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Adopting unsaturated flow properties in thedesign of earthen dams: An integrated designapproach taking into account hydrologic andgeotechnical events

CONFERENCE PAPER · APRIL 2005DOI: 10.13140/2.1.3927.2329

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Mahmoud Al-Riffai

University of Ottawa

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ADOPTING UNSATURATED FLOW PROPERTIES IN THE DESIGN OFEARTHEN DAMS: AN INTEGRATED DESIGN APPROACH TAKING INTOACCOUNT HYDROLOGIC AND GEOTECHNICAL EVENTS M. Al-RiffaiDepartment of Civil Engineering, University of Ottawa,Ottawa, Ontario, Canada, K1N 6N5

ABSTRACT

In the field of geotechnical engineering, the degree of saturation is a critical parameter since its effect on pore pressures cansignificantly influence the slope stability of an earthen dam. In the event of a high intensity storm, quasi-saturated soilconditions in the downstream slope will result in an increase in the local soil coefficient of permeability. In addition, it is likelyother activities such as piping may also have further adverse affects. This paper investigates the different methods forachieving unsaturated conditions and maintaining them in earth retaining structures. Furthermore, constitutive relationshipsthat exist between the unsaturated coefficient of permeability and other soil parameters such as soil material, soil layerthickness, poresize and water content are investigated using an integrated approach taking into account hydrologic andgeotechnical events.

RÉSUMÉ

Dans le monde géotechnique, le degré de saturation est un paramètre critique puisque son effet sur la pression de pore peutminer la stabilité de pente d'un barrage de terre. En cas d'une averse de pluie intense, des conditions de sols quasi-saturésdans le bas de la pente peuvent amplifier la perméabilité locale du sol. La canalisation naturelle peut aussi avoir davantaged’effets défavorables. Cet article étudie les différentes méthodes pour réaliser des conditions insaturées ainsi que sonapplication aux barrages de terre. Tandis que la connaissance des rapports constitutifs existe entre la conductivitéhydraulique et les paramètres de conception (c.-à-d. matériel de sol, épaisseur de couche, pore-taille et teneur en eau) uneanalyse intégrée est nécessaire pour définir les variables de commande.

1. INTRODUCTION

Dam embankments have provided a benefit to humansocieties by means of generating power, regulating floodsand water storage in times of drought. Yet over the last 70

years, records of dam failures throughout the globe showthat about 138 dams have failed (Foster et al. 2000). Thisfigure accounts for 1.2% of the dams built and does notinclude the dams that have failed in China and Japan pre-1930. Dam failure can be disastrous to the very humancommunities they serve. Floods produced as a result of therelease of large amounts of stored water can be perilous tolocal communities and environments. A burst dike along theYangtze River in 1998 resulted in a flash flood, killingthousands of people and leaving millions homeless! (BBC,1998).

The outflow hydrograph emanating from the flood ischaracterized by a rising limb, a peak discharge andrecessing limb. The time to peak and peak discharge is

greatly a function of the erodibility of the dam and thebreach location (Figure 1). As more water is released fromthe reservoir, soil material along the breach channel erodesallowing a larger quantity of water to flow. Although theareas under both graphs (reservoir volume) are the same,the attenuation to the hydrograph for the soil with a lowerodibility decreases the peak discharge and increased thepeak time. Such flood characteristics are more favorablethan those attained by a soil with high erodibility since moretime is available for the evacuations of local communities. Italso decreases the hazard potential of the flood. It is to the

interest of the designer and flood hydrologist to maximizethe unsaturated zone within an earthen embankment sincematric suction increases the cohesive forces between soilparticles, consequently increasing the shear strength.

This paper examines the different factors that may prolongand expand the unsaturated zone under hydrologic andgeotechnical and events. Nowadays, with the surge ofvarious Finite Element Applications, it is possible toincorporate the different failure methods of an earthenembankment by integrating such causable events within theboundary conditions of a preliminary embankment design. Itis also necessary to develop the collective approach withrespect to the selection of the different elements affectingthe design of dam embankments. In order to do so, onemust first consider which soil materials will be used as thecontrol variable (Xu et al., 2003) for achieving optimalhydraulic properties. This can be achieved by initiallydefining the hydrologic and geotechnical factors that arelikely to be exerted during the lifetime of the earth

embankment.

2. BREACHING MECHANISMS

Whether seepage in the form of piping will prevail over astability collapse due to excessive precipitation (orsignificant seismic activity) or from erosion occurring fromovertopping, it is possible that more than one event willresult in dam breaching.

https://www.researchgate.net/publication/237370682_Statistics_of_embankment_dam_failures_and_accidents?el=1_x_8&enrichId=rgreq-d9a16337-fa65-40fe-ad18-1497821bd36c&enrichSource=Y292ZXJQYWdlOzI2NTAxNDgyNztBUzoxMzQyNzE1NTM1MTE0MjRAMTQwOTAyNDI0MTY5NQ==https://www.researchgate.net/publication/237370682_Statistics_of_embankment_dam_failures_and_accidents?el=1_x_8&enrichId=rgreq-d9a16337-fa65-40fe-ad18-1497821bd36c&enrichSource=Y292ZXJQYWdlOzI2NTAxNDgyNztBUzoxMzQyNzE1NTM1MTE0MjRAMTQwOTAyNDI0MTY5NQ==

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Figure 1. Flood Hydrograph as a result of dam breach.

2.1 Piping

Piping accounts for 43% of dam failures (Table 1), andoccurs when the homogeneity of the soil in the upstreamside of the embankment is disrupted by seepage of waterthrough propagating voids below the phreatic surface of theembankment. The continuous void eventually reaches thedownstream side of the embankment and may vary inappearance from a ”soft” wet area to a flowing “spring”(Ohio Department of Natural Resources, 1994). It istherefore necessary to thoroughly compact theembankment during its construction. There are on the otherhand, other factors that are not within human control, suchas burrowing activity by local fauna and lead to pipingerosion. Onda and Itakura, 1997, found that river crabs areable to excavate their burrows in cohesive soils, burrowinginto and below the ground water table (i.e. below thephreatic surface in an embankment dam) in a “J” shapewithin hydraulic gradients ranging between 0.21 and 0.25.

Approximately two thirds of piping failures occur during theinitial filling phase of the dam up to the first 5 years ofoperation (Fell et al., 2003). Although not fully understood,

the piping phenomenon has been defined by someresearchers (Foster et al., 2002, and Craig, 2004) to be offour types (the first two types are illustrated in Figure 2):

Backward erosion piping: where erosion originatesat the downstream toe of the embankment andworks it way upstream towards the reservoir.

Concentrated leak piping: where a crackoriginating from the water source to the exit pointcauses erosion to advance in the direction ofdecreasing head.

Suffusion: this occurs as a result of fine soilmigrating downstream as a result of high porewater pressures (PWP) destabilizing the hydraulicgradient of the seepage path.

Blowout: this occurs as the high PWP in thedownstream foundation of the dam diminish theeffective stress condition, and is usually followedby backward erosion.

The material in dam embankments therefore, should becoarse grained since it will yield the least consolidationsettlement and minimum burrowing conditions.

2.2 Overtopping

Overtopping accounts for approximately 45% of damfailures (Table 1) and occurs when the head water heightexceeds that of the dam crest. This may be due to storms ofhigh intensity where the filling rate of the reservoir is higherthan rate of release from the spillways or gates or simplydue to a malfunction in the spillway gates. Overtopping iscaused primarily as a result of but not limited to rainfall.Head levels in a reservoir can increase from broken utilitylines, utility trenches, street upgrades, permeable layers,

gravel packed subdrains (Croney et al. 1958). Singh, 1996,identifies the flow above the dam into three regimes (Figure3):

Zone 1: The flow depth is above critical(subcritical) and pertains to a low energy level (thedatum being the crest elevation). The low hydraulicforces attributed to the subcritical flow induce smalltractive forces on the bed material and erosion willtake place in highly erodible materials for thislocality.

https://www.researchgate.net/publication/237370678_A_method_for_assessing_the_relative_likelihood_of_failure_of_embankment_dams_by_piping_Reply?el=1_x_8&enrichId=rgreq-d9a16337-fa65-40fe-ad18-1497821bd36c&enrichSource=Y292ZXJQYWdlOzI2NTAxNDgyNztBUzoxMzQyNzE1NTM1MTE0MjRAMTQwOTAyNDI0MTY5NQ==https://www.researchgate.net/publication/237370678_A_method_for_assessing_the_relative_likelihood_of_failure_of_embankment_dams_by_piping_Reply?el=1_x_8&enrichId=rgreq-d9a16337-fa65-40fe-ad18-1497821bd36c&enrichSource=Y292ZXJQYWdlOzI2NTAxNDgyNztBUzoxMzQyNzE1NTM1MTE0MjRAMTQwOTAyNDI0MTY5NQ==

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Zone 2: In this region the water profile experiencesa drawdown effect where the flow depth is belowcritical (supercritical) and pertains to a low energylevel since the there is no change in elevation. Thehigh hydraulic forces have little impact on bedmaterial erosion due to the limited distance overwhich they are exposed to.

Zone 3: In this region, flow is supercritical (withFroude No. > 1) and pertains to a high energylevel. The high hydraulic forces generated willinduce significant erosion to the bed material.Erosion can also be induced if a hydraulic jumpoccurs along the downstream slope leading tomomentous scour in the locality. However, erosioncan be initiated anywhere regardless whether thehydraulic jump occurs or not. It is first initiated by asmall overfall in the downstream slope through thedevelopment of a scour hole. The propagation ofthe dug channel in the downstream face of theembankment then erodes downward and upstreamwhere the channel length is increased such asthere is a continuous flow from the reservoir to thedownstream slope (Figures 4 and 5).

2.3 Slope Instability

Slope failures account for 7% of dam failures (Table 1) andoccur in two regions; upstream and downstream side of theembankment. Their occurrence is due to the high porewater pressures (i.e. low effective stress) that reduce thefactor of safety to a value less than one. While liquefactionmay not directly cause slope instability, yet a suddenincrease in pore pressures as a result of seismic activities

may render the instability more catastrophic (Eckersley,1985).

2.3.1 Upstream

Upstream slope failures are a result of rapid drawdown ofthe reservoir head mainly due to breach in another location

upstream of the reservoir. During this phenomenon theresidual high PWP and are no longer confined by thehydrostatic forces that used to exist on the saturatedupstream slope of the embankment. This failure method isattributed to clayey banks where the release of the highPWP occurs over a very large period of time, due to lowhydraulic conductivities in fine soils.

2.3.2 Downstream

Downstream slope failures occur due to reduced shearstrength along a failure slip surface. They are especiallypredominant during meteorological events such as stormsor by frozen soil surcharge. A study by Crosta and di Prisco,1999, showed that “tunnel scouring” (a process by which

water seeps through the soil surface, increasing localrecharge) is a factor that can be combined with hydrologicand geotechnical events to cause downstream slope failure.Different mechanisms of tunnel scouring (Figure 6) areattributed to drying shrinkage, human activity (such asincision from large wheeled off-road vehicles), biogenicfactors (such as rodents) and seepage erosion (such aspiping). Such point sources (representing surface erosion)increase the recharge in the soil, eventually increasing theelevation of the ground water table (GWT) and leading toslope failure (Figure 7 and 8).

Table 1. Dam embankment failures up to 1986 excluding dams constructed in Japan pre-1930 and China (afterFoster et al. 2000).

Mode of Failure No. of Cases % Failures Average Frequency (%)Overtopping

Overtopping 46 33.1 0.41Spillway-Gate 16 11.5 0.14

Total Overtopping 62 44.6 0.55

PipingThrough Embankment 39 28.1 0.35

Through Foundation 19 13.7 0.17From Embankment into Foundation 2 1.4 0.02

Total Piping 60 43.2 0.54

SlidesDownstream 6 4.3 0.05

Upstream 1 0.7 0.01Earthquake-Liquefaction 2 1.4 0.02Total Slides 9 6.5 0.08

Total Unknown Mode 8 5.8 0.07

Total Failures 139

No. of Embankment Dams 11,192

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Figure 2. Model for development of failure by piping (a) backward erosion, and (b) concentrated leak (after Foster and Fell,1999)

Figure 3. Hydraulic flow regimes and erosion zones duringovertopping (afterPowledge et al., 1989). Figure 4. Idealized breach profile for earth dams (after

Singh, 1996).

Figure 5. Downstream face longitudinal slope growth (afterFread, 1988).

https://www.researchgate.net/publication/245295928_Mechanics_of_Overflow_Erosion_on_Embankments_II_Hydraulic_and_Design_Considerations?el=1_x_8&enrichId=rgreq-d9a16337-fa65-40fe-ad18-1497821bd36c&enrichSource=Y292ZXJQYWdlOzI2NTAxNDgyNztBUzoxMzQyNzE1NTM1MTE0MjRAMTQwOTAyNDI0MTY5NQ==https://www.researchgate.net/publication/245588971_BREACH_An_erosion_model_for_earthen_dam_failures?el=1_x_8&enrichId=rgreq-d9a16337-fa65-40fe-ad18-1497821bd36c&enrichSource=Y292ZXJQYWdlOzI2NTAxNDgyNztBUzoxMzQyNzE1NTM1MTE0MjRAMTQwOTAyNDI0MTY5NQ==https://www.researchgate.net/publication/245588971_BREACH_An_erosion_model_for_earthen_dam_failures?el=1_x_8&enrichId=rgreq-d9a16337-fa65-40fe-ad18-1497821bd36c&enrichSource=Y292ZXJQYWdlOzI2NTAxNDgyNztBUzoxMzQyNzE1NTM1MTE0MjRAMTQwOTAyNDI0MTY5NQ==https://www.researchgate.net/publication/245295928_Mechanics_of_Overflow_Erosion_on_Embankments_II_Hydraulic_and_Design_Considerations?el=1_x_8&enrichId=rgreq-d9a16337-fa65-40fe-ad18-1497821bd36c&enrichSource=Y292ZXJQYWdlOzI2NTAxNDgyNztBUzoxMzQyNzE1NTM1MTE0MjRAMTQwOTAyNDI0MTY5NQ==https://www.researchgate.net/publication/245588971_BREACH_An_erosion_model_for_earthen_dam_failures?el=1_x_8&enrichId=rgreq-d9a16337-fa65-40fe-ad18-1497821bd36c&enrichSource=Y292ZXJQYWdlOzI2NTAxNDgyNztBUzoxMzQyNzE1NTM1MTE0MjRAMTQwOTAyNDI0MTY5NQ==

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Figure 8. Evolution of the saturated domain with time withinthe slope as obtained by numerical modeling (a) 1 month(b) 5 months after deep incisions were made (after Costaand di Prisco, 1999).

3. UNSATURATED FLOW: SOIL WATERCHARACTERSTIC CURVE (SWCC)

The higher matric suction is the potential driving energy intransporting flow in unsaturated soil conditions (Karube andKawai, 2001). Several researchers have developed modelsfor describing the Soil Water Characteristic Curve (SWCC)and flow behavior and in unsaturated soils. The SWCCequation suggested by Fredlund and Xing, 1994, gives thebest fit among all other equations (Leong and Rahardjo,1997) developed as well as having a minimum number ofparameter constants and low sensitivity (especially at lowsuction ranges). The sigmoid curve describing thedesorption SWCC (Figure 9) is as follows:

mb

sw

ae

C

ln

)( [1]

Where:

θw = volumetric water content;θ s = saturated water content;Ψ = suction pressure (kPa);e = natural base of logarithms;a = suction related to air entry value of the soil;n = parameter that controls the slope at the

inflection point in the SWCC;

Note: The inflection point or air entry value corresponds tothe matric suction where the ratio of the change in watercontent with respect to the change in matric suction ishighest.

m = parameter that is related to the residual watercontent, θ r ; and

C(Ψ) is a correction factor (equal to unity at low suctionranges) and can be defined as:

r

r C

000,000,1

1ln

1ln

1 [2]

Where:

Ψ r = constant related to the matric suction (kPa)corresponding to the residual water content, θ r .

A typical value is about 1500 kPa (Fredlund et al., 1994). Toobtain the parameters a, n and m, experimental data shouldbe used beyond the value θ r .

Figure 9. Typical soil-water characteristic curve for a siltysoil (after Fredlund and Xing, 1994).

3.1 Unsaturated Hydraulic Conductivity

As defined by Karube and Kawai, 2001, as the suction inthe soil is increased due to the migration of pore water(caused by a potential difference in matric suction), the"bulk water begins to drain away". Researchers such asDexter, 2004, have developed empirical formulations thatdetermine the unsaturated hydraulic conductivity at theinflection point based on the desaturation parameter, S(slope at inflection point) and hi (matric suction) as follows:

[3]

Or;

[4]

https://www.researchgate.net/publication/223338370_Soil_physical_quality_Part_III_Unsaturated_hydraulic_Conductivity_and_general_conclusions_about_S-theory?el=1_x_8&enrichId=rgreq-d9a16337-fa65-40fe-ad18-1497821bd36c&enrichSource=Y292ZXJQYWdlOzI2NTAxNDgyNztBUzoxMzQyNzE1NTM1MTE0MjRAMTQwOTAyNDI0MTY5NQ==https://www.researchgate.net/publication/223338370_Soil_physical_quality_Part_III_Unsaturated_hydraulic_Conductivity_and_general_conclusions_about_S-theory?el=1_x_8&enrichId=rgreq-d9a16337-fa65-40fe-ad18-1497821bd36c&enrichSource=Y292ZXJQYWdlOzI2NTAxNDgyNztBUzoxMzQyNzE1NTM1MTE0MjRAMTQwOTAyNDI0MTY5NQ==

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Models by Van Genuchten-Mualem, Brooks-Corey-Burdineas well as Fredlund et al. , 1994, were analyzed by Meerdinket al., 1996 and Chiu and Shackelford, 1998. Resultsshowed that there is a tendency to underestimate theunsaturated hydraulic conductivity by several orders ofmagnitude for compacted clays using the above models.Meerdink et al., 1996, therefore notes to designers the poor

selection of parameters describing unsaturated flow maysignificantly affect the unsaturated hydraulic conductivityprediction of a soil in numerical analyses.

Figure 10 shows the hydraulic conductivity of three soilseach with a different pore size. As pore size increases, thesaturated hydraulic conductivity increases. However, forunsaturated soils, especially at high suction the reverse istrue. At high matric suctions, the larger pores empty firstunder drying, and fill last under wetting. Therefore, the largepores in dry of optimum soils become hydraulically inactiveat high suctions and greatly reduce the tortuousity of thewater flow path (Meerdink et al., 1996).

Figure 10. Hydraulic conductivity versus negative porewater pressure head for gravel, sand and soil (afterStormont, 1995)

3.2 Hysteresis

As shown in Figure 11, the adsorption curve is lower than

the desorption curve. During the wetting (adsorption)process, occluded air bubbles render the soil at lowersaturation degrees in comparison to the drying phase underthe same matric suction. Therefore, this lower degree ofsaturation causes a more tortuous path for water to flow,hence a lower permeability (Figure 12). As the soilcontinues to saturate, matric suction is reduced, however,the maximum water content (at zero suction) is less thanthe initial value before desorption. The difference betweenthe initial water content before desorption and maximum

water content during adsorption is the residual air content,and corresponds to the occluded air bubbles.

Figure 11. SWCC showing hysteresis effect due toadsorption and desorption (after Fredlund and Xing, 1994).

Figure 12. Hysteresis in unsaturated hydraulic conductivityin Wenatchee silty clay (after Meerdink et al., 1996)

Since data for permeability and degree of saturation withrespect to matric suction are carried out during the dryingstage due to ease of measurement, the predictedunsaturated hydraulic conductivity of a soil undergoingwetting (e.g. during a rainfall event) will provide aconservative design.

4. DAM EMBANKMENT DESIGNCONSIDERATIONS

4.1 Piping

Apart from burrowing activity and surface erosion, pipingmay also occur as a result of cracks introduced in to theembankment during the process of settling. Regardless ofhow it is caused, it can be hindered by decreasing thetortuousity of the voids within the embankment. This can beachieved by constructing the dam with a central core of low

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permeability (Figure 13a). This means that the embankmentis no longer of a homogenous soil and will increase thecomplexity of the analysis of the internal flow nets.Furthermore, this may be particularly dangerous due to therelatively large hydraulic gradients from the core to theadjacent soil (Craig, 2004) hence causing internal erosion.

4.1.1 DrainageIn clay core embankments, pore pressures are higher thanpredicted due to the choking effect that occurs when finematerial is eroded within cracks and transported andtrapped in the upstream face of the filter creating a“relatively impervious skin” (Sherard, 1984). The high porepressures on the downstream side of the core will result inhigher exit gradients which can lead to serious erosion(LeBihan and Leroueil, 2002). Solving this problem can becarried out by installing a “chimney” drain on thedownstream side of the central core (Figure 13a), and byintercepting the seepage path of the flow line this willmaintain the downstream slope of the embankment inunsaturated conditions (Craig, 2004). The unsaturatedconditions in the downstream slope will increase soil suctionand decrease the local hydraulic conductivity whileincreasing the shear strength. Both are favorable conditionsregarding earthen dam design.

Craig, 2004, also suggests methods for eliminating orreducing under seepage by elongating the flow pathbeneath the embankment. A “grout curtain” may be installedbelow the central core when the foundation material ishigher in permeability than the embankment. It is unclear,however, whether the equivalent permeability of the dam orthat of the coarser material should be considered. Anothermethod aimed at increasing the seepage path in thefoundation and reducing under seepage is by incorporatingan impervious upstream blanket above the foundation of thedam (Figure 13b).

Figure 13. (a) Central core and chimney drain, and (b) groutcurtain (after Craig, 2004)

Since piping occurs as internal erosion along a path ofhighest hydraulic conductivity, it will be unlikely for theseepage to propagate along an unsaturated soil medium.

Assuming the seepage is conveyed from the upstreamtowards the downstream slope, it will tend to deviatedownwards with the phreatic surface. Therefore,maximizing the area of unsaturated zone by the use ofcoarse grained filters as described above is necessary.However, the pore sizes of the filter material must be smallenough to prevent the transport of the erodible soils

(Cedergren, 1989). Studies by Bertram, 1940, have shownthat two criteria must be satisfied for a conservative filterdesign:

D15 ) f /D85 )s < 4 to 5 [5]

and;

D15 ) f /D15 )s < 4 to 5 [6]

Where D15 ) f is the diameter of the 15% finer for the filterparticles, D85 ) s is the diameter of the 85% finer for the soilparticles and D15 )s is the diameter of the 15% finer for thesoil particles. Criterion one is also known as the “pipingratio”.

Note: The U.S. Department of the Army, Corps ofEngineers, 1986, states that the second criterion translatesinto the following expression:

D50)f /D50)s 25 [7]

Where D50 ) f and D50 )s is the diameter of the 50% finer forthe filter and soil particles respectively, and that the filterparticles would 25 times more permeable than the soilparticles. However, Army Corps of Engineers, 1986, alsomention that the second criterion is valid for soils with agradation curve parallel to that of the filter material, and thatfurther filtration tests must be carried out to determine thefilter size particles (Cedergren, 1989). For example, with CLand CH clays, filter particle size can be up to 0.4 mm.

Other methods can be carried out to increase theunsaturated zone within the downstream slope and will bediscussed herein this paper. Heed must be taken in order tonot to significantly desaturate the downstream slope, sincethis could lead to cracks due to drying shrinkage(Cedergren, 1989).

4.1.2 Compaction

An important factor that must be considered in the design ofearthen dams is Compaction. As void ratio is reduced, poresize is reduced, causing a higher capillary tension in the soil

(Karube and Kawai, 2001). Results by Meerdink et al.,1996, have showed that a lowered hydraulic conductivity ismore sensitive to the compactive effort rather than moldingwater content (i.e. wet of optimum or dry of optimum). In thecase where the dam embankment is non-homogenous (i.e.contains a clay core), maximizing the matric suction andconsequently reducing the hydraulic conductivity of the claycore is still a concern. It is first necessary to identify thephreatic surface in the cross-sectional domain in order tocompact the soil corresponding to the saturated-unsaturated zones. However, the phreatic surface is

https://www.researchgate.net/publication/237371217_A_model_for_gas_and_water_flow_through_the_core_of_earth_dams?el=1_x_8&enrichId=rgreq-d9a16337-fa65-40fe-ad18-1497821bd36c&enrichSource=Y292ZXJQYWdlOzI2NTAxNDgyNztBUzoxMzQyNzE1NTM1MTE0MjRAMTQwOTAyNDI0MTY5NQ==https://www.researchgate.net/publication/225904409_The_role_of_pore_water_in_the_mechanical_behavior_of_unsaturated_soils_Geotech_Geol_Eng?el=1_x_8&enrichId=rgreq-d9a16337-fa65-40fe-ad18-1497821bd36c&enrichSource=Y292ZXJQYWdlOzI2NTAxNDgyNztBUzoxMzQyNzE1NTM1MTE0MjRAMTQwOTAyNDI0MTY5NQ==https://www.researchgate.net/publication/237371217_A_model_for_gas_and_water_flow_through_the_core_of_earth_dams?el=1_x_8&enrichId=rgreq-d9a16337-fa65-40fe-ad18-1497821bd36c&enrichSource=Y292ZXJQYWdlOzI2NTAxNDgyNztBUzoxMzQyNzE1NTM1MTE0MjRAMTQwOTAyNDI0MTY5NQ==https://www.researchgate.net/publication/225904409_The_role_of_pore_water_in_the_mechanical_behavior_of_unsaturated_soils_Geotech_Geol_Eng?el=1_x_8&enrichId=rgreq-d9a16337-fa65-40fe-ad18-1497821bd36c&enrichSource=Y292ZXJQYWdlOzI2NTAxNDgyNztBUzoxMzQyNzE1NTM1MTE0MjRAMTQwOTAyNDI0MTY5NQ==

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dependant on the compactive effort and not only thegeometry of the embankment. Hence, determining thecompactive effort necessary for the saturated-unsaturatedzone of the clay core will be through an iterative processwith the available FEM techniques. The process, by whichsuch techniques will be used, will be discussed later on inthis paper.

A study by Vanapalli et al, 1997 has shown that forsaturated soils, the permeability is lowest for wet ofoptimum compaction (Figure 14). This lowest permeabilitycontinues to decrease with applied stress. The study hasalso demonstrated that shear strength is higher for wet ofoptimum specimens (Figure 15). Hence, it is necessary tocompact the saturated zone of the clay core and remainingcoarse soil under the phreatic surface of the embankmentat wet of optimum in order to reduce the possibility ofpiping.

Figure 14. Saturated coefficient of permeability test resultsfrom one-dimensional, consolidation tests (after Vanapalli etal., 1997).

Figure 15. Shear strength versus suction for specimenstested with different “initial” water contents under 25kPa netnormal stress (after Vanapalli et al., 1997).

Other studies by Watabe et al., 2000, on glacial till innorthern Quebec do not refer to the optimum moisturecontent, rather the compaction degree of saturation as acontrol variable. It has shown that at different compactiondegrees of saturation, permeability and pore size diametercorresponding to air entry values vary significantly (Watabeet al., 2000). For a specimen compacted at 94% degree of

saturation, its hydraulic conductivity is 100 smaller than thatof a specimen compacted at 58% degree of saturation.Furthermore, pore size diameter is 6 times smaller for theformer specimen, rendering both parameters favorable forthe reduction of the seepage properties within theembankment core (Figure 16). This study can also beuseful when considering the compaction degree of

saturation for the lining cover of the embankment dam.When compaction takes place at degrees of saturation lessthan that of optimum for this type of till, the hydraulicconductivity does not vary significantly with respect to voidratio. This approach can be utilized if the local borrowmaterial for the embankment core is an expansive soil.

Figure 16. Hydraulic conductivity as a function of thecompaction degree of saturation at a void ratio equal 0.25,and (b) Pore diameter corresponding to the air entry valueas a function of the compaction degree of saturation (afterWatabe et al., 2000).

4.2 Overtopping

The initiation of the breach channel during overtopping isfollowed by an increase in channel depth due to downwarderosion. As the channel depth increases, the stability of thechannel sides is undermined, hence at certain times,

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wasting of the sides will occur. The channel widthmeanwhile will continue to erode downwards causing thefurther vulnerability to the side slopes. It is thereforeimportant to note that the erodibility of unsaturated soilwould be less than that of saturated soil due to its highershear strength. For this reason, the frequency of side slopeinstability caused by the breach will be less than that of

unsaturated soil. The enhanced shear strength of thedownstream side will inhibit the lateral breachingmechanism and therefore delay the erosion process andconsequently the peak discharge of the flooding event.Since the same volume of water will escape from thereservoir, therefore the peak discharge will also beattenuated.

It is assumed that any embankment design does in fact takeinto account the prevention of overtopping. Nevertheless,this paper will consider overtopping in extreme climaticconidtions. The erosional effect of overtopping, however,may be hindered by installing lining covers made ofcompacted fine soils on the crest and downstream slope ofthe dam. The cohesive strength of the lining covers will forma provisional resistance to the high shear stresses in thesupercritical flow regime.

4.3 Slope Instability

Slope failures herein this paper, will only refer to failure ofdownstream slopes, since they are more affected by thedegree of saturation. While upstream slopes are completelysaturated, their material selection should be that of a coarsegrained soil in case of a rapid drawdown was to occur. Thecoarse grained soil will quickly drain the pore water andrelease any residual PWP during the drawdown process.Nevertheless, numerical analyses regarding PWP andconsequent shear strength (i.e. slope stability) should beconducted even for upstream slopes comprising of coarsegrained materials.

4.3.1 Clay Core Unsaturated Zone

Compaction should take place on the dry side of optimumduring construction (Figure 17) of the unsaturated zone ofthe clay core. Eventually, the suction present in the soil willincrease as the soil dries and since the rate of permeabilityfor clay is very low, this will be useful for guaranteeing thatthe embankment core will maintain itself in a state ofunsaturated condition after construction.

The study by Cokca et al., 2004 on compaction ofunsaturated clays, showed that shear strength is enhancedas moisture content is reduced at the dry side of optimumas higher friction angles as well as higher suction areexhibited between the (flocculated) clay aggregates (Figure18). It is shown, however, that the cohesion corresponds toa maximum value at the optimum water content (Figure 19).However, an analysis using the shear stress equation forunsaturated soils (shown below) for each individually testedwater content, must be carried out before concluding themost favorable moisture content:

b

waa uuuc tan)('tan)('f [8]

Where:

f = shear strength at failure;c’ = unsaturated soil cohesion;

ua = net normal stress; ' = angle of internal friction of the saturated soil;

ua -uw = matric suction of the unsaturated soil; and b

= angle of internal friction of the unsaturated soil.

Figure 17. Suction versus moisture content relation (afterCokca et al., 2004).

Figure 18. Angle of friction versus moisture contentrelationship (after Cokca et al. 2004).

Figure 19. Cohesion versus moisture content relationship(after Cokca et al. 2004).

https://www.researchgate.net/publication/225225335_Effects_of_compaction_moisture_content_on_the_shear_strength_of_an_unsaturated_clay?el=1_x_8&enrichId=rgreq-d9a16337-fa65-40fe-ad18-1497821bd36c&enrichSource=Y292ZXJQYWdlOzI2NTAxNDgyNztBUzoxMzQyNzE1NTM1MTE0MjRAMTQwOTAyNDI0MTY5NQ==https://www.researchgate.net/publication/225225335_Effects_of_compaction_moisture_content_on_the_shear_strength_of_an_unsaturated_clay?el=1_x_8&enrichId=rgreq-d9a16337-fa65-40fe-ad18-1497821bd36c&enrichSource=Y292ZXJQYWdlOzI2NTAxNDgyNztBUzoxMzQyNzE1NTM1MTE0MjRAMTQwOTAyNDI0MTY5NQ==

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Reduced shear strength of a saturated clay core can be aresult of relatively high permeability (i.e. high PWP).Therefore it is necessary to conduct a balance between thedesired shear strength and the source hydraulicconductivity by FEM analyses. This process will minimizefailures caused by the simultaneous effect of an increasedhydraulic conductivity and lowered shear strength. For the

same compactive effort, soils dry of optimum with aflocculated arrangement exhibit a higher hydraulicconductivity than soils wet of optimum represented by adispersed arrangement. However, at higher suctions, thisvariation was shown to diminish (Meerdink et al., 1996).

4.3.2 Clay Covers

Soil suction in slope stability analyses is often ignored dueto the perception that soil suction will continuously dissipatein the soil sub-layers when water percolates under theeffect of rainfall (i.e. wetting process) (Zhang et al., 2004).In order to diminish matric suction by rainfall, it must be sothat the intensity of rainfall even is equivalent of thesaturated permeability of the ground surface and enduredover a long period of time (Zhang et al., 2004). Henceassuming a worst case scenario where the surface layer ofthe soil has presumably been subjected to consecutiverainfall events (i.e. fully saturated conditions are in effect),clay which exhibits relatively low permeability can be usedas a lining cover for the dam. This design measure willtherefore play an important role in maximizing stabilityespecially under major hydrologic events.

In situ suction measurements conducted by Sweeney,1982, in Hong Kong demonstrated that intermediate depthsin a decomposed rhyolite soil of permeability rangingbetween 10 -5 m/s to 10-7 m/s, were not affected following arainstorm (Figure 20). In contrast, in suction measurementscarried out by Anderson, 1983, on colluvium with asaturated coefficient of permeability ranging between 10-4 m/s to 10-7 m/s dissipated suction values up to 10 mfollowing a heavy rainstorm (Figure 21).

Therefore, with respect to the fine soil covers on the crestand downstream side of the dam, compaction must becarried out in favor of hydraulic conductivity. A study bySmith et al., 1999, showed that at moisture contents 0.5 to1.5 % wetter than optimum, a lower permeability for collieryspoils is achieved. A disadvantage of compaction wet ofoptimum is that desiccation cracking may occur, diminishingthe favorable effect of lowered hydraulic conductivity(Meerdink et al., 1996). A study by Elsbury et al., 1990,yielded similar results for clays. Also at higher compactiveefforts, yield a lower permeability (Figure 22). More data isneeded for quantifying the degree of compaction versushydraulic permeability with respect to soil properties and theSWCC.

It is also necessary to incorporate certain hydrologicprocesses into the design analysis. Infiltration due to severerainfalls may increase the PWP on the downstream side ofthe dam, and undermine the stability of the slope. Liningcovers on the downstream slope will also minimize thedownward moisture flux in the event of a rainfall event and

consequently maintain the high matric suction existingwithin the coarser soil below (personal communication,Vanapalli, 2005), another motive attributed to their use.

Figure 20. Suction measurements in a weathered rhyolite inHong Kong (after Sweeney, 1982).

Figure 21. Suction measurements in a colluvium in HongKong (after Anderson, 1983).

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Figure 22. Effect of moisture content on compaction andpermeability (after Smith et al., 1999).

Assuming that the coarser material is in an unsaturatedstate and under relatively high matric suction (300 – 400kPa), its permeability will be lower than that of the top(clayey) soil (Figure 10). Furthermore, if these linings areinstalled on a slope, they will laterally divert the flow paththrough a low saturated permeability layer before reachingthe coarser soil below. This occurs as a result of thecapillary barrier effect sustained at the fine-coarse soilinterface. This phenomenon will cease once the suction atthe interface reaches a critical value (i.e. of equalpermeability) to allow downward seepage (dipping) to takeplace. This process can be useful as a method to maintainthe negative pore water pressures in the underlying soil.

4.3.3 Layer Dimensions and Hydraulic Conductivity

Infiltration will initiate into the topsoil when the matricsuction increases to a point where it is near the water entryvalue and the moisture content will represent that of aresidual value. This matric suction is at a value lower thanthat of air entry value (Figure 11). A study by Khire et al.,2000, was conducted to illustrate the different designvariables that must be considered when design capillarybarrier systems. It was found that as the surface layerthickness increases, lateral diversion was more evident, thisproportionality decreased at certain thicknesses. Moreover,it was found that lateral diversion is also a function ofrelative hydraulic conductivity between the coarse and finegrained soils (Khire et al., 2004).

Figure 23 below can be used to select the materialscapable of performing a lateral diversion. It is important totake into account the hysteretic behavior of unsaturatedsoils in order to properly simulate evaporation (drying) andprecipitation (wetting) within the simulation.

According to the study made by Khire et al., 2000, thethickness of the coarser layer also played a role in thelateral diversion phenomenon. As this thickness increased,percolation was reduced; nevertheless, this variable wasnot as predominant as the thickness of the top layer soil.

Another key variable in soil cover design is the hydraulicconductivity of the top soil layer. As saturated hydraulicconductivity decreases, infiltration through the coarse layersalso decreases. It was demonstrated that the grain size ofthe coarser soil affects the water storage capacity of thefine soil layer; as coarser soils were used, the water storagecapacity of the fine soil was increased, reducing infiltration

into the coarser soil. A study by Stormont and Morris, 1997, suggests that anintermediate layer (or Unsaturated Drainage Layer, UDL)such as fine-grained sand may improve the performance ofthe lateral drainage mechanism if it is conductive enough tolaterally divert the seepage flow (Figure 24).

Figure 23. (a) SWCC, and (b) Unsaturated hydraulicconductivity functions for various soils (after Khire et al.,2000).

It is not imperative that the UDL be fine of sand asillustrated in Figure 24, however, there lie certain restraintswith respect to the spectrum of grain sizes available forselection.

It may be important to note that the hydraulic gain of usingan UDL may not be financially feasible, since this willincrease the complexity of the design as well as material

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and labor requirements. A study by Morris and Stormont,1999, on landfill sites mentions that increasing the lateraldiversion in basic capillary barriers can be carried out bymodifying the fine grained soil lining the embankment. Suchmodification may comprise of an additional vegetative layerfor increased water adsorption by plant roots (Figure 25).This will also increase the local evapotranspiration rate, and

eventually maintain unsaturated conditions. The type ofvegetation that will grow on the soil cover is dependent onclimatic and regional conditions; however, it is beneficial togrow vegetation that is not influenced by varying climates,so as to preserve its longevity. Morris and Stormont, 1999,

also state that the primary variables for lateral diversion arethe unsaturated hydraulic conductivity of the fine soil andthe gradient of the soil interface. An increase in gradientincreases the diversion length (Figure 26). The non-dimensional diversion length represents the ratio betweenthe diversion length to the difference between the maximumand minimum diversion length for the corresponding slopes.

Another important variable is the shape of the SWCC whichis governed by the soil characteristic parameters forunsaturated flow (i.e. water entry value, water storage, anddesaturation rate).

Figure 24. Lateral drainage in unsaturated soils due to (a) capillary barrier (b) inclusion of intermediate material to formunsaturated drainage layer (UDL) (after Stormont and Morris, 1997).

Figure 25. Schematic of capillary barrier showing vegetativecover (after Morris and Stormont, 1999).

Figure 26. Nondimensionalized diversion length (afterMorris and Stormont, 1999).

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A study by Smesrud and Selker, 2001, showed that amaximum lateral diversion length can be achieved with amaximum particle size contrast ratio. Nevertheless, it is alsonecessary to ensure the integrity of the coarse-fine soilinterface and the local slope stability; hence it was shownthat an underlying layer 2.5 times coarser than the coveringlayer will yield 80% of maximum diversion. A larger contrast

ratio will cause migration of the fine soil into the coarserlayer, therefore diminishing the very textural distinction ofthe interface responsible for this phenomenon. For simplecapillary barrier systems, Khire et al. 2000, suggest threesteps to follow regarding the design process:

First it is necessary to define the meteorologicaldata that will be used in the simulation. The criticaltime where infiltration will occur is whenprecipitation (P ) exceeds evapotranspiration (ET ),or ET – P 0 . Since this formulation does nottake into account surface runoff and storageinterception, the storage capacity, S R , of the topsoil can be expressed as follows:

aP ET P S R [9]

Where a is the runoff coefficient and can be approximatedto be between 5-10%.

Second, the surface layer thickness can beestimated using the equation below:

L

B R dz z S

0

)( [10]

Where:

θ(z + Ψ B ) = relationship between the watercontent and the suction (i.e.SWCC);

z = distance above the coarse soillayer; and

L = thickness of the fine soil layer.

Third, the layer thickness is adjusted usingnumerical analysis; and

Finally, the thickness may be adjusted to accountfor other factors such as desiccation, wind andwater erosion and a factor of safety to account forexcessive percolation.

5. FEM TECHNIQUES

Finite-Element Methods (FEM) or Finite-Elements Analysis(FEA) has helped engineers and scientists over the past 60years to predict a stress and/or strain states within a finiteboundary. The area or volume for 2D and 3D modelingrespectively of interest is divided in a mesh where boundaryconditions are known where each division corresponds toone element. With knowledge of the constitutiverelationships between the state variables (stress and

hydraulic) and material variables, the effect of the boundaryconditions can be transferred through the entire mesh. Agreater number of nodes (i.e. connections betweenelements) will yield more accurate results; however, mostseepage problems are solved with less than 2000 nodes.With respect to FEA in earthen embankments, engineersare mostly concerned with flow behavior and PWP. With

information on the latter, it is possible to conduct a slopestability analysis based on initial conditions of theembankment (i.e. steady state seepage) or underhydrologic and/or geologic events (i.e. transient seepageand dynamic loading). To model seepage in earthenembankments, two functions are used; SWCC (i.e. watercontent as a function of suction) and permeability as afunction of suction. The embankment cross-section is thennumerically analyzed and where slope stability isconsequently investigated using the principle of effectivestress and shear strength at failure.

5.1 Saturated-Unsaturated Flow Seepage

Before the development of FEA, seepage in earthenembankments was determined by the method ofCasagrande, where designers did not take into account thenegative pore-water pressures within the flow-net. However,this method may not be very effective for predictingseepage, PWP, seepage face position and water tableposition (Chapuis and Aubertin, 2001). A numerical analysison a large dike by Crespo, 1994, predicted the flow rate tobe 10 to 20% higher than a similar study by Bowles, 1984,where negative PWP were ignored. The study by Chapuiset al., 2001, obtained a flow rate equal to that of Crespo,1994, using a later version of SEEP/W with 1145 elementsof 1.0 m as opposed to 295 elements of 2m. The results ofChapuis et al., 2001, yielded a higher water table level andhence a larger seepage surface on the downstream side ofthe dam. Therefore it is cautioned to take into accountunsaturated flow seepage during the design of thedownstream slope of the dam in order to avoidcomplications arising from freeze-thaw cycles in the winter(Chapuis and Aubertin, 2001). Also by determining thenegative PWP in the downstream side of the dam, a moreaccurate analysis can be conducted with respect to slopestability (Chapuis and Aubertin, 2001).

The biggest challenge in numerically modeling the hydraulicaspect of earth dams is the method by which the phreaticsurface is determined (Xu et al., 2003). Using the FEAcomputer application, SEEP/W, does not immediatelycalculate the water table level in an earth embankment, andtherefore its location must be obtained by simultaneouslyanalyzing all factors affecting the unsaturated flow seepage.This can be carried out using a series of iterations (Chapuisand Aubertin, 2001) as previously mentioned. Chapuis and

Aubertin, 2001, explain the iteration process as follows:

The first simulation will yield nodes in thedownstream side with a head higher than thereservoir elevation. These nodes will then beassigned a boundary condition that of the phreaticsurface).

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During the second calculation, if any downstreamnodes indicate a head higher than elevation, thenthey will be set equal to the elevation for the thirdsimulation.

The iterations cease once all nodes along theslope illustrate a PWP equal to zero or negative.

It is of the designer’s objective to achieve lowering of theposition of the phreatic surface as much as possible inorder to reduce the total seepage flow (Xu et al., 2003).Hence in order to optimize the design, multiple analysesmust be carried using the various soil input design variablesas well as the hydrologic, geotechnical and environmentalboundary conditions. A study by Xu et al., 2003, suggeststhe use of a performance index regarding the choice of howtwo soil materials are allocated, formulates the optimizationof an embankment design. Their main criterion is based onthe satisfaction of zero seepage on the downstream side ofthe embankment and negative PWP in the air boundary (topsurface).

5.2 Hydrologic Processes and Unsaturated Soils

It can be seen from studies by Sweeney, 1982, and Anderson, 1983, how the saturated permeability and rainfallintensity play an important role in maintaining unsaturatedconditions. Zhang et al., 2004 state that for a rainfall eventless than one or more orders of magnitude than thesaturated coefficient of permeability, the long-term matricsuction is maintained.

By taking into account Darcy's law and the law of continuitythrough a 2-D soil element, the partial differential equationfor the transient flow through unsaturated soil is derived byZhang et al., 2004, as follows:

t h g m

yhk

x xhk

x ww

y x

2 [11]

Where:

k x &k y = unsaturated coefficient of permeabilityin the x and y-direction respectively;

h = hydraulic head;t = time;m2

w = water storage coefficient, or the slope of thevolumetric water content versus matric suctionwhere the change in net normal stress, d(σ – ua),is equal to zero;

ρ w = density of water; andg = gravitational acceleration.

The hydrologic processes required will be defined andintegrated within the boundaries of the embankment design.Such hydrologic boundary conditions are; rainfall intensityand duration (i.e. precipitation), evapotranspiration, surfacerunoff and interception. Infiltration, on the other hand, is astrong function of the former processes. Althoughgeotechnical engineers consider infiltration as the mostimportant hydrologic process in their work, it is equallyimportant to be able to model all hydrologic processes

within the dam embankment challenge. The study carriedout by Zhang et al., 2004, states that additional parametersgoverning seepage such as the SWCC, permeabilityfunctions and processes governing infiltration undertransient situations are also required. In their numericalanalysis using SEEP/W, infiltration was modeled withrespect to the hydrologic processes in steady state as well

as transient conditions.The Combined Hydrology And Stability Model (CHASM)was selected in the study by Wilkinson et al. 2002, toassess the effects of vegetation and slope plan topographyon slope stability during storm events. This model allowsanalysis with respect to the hydrologic phenomenaassociated with vegetation such as interception andevapotranspiration, and their effect on slope stability. Thestudy by Wilson el al. 2002, show that the model's capacityto capture variable plan topography and plantation coversrenders it very useful for predicting the rainfall thresholdyielding slope instability.

5.2.1 Storm Simulations

It is often debated how storm events should be taken intoconsideration when simulating storms. Research studiesconducted by Khire et al., 2000, state that it is necessary toconduct simulations that represent precipitation over anumber of years using the most rigorous meteorologicaldata. Three different return periods where therefore studiedby Ng et al., 2001. They found that increasing the returnperiod of the storm from 10 years to 100 years producedthe most significant increase in PWP. It was also shownthat simulating a storm with duration of 24 h in comparisonto 168 h resulted in the highest PWP build-up in theunsaturated slope. This is due to the higher rainfall intensityof the 24 hour storm. The numerical analysis conducted byNg et al. 2001 utilizes the FEMWATER model, which is a3D finite-element application simulating groundwater flow insaturated and unsaturated porous media (Figure 27).

Figure 27. Three-Dimensional FEM mesh usingFEMWATER (after Tung et al. 1999).

Another model (SEEP/W and SLOPE/W) similar to CHASMused a similar approach for investigating how the reduction

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of matric suction led to slope failures in Manitoba byincluding an additional factor, evapotranspiration. However,the study conducted by Blatz et al., 2004, did notconfidently determine the magnitude of evapotranspiration,but yielded a high sensitivity with respect to the factor ofsafety (Figure 28). This emphasizes that evapotranspirationis an important factor when trying to model the net moisture

flux during a rainfall event; nevertheless, it must bedetermined using more appropriate methods to account forevapotranspiration.

Infiltration was calculated based on the followingrelationship:

aP ET P I [12]

Where:

I = infiltration rate (cm/day);P = precipitation rate (cm/day);ET = evapotranspiration rate (cm/day); anda = runoff coefficient based on a given return period.

Penman, 1948, stated that evapotranspiration for sparsevegetative layers with adequate availability of water can beapproximated to evaporation from a free water surface. Theevaporation, E (cm/day), can then be calculated based onMeyer’s formula (194 4):

54.2))(1.01(0106.0 a s eeU E [13]

Where:

U = wind speed at two meters height (mph);e s = saturated vapor pressure (mb); and e a = actual vapor pressure (mb).

Figure 28. Factor of safety versus percentage change inevapotranspiration (after Blatz et al. 2004).

5.2.2 Moisture Flux

It may be necessary to demonstrate two seepage scenariosduring rainfall events; seepage under steady stateconditions where the moisture flux,q, into and out of the soilreach equilibrium, or, under transient conditions where thePWP response over a certain time period is to be

investigated (Zhang et al., 2004). The former scenario isrelevant to rainfalls after prolonged durations where as thelatter is applicable at the inception of a rainfall.Nevertheless, both approaches should be used todetermine the change in matric suction with respect tovarious depths. The study by Kasim, 1997, and Kasim etal., 1998, has shown that for a rainfall event less than oneor more orders of magnitude than the saturated coefficientof permeability of the top soil layer, the long-term matricsuction is maintained. Yet it is important to quantify therainfall intensity and duration as well as the soil parametersthat are in agreement with this concept.

A numerical simulation using SEEP/W conducted by Zhanget al., 2004, has shown that with respect to steady stateseepage, the negative pore water pressures are constantwith respect to depth and the ratio q/k sat of the coarser layer(i.e. sand) is less than unity and the net ground flux is zero(Figure 29). Simulation of the transient seepage scenario(also conducted using SEEP/W) showed that the PWP weredecreasing with time during soil saturation, but were limitedto a constant value in the final state (Figure 30). It wasfound that under transient seepage scenarios (the moistureflux in is greater than the flux out of the soil), PWP aremaintained negative when q/k sat is less than unity where asPWP are equal to zero when q/k sat is greater than or equalto unity.

5.2.3 Effects of SWCC on Infiltration

The study by Zhang et al., 2004, investigated theparameters of the SWCC with respect to infiltration. Severalsimulations where carried out using the formulation byFredlund and Xing, 1994, for different values of thea , m and n paramete rs characterizing a soil’s SWCC. Thefollowing observations where noted in the study by Zhang etal, 2004, for steady state seepage:

It was found that the higher the a parameter (i.e.corresponding to AEV) with respect to the SWCCthe greater suction was reduced and the deeperthe affected zone;

The “n” parameter (corresponding to the slope ordesaturation rate at the inflection point) did not

significantly affect suction nor depth of the affectedzone;

This highlights an important postulation by Kasim, 1997,that the matric suction corresponding to a steady staterainfall flux can be extrapolated from the permeabilityfunction curve.

The study by Zhang et al, 2004, for transient seepage foundthat the lower the a parameter with respect to the SWCCthe depth uniformity of the wetting front and the transient

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time for it to progress downwards increases. This can beexplained such that at high suctions, the permeability islower for soils with a lower air entry value, hence limiting thepercolation. However, for a larger moisture flux, q, the ratioof q/k sat is larger for soils with lower air entry values, and sothe PWP will vary significantly along the depth of the soil.While the results obtained above were obtained from a FEM

analysis that has fixed the water table boundary at aspecific height, further FEM analyses indicated that theGWT significantly rose for soils with a lower water storagecoefficient.

Figure 29. Infiltration into an unsaturated soil under steadystate conditions with various ground surface moisture fluxes(after Zhang et al., 2004).

Figure 30. Infiltration into an unsaturated soil undertransient seepage conditions with two different groundsurface fluxes (a) q < ksat, and (b) q > ksat (after Zhang et al.,2004).

This highlights the importance of allowing a floating GWTwithin a numerical analysis (Figure 31). The study by Zhanget al., 2004, states that enduring the permanence of matricsuction, the ratio of moisture influx tok sat should be lessthan 0.01 for an air entry parameter greater than 100.

5.3 Capillary Barriers

Numerical studies conducted by Morris and Stormont,1997a and 1997b, showed that using capillary barriers on aslope of 10% completely diverted the downward moistureflux and maintained the negative pore water pressures inthe underlying layer at a nearly constant value. The studycarried out by Khire et al., 2004, comprised of a numericalanalysis using the UNSAT-H model due its ability tosimulate unsaturated flow, evaporation and transpiration aswell as its favorable results with respect to fieldobservations. A disadvantage of this one-dimensionalmodel is that it ignores lateral drainage and will tend to overpredict infiltration. They argue that there are no otherapplication is available for validating field observationsespecially for long-term hydrologic simulations.

Although it is necessary to maximize the surface runoff andminimize interception storage when considering the designof the top soil cover, the significant erosion caused by runoffover time might diminish the effect of the cover lining andconsequently the permanence of matric suction in the soilbelow. Models such as the Water Erosion Prediction Project(WEPP) have been used by the USDA since 1995 to predictthe runoff and erosion. It bases its prediction primarily onthe k sat of the top soil and may be included in the analysisby simulating an optimum balance between surface runoff,erosion and evapotranspiration by vegetative covers(Blanco-Canqui, 2002).

Morris and Stormont, 1999, also conducted a numericalanalysis by modifying an existing computer code,TRACER3D, capable of simulating 3D saturated andunsaturated flow behavior in soil. By simulating 2D flow,and accounting for an evapotranspiration distribution usingthe HELP (Hydrologic Evaluation of Landfill Performance)model developed by Schroeder et al. 1994, the authorsdeveloped a model capable of simulating lateral diversionperformance (Figure 32).

5.4 Dam Breach

Several models have been developed over the past 20years to simulate the breach mechanism and formation ofthe breach channel. Sediment transport rates incorporatesoil cohesion and surface roughness during the erosionprocess. The breach enlargement by sudden collapse takesinto account side slope instability of the breach channel andthe shearing of wedge-shaped soil masses by hydrostaticforces in the reservoir (Figure 33). However, the BREACHmodel does not take into account the variance in soilcohesion in the cross-sectional domain (Fread, 1988), or inother words the effect of matric suction on slope stabilityand the erosion rate (especially in cohesive soils).

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Figure 31. Transient seepage analysis (after Fredlund, 2003; Budapest,Hungary). Figure 32. Schematic of Numerical Model (after

Morris and Stormont, 1999).

Figure 33. Water and sediment outflow hydrographs from the hypothetical failure of the homogenous embankment (afterMohamed et al. 1999).

Figure 34. Dam embankment considered in study.

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6. DISCUSSION – INTEGRATED PARAMETRICDESIGN

Definition of the input parameters and design variables isthe first step for planning an integrated design process inearth embankments. The input parameters may beconsidered as the hydrologic, geotechnical and

environmental conditions that will act as the major influenceon the simulation and consequently on the design (Table 2).For the purpose of this study, a typical dam embankmentdesign was selected consisting of mainly a coarse material,a central clay core and a toe drain (Figure 34). The designvariables are related to the dam embankment geometry andzoning (Table 3).

6.1 Design Guidelines

The next step is to link the design variables and inputparameters in a simple cause and effect relationship (Table3). This will guide the designer for the selection and/ormanipulation of the design variables to conform to thetesting requirements regarding the slope stability anderodibility corresponding to the input variables. Although thecause and effect relationship between the design variablesmay be complex (i.e. involving a number of relationships),only the dominant causes and resulting impacts aredefined. A similar relationship also exists between the inputvariables (Table 2).

6.2 Simulation Process Flowchart

The resulting design must not only maximize theunsaturated zone, but it must be tested with respect to themost common failure modes within earth embankments (i.e.slope instability and erosion). The ability of the 2-D SEEP/Wto simulate saturated-unsaturated flow seepage and GWTpositioning as a result of seepage erosion andmeteorological activity renders the package valuable for thedesign. Other advantages of SEEP/W are that it is capableto simulate infiltration in both steady state and transientconditions under various meteorological inputs as well as itsability to interface with SLOPE/W and QUAKE/W (GEO-Slope 2004) for carrying out slope stability analyses anddynamic loading. A conceptual algorithm detailing theinterface with the various simulation models and bothdesign variables and input parameters was developed toguide the design process (Figure 35). The HELP model willthen be run in parallel to simulate for a more accuratedistribution of evapotranspiration, by capturing data fromSEEP/W during the hydrologic modeling phase. It is thennecessary to test the model at the defined time interval for astable GWT as well as ET distribution. Once these eventshave been stabilized, the process may continue and takeinto account the analyses of the slope stability (e.g.SLOPE/W) and erosion models (e.g. WEPP). In the casewhere the design yields a failure with respect to slopestability and/or erosion, the design variables can be fine-tuned in accordance with the design guidelines mentionedabove (Table 3). Finally, the algorithm will proceed througha succession of time intervals until the entire storm durationis fulfilled.

7. SUMMARY AND CONCLUSIONS

Specific design considerations pertinent to maximizing theunsaturated zone within an embankment such asappropriate drainage, embankment material selection,compactive efforts, optimum moisture content as well as aclay lining cover are proposed. Hydrologic and geotechnical

events causing earthen embankment breaching, definedherein as input parameters, will be integrated vis-à-visinterfacing seepage, slope stability and hydrologic FEMmodules. Optimizing the design variables will be performedby means of a “conceptual” design algorithm that will guidethe designer to simulate the rigorous input parametersunder transient as well as steady state conditions. Furtherstudies on predicting outflow hydrographs in dam breachingmechanisms should also consider slope stability anderosion in the unsaturated zone, especially with respect tocohesive soils.

8. ACKNOWLEDGEMENTS

The writer wishes to acknowledge the guidance,encouragement and insight of Professor Sai Vanapallitowards this term paper and also express his appreciationand recognition to the organizers and fellow CivilEngineering undergraduate and graduate students of thefirst Students’ Conference on Unsaturated Soil Mechanics conducted at the University of Ottawa, Ottawa, Ontario,Canada; April 3rd, 2005.

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Table 2. Input parameters: cause-effect relationship between other input parameters and/or design variables.

Table 3. Design variables: cause-effect relationship between other design variables and/or input parameters.

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Figure 35. Design Process Algorithm

SEEP/WHELP (ET)

SEEP/W(GWT Data)

StableGWT

StableET

StableGWT

SLOPE/W

Stability

WEPP

GeotechnicalInput

Parameters

Erosion

Yes No

No Yes

Yes No

HydrologicInput

Parameter

Yes

No

DesignVariable

No

Guideline

Yes

Next TimeStep

A

RedefineDesign

Variables

A

SEEP/W(ET & GWT Data)

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9. REFERENCES

Anderson, M.G. 1983. Prediction of soil suction for slopes inHong Kong. Geotechnical Control Office Publication1184, Special Projects Division, EngineeringDevelopment Department, Hong Kong.

BBC 1998. Asia-Pacific China f loods ‘ worst ever’.

Bertram, G.E. 1940. An experimental investigation of

protective filters, Publications of the Graduate Schoolof Engineering, Harvard University, No. 267, January1940.

Blanco-Canqui, H., Gantzer, C.J., Anderson, S.H., Alberts,E.E., and Ghidey, F. 2002. Saturated hydraulicconductivity and its impact on simulated runoff forclaypan soils, Soil Sciences Society AmericanJournal, 66: 1596-1602.

Blatz, J.A., Nelson, J.F., and Graham, J. 2004. Effects ofnear-surface environmental conditions on instability ofan unsaturated soil slope, Canadian GeotechnicalJournal, 41: 1111-1126.

Bowles, J.E. 1984. Physical and Geotechnical Properties ofSoils. 2nd ed. McGraw-Hill, New York.Cedergren H.R. 1989. Seepage, Drainage and Flow Nets.

Sacramento: Wiley.Chapuis, R.P. and Aubertin, M. 2001. A simplified method

to estimate saturated and unsaturated seepagethrough dikes under steady-state conditions,Canadian Geotechnical Journal, 38: 1321-1328.

Chapuis, R.P., Chenaf, D., Bussière, B., Aubertin, M., andCrespo, R. 2001. A user’s approach to assessnumerical codes for saturated and unsaturatedseepage conditions, Canadian Geotechnical Journal,38: 1113 – 1126.

Chiu, T and Shackelford, C.D. 1998. Unsaturated hydraulicconductivity of compacted sand-kaolin mixtures,Journal of Geotechnical and GeoenvironmentalEngineering, 124(2): 160-170.

Cokca, E., Erol, O., and Armangil, F. 2004. Effects ofcompaction moisture content on the shear strength ofan unsaturated clay, Geotechnical and GeologicalEngineering, 22: 285-297.

Craig, R.F. 2004. Craig Soil Mechanics. London: SponPress.

Crespo, R. 1994. Modélisation des écoulements à traversles ouvrages de retenue et de confinement desrésidus miniers par un logiciel d’éléments finis.M.Sc.A. thesis, École Polytechnique de Montréal,Montréal.

Croney, D., Coleman, J.D. and Black, W. P. M. 1958.Movement and distribution of water in relation tohighway design and performance, Highway ResearchBoard Special report (40) Washington, HighwayResearch Record.

Crosta, G. and di Prisco, C. 1999. On slope instabilityinduced by seepage erosion, Canadian GeotechnicalJournal, 36: 1056-1073.

Dexter, A.R. 2004. Soil physical quality Part III: Unsaturatedhydraulic conductivity and general conclusions aboutS-theory, Geoderma, 120: 227-239.

Eckersley, J.D. 1985. Flowslides in stockpiled coal.Engineering Geology, 22: 13 –22.

Elsbury, B.R., Daniel, D.E., Sraders, G.A., and Anderson,D.C. 1990. Lessons learned from compacted clayliner, Journal of Geotechnical Engineering, 1(11):1641-1660.

Fell, R., Wan, C.F., Cyganiewicz, J., and Foster, M. 2003.

Time for development of internal erosion and piping inembankment dams, Journal of Geotechnical andGeoenvironmental Engineering,129(4): 307-314.

Foster, M. and Fell, R. 1999. A framework for estimating theprobability of failure of embankment dams by internalerosion and piping using event tree methods. UNICIVReport No. R-377, School of Civil and EnvironmentalEngineering, University of New South Wales, Sydney,

Australia.Foster, M., Fell, R., and Spannagle, M. 2000. The statistics

of embankment dam failures and accidents. CanadianGeotechnical Journal, 37: 1000-1024.

Foster, M., Fell, R., and Spannagle, M. 2002. A method forassessing the relative likelihood of failure ofembankment dams by piping: Reply1. CanadianGeotechnical Journal, 39: 497-500.Fread, D.L. 1988. BREACH: An Erosion Model for EarthenDam Failures, (1991 Revision). National WeatherService, Office of Hydrology, Silver Spring, Maryland.

Fredlund, D.G. 2003. Saturated-unsaturated soil mechanicsas the solution to a series of partial differentialequations, Second Symposium and Short Course onUnsaturated Soils and Environmental Geotechnics,Budapest, Hungary, November 3-4, 2003.

Fredlund, D.G. and Xing, A. 1994. Equations for the soil-water characteristic curve, Canadian GeotechnicalJournal, 31: 521 –532.

Fredlund, D.G., Xing, A., and Huang, S. 1994. Predictingthe permeability function for unsaturated soils usingthe soil-water characteristic curve, CanadianGeotechnical Journal, 31:533 – 546.

Karube, D. and Kawai, K. 2001. The role of pore waterpressures in the mechanical behavior of unsaturatedsoils, Geotechnical and Geological Engineering, 19:211-241.

Kasim, F.B. 1997. Effects of steady state rainfall on longterm matric suction conditions in slopes. InternalEngineering Research Report, Unsaturated SoilsGroup, University of Saskatchewan, Saskatoon,Saskatchewan.

Kasim, F.B., Fredlund, D.G., and Gan, J.K.-M. 1998. Theeffect of steady state rainfall on the matric suctionconditions in soil, Slope engineering in Hong Kong,Rotterdam, The Netherlands, pp. 75 – 85.

Khire, M. V., Benson, C.H., and Bosscher, P.J. 2000.Capillary barriers: Design variables and waterbalance, Journal of Geotechnical andGeoenvironmental Engineering, 126(8): 695 –708.

LeBihan, J.-P. and Leroueil, S. 2002. A model for gas andwater flow through the core of earth dams, CanadianGeotechnical Journal, 39: 90-102.

Leong, E.C. and Rahardjo, H. 1997. Review of soil watercharacteristic curve equations, Journal ofGeotechnical and Geoenvironmental Engineering,123(12): 1106-1117.

http://news.bbc.co.uk/1/hi/world/asia-pacific/156349.stmhttp://news.bbc.co.uk/1/hi/world/asia-pacific/156349.stmhttp://news.bbc.co.uk/1/hi/world/asia-pacific/156349.stmhttp://news.bbc.co.uk/1/hi/world/asia-pacific/156349.stmhttp://news.bbc.co.uk/1/hi/world/asia-pacific/156349.stm

8/18/2019 Al Riffai, 2005

24/24

Meerdink, J.S., Benson, C.H., and Khire, M.V. 1996.Unsaturated hydraulic conductivity of two compactedbarrier soils, Journal of Geotechnical Engineering,122: 565-576.

Meyer, A.F. 1944. Evaporation from lakes and reservoirs,Minnesota Resources Commission, St. Paul,Minnesota.

Mohamed, A.A.M., Samuels, P.G., Ghataora, G.S., andMorris, M.W. 1999. A new methodology to model thebreaching of non-cohesive homogeneousembankments, Proceedings of the 4 th CADAMWorkshop, Zaragoza, November 1999.

Morris, C.E. and Stormont, J. 1997a. Capillary barriers andsubtitle D covers: estimating equivalency, Journal ofEnvironmental Engineering,123(1): 3-10.

Morris, C.E. and Stormont, J. 1997b. Numerical simulationsof capillary barrier field tests, Proceedings, 1997International Containment Technology Conference,St. Petersburg, Florida.

Morris, C.E. and Stormont, J. 1999. Parametric study ofunsaturated drainage layers in capillary barrier,Journal of Geotechnical and GeoenvironmentalEngineering, 125(12): 1057 – 1065.Ng, C.W.W., Wang, B., and Tung, Y.K. 2001. Three-dimensional numerical investigations of groundwaterresponses in an unsaturated slope subjected tovarious rainfall patterns, Canadian GeotechnicalJournal, 38: 1049-1062.

Ohio Department of Natural Resources 1994. Fact Sheet94-31. Dam safety: seepage through earthen dams,Division of Water.

Onda, Y. and Itakura, N. 1997. An experimental study onthe burrowing activity of river crabs on subsurfacewater movement and piping erosion. Geomorphology,20: 279-288.

Penman, H.L. 1948. Natural evapotranspiration from openwater, bare soils and grass. Proceedings of the RoyalSociety of London,Series A, 193: 120 – 145.

Powledge, G.R., Ralston, D.C., Miller, P., Chen, Y.H.,Clopper, P.E., and Temple, D.M. 1989. Mechanics ofoverflow erosion on embankments. II: hydraulic anddesign considerations, Journal of HydraulicEngineering, 115(8): 1056-1075.

Schroeder, P.R., Aziz, N.M., Lloyd, C.M., and Zappi, P.A.1994. The hydrologic evaluation of landfillperformance (HELP) model: Engineeringdocumentation for version 3, U.S. EnvironmentalProtection Agency Risk Reduction EngineeringLaboratory, Cincinnati.

Sherard, J.L. 1984. Discussion of Dascal 1984.Proceedings of the International Conference on CasesHistories, Geotechnical Engineering,4:1613 – 1616.

Singh, V.P. 1996. Dam Breaching Modeling Technology.Dordrecht: Kluwer Academic.

Smesrud, J.K. and Selker, J.S. 2001. Effect of soil particlesize contrast on capillary barrier performance, Journalof Geotechnical and Geoenvironmental Engineering,127(10): 885-888.

Smith, C.C., Cripps, J.C., and Wymer, M.J. 1999.

Permeability of compacted colliery spoil – aparametric study, Engineering Geology, 53: 187-193.Stormont, J.C. 1995. The effect of constant anisotropy on

capillary barrier performance, Water ResourcesResearch, 31: 783 –785.

Stormont, J.C. and Morris, C.E. 1997. Unsaturated drainagelayers for diversion of infiltrating water, Journal ofIrrigation and Drainage Engineering,123(5): 364-366.

Sweeney, D.J. 1982. Some in situ soil suctionmeasurements in Hong Kong’s residual soil slopes,Proceedings of the 7 th Southeast Asian RegionalConference, Hong Kong, 22 – 26 November 1982,Southeast Asian Geotechnical Society, 1: 91 – 106.

Tung, Y.K., Ng, C.W.W., and Liu, J. 1999. Lai Ping Roadlandslide investigation – three-dimensionalgroundwater flow computations, Technical Report ofthe Geotechnical Engineering Office of the Hong KongSpecial Administrative Region, Hong Kong.

U.S. Department of the Army, Corps of Engineers, Office ofthe Chief of Engineers, 1986. Seepage analysis andcontrol for dams, Engineering Manual EM 1110-2-1901, 30 September, 1986, pp. D-1 to D-5; (1986a), p.D-6.

Vanapalli, S.K., Fredlund, D.G., and Pufahl, D.E. 1997.Saturated-unsaturated shear strength and hydraulicconductivity behavior of a compacted glacial till, 50th Canadian Geotechnical Conference, Ottawa, October20-22, pp. 625-632.

Watabe, Y., Leroueil, S., and LeBihan, J.-P. 2000. Influenceof compaction conditions on pore-size distribution andsaturated hydraulic conductivity of a glacial till,Canadian Geotechnical Journal, 37: 1184-1194.

Wilkinson, P.L., Anderson, M.G., and Lloyd, D.M. 2002. Anintegrated hydrological model for rain-inducedlandslide prediction, Earth Surface Processes andLandforms,27: 1285-1297.

Xu, Y.-Q., Unami, K. and Kawachi, T. 2003. Optimalhydraulic design of earth dam cross section usingsaturated-unsaturated seepage flow model. Advancesin Water Resources, 26: 1-7.

Zhang, L.L., Fredlund, D.G., Zhang, L.M., and Tang, W.H.2004. Numerical study of soil conditions under whichmatric suction can be maintained, CanadianGeotechnical Journal, 41: 569-582.

http://www.dnr.state.oh.us/water/pubs/fs_div/fctsht31.htmhttp://www.dnr.state.oh.us/water/pubs/fs_div/fctsht31.htmhttp://www.dnr.state.oh.us/water/pubs/fs_div/fctsht31.htmhttp://www.dnr.state.oh.us/water/pubs/fs_div/fctsht31.htm