naturwissenschaftliche Fakultät, Technische Universität Braunschweig BRUNE, M.; RAMKE, H.-G.; COLLINS, H.-J.; HANERT, H. H., 1991: Incrustation Processes in Drainage Systems of Sanitary Landfills

in: Sardinia 91: Third International Landfill Symposium, Cagliari CISA - Environmental Sanitary Engineering Centre, Cagliari, Italy

DIN 19667, 1991: Dränung von Deponien Technische Regeln für Bemessung, Bauausführung und Betrieb GDA-EMPFEHLUNG E 2-14, 1997: Design Principles for Leachate Collection Systems in Bottom Liner Systems Technical Recommendations of the Technical Committee on Geotechnics of Landfills (Entwurfsgrundsätze zu Basis-Entwässerungssystemen für Siedlungsabfalldeponien) GDA-Empfehlungen Geotechnik der Deponien und Altlasten, 3. Auflage herausgegeben von der Deutschen Gesellschaft für Geotechnik e.V. (DGGT) Verlag Ernst & Sohn, Berlin GDA-EMPFEHLUNG E 2-20, 2003: Drainage Layers in Landfill Capping Systems (Entwässerungsschichten in Oberflächenabdichtungssystemen) Technical Recommendations of the Technical Committee on Geotechnics of Landfills GDA-Empfehlungen Geotechnik der Deponien und Altlasten Deutsche Gesellschaft für Geotechnik e.V. (DGGT), Die Bautechnik, Heft 9 GERMAN GEOTECHNICAL SOCIETY, 1993: Geotechnics of Landfill Design and Remedial works

- Technical Recommendations – GLR, second edition Edited by the German Geotechnical Society for the International Society of soil Mechanics and Foundation Engineering GIROUD, J.P.; HOULIHAN, M.F., 1995: Design of Leachate Collection Layers In: Sardinia 95, Fifth International Landfill Symposium CISA, Environmental Sanitary Engineering Centre, Cagliari, Italy


LESAFFRE, B., 1987: Analytical Formulae for Travers Drainage of Sloping Lands with Constant Rainfall Irrigation and Drainage Systems, Vol. I, No. 2 McBean, E.A.; Poland, R., Rovers, F.A.; Crutcher, A.J., 1982: Leachate Collection Design for Containment Landfills Journal of the Environmental Engineering Division, ASCE, No. EE 1 MCENROE, B., 1989 : Hydraulics of Leachate Collection and Cover Drainage In: Landfill Concepts, Environmental Aspects, Lining Technology, Leachate Management, Industrial Waste and Combustion Residues Disposal 2nd International Symposium, Porto Conte ISWA - Italian Section, Milano Academic Press, London, San Diego MCENROE, B., 1993: Maximum Saturated Depth over Landfill Liner Journal of Environmental Engineering, Vol. 119, No. 2 MOORE, C.A., 1980: Landfill and Surface Impoundment Performance Evaluation Manual United States Environmental Protection Agency Office of Water and Waste Management, Washington DC, EPA/560/SW-869c RAMKE, H.-G., 1987: Leachate Collection Systems of Sanitary Landfills

in: Sanitary Landfilling: Process, Technology and Environmental Impact, International Symposium, ISWA - Italian Section, Cagliari, Academic Press, London, San Diego

RAMKE, H.-G.; BRUNE, M., 1990:

Integrity and Failure Mechanisms of Drainage Layers in Bottom Liner Systems, Final Research Report (Untersuchung zur Funktionsfähigkeit von Entwässerungsschichten in Deponiebasisabdichtungssystemen, Abschlußbericht), Bundesminister für Forschung und Technologie, FKZ 14504573

RAMKE, H.-G., 1991: Hydraulic Assessment and Calculation of Leachate Collection Systems of Sanitary Landfills - Water

Balances, Hydraulic Characteristics and Methods of Calculation - Ph.D. thesis (Hydraulische Beurteilung und Dimensionierung der Basisentwässerung von Deponien fester Siedlungsabfälle -

Wasserhaushalt, hydraulische Kennwerte, Berechnungsverfahren – Dissertation) Mitteilungen aus dem Leichtweiss-Institut für Wasserbau, Heft 114, Technische Universität Braunschweig RAMKE, H.-G., 1998: Leachate Collection and Discharge (Sickerwassersammlung und –ableitung) in: Handbuch der Müll- und Abfallbeseitigung, Kennziffer 4545, Erich Schmidt Verlag, Berlin RAMKE, H.-G., 2002: Collection of Surface Runoff and Drainage of Landfill Capping Systems (Oberflächenwassersammlung und –ableitung) in: Handbuch der Müll- und Abfallbeseitigung, Kennziffer 4542, Erich Schmidt Verlag, Berlin RAMKE, H.-G., 2005: Specific Requirements on Landfill Technology under Arid Climates in Developing Countries and Newly

Industrialising Countries (Besondere Anforderungen an die Deponietechnik unter ariden Klimabedingungen in Entwicklungs- und Schwellenländern

– Erfahrungen bei der Planung der Deponie Teheran) in: Klappperich, H.; Katzenbach, R.; Witt, K. J. (HRSG.), 2005: 2. Symposium Umweltgeotechnik, CiF e.V. publication 3,

Freiberg SCHMID, B.H., 1993: Die maximale Wassertiefe über gleichmäßig beaufschlagten, geneigten Dichtungshorizonten Wasser und Boden, Heft 9 ZIMMER, D.; HARTANI, T.; LESAFFRE, B, 1997:

Transient Saturated Flow Euqations for sloping Drainage Systems in: Sardinia 97: Sixth International Landfill Symposium, Cagliari, CISA - Environmental Sanitary Engineering Centre, Cagliari, Italy

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