2014 Fleshman Rice Piping

Laboratory Modeling of the Mechanismsof Piping Erosion Initiation

Mandie S. Fleshman, S.M.ASCE1; and John D. Rice, Ph.D., P.E., G.E., M.ASCE2

Abstract: A laboratory modeling program has been conducted to assess the mechanics of initiating the piping erosion process in sandy soils.Themodels were performed on several soils, differing in gradation, grain size, grain shape, and specic gravity. Observations andmonitoring ofpore pressures within the samples during the modeling identied four stages in the development of piping initiation: initial movement, progres-sive heave, boil formation, and total heave. By linking the observed behavior with themeasured pore-pressure regime in the sample, a model forthe mechanics of piping development has been developed. Finite-element seepage analyses were performed to model the progression of pipingdevelopment in the laboratory models and corroborate the developed model of mechanics. The ndings of the study identied a newmodel forthe initiation of piping development that can be applied to the assessment of piping in theeld.DOI: 10.1061/(ASCE)GT.1943-5606.0001106. 2014 American Society of Civil Engineers.

Author keywords: Internal erosion; Piping; Laboratory modeling; Dam; Levee.

Introduction

Internal erosion is the erosion of soil or rock as a result of forcesimposed by subsurface water ow or seepage. Internal erosion mech-anisms take several forms, including heave, piping, concentrated leakerosion, contact erosion, and suffusion [International Commission onLarge Dams (ICOLD) 2012]. The effects of these various internalerosionmechanisms have been reported to account for approximatelyhalf the dam and levee failures and incidents throughout the world(Foster et al. 2000; Richards and Reddy 2007).

The assessments of some of these mechanisms are quite straight-forward. For example, a method for assessing the heave mechanismwas derived by Terzaghi in the early 1900s (Terzaghi 1922; Terzaghiand Peck 1948). Terzaghis work compared the vertical hydraulicgradient at the ground surface (the exit gradient) with the criticalgradient icr needed to initiate erosion in the affected soil. In this case,the critical gradient is a function of soil buoyant unit weight g9 bymeans of

icr g9=gw (1)

where gw 5 unit weight of water.Terzaghi understood the limitations of his derivation and dif-

ferentiated between the heave mechanism and the mechanics ofsubsurface erosion, which Terzaghi claimed to defy theoreticalapproach (Terzaghi and Peck 1948). Although Terzaghi made itclear that his derivation was intended to model the heave mech-anism, the critical gradient, as described by Eq. (1), often has been

used to assess piping potential. For example, the hydraulic gradientacross a low-permeability blanket layer is often calculated to assessthe potential for piping in the underlying sand layer, as shown inFig. 1 (sandboil formation). It is commonpractice to compare the exitgradient with data from observed past performance (such as thatpresented in Fig. 2) to assess the potential for seepage and sand boilformation [U.S. Army Corps of Engineers (USACE) 2005]. Fig. 2presents calculated exit gradients from the U.S. Army WaterwaysExperiment Station Mississippi River study (U.S. Army WaterwaysExperimentation Station 1956) plotted verses the observed seepageand sand boil formation. Of note in Fig. 2 is the large spread of datacorrelating with similar observed behavior. This variation is likelyattributable to use of the analysis for the heavemechanism as an indexfor piping behavior and is a result of a variety of other factors thataffect piping behavior and are not accounted for in the analysis forheave.

Based on the preceding discussion, it is apparent that greaterunderstanding of the piping mechanism is needed. This paper pres-ents the results of a laboratory study of the piping mechanism andsoil parameters that affect the hydraulic conditions needed to ini-tiate piping. The results are presented with respect to the variousstages of initiation of piping that were observed in the laboratorymodels.

Previous Studies on Piping

Some of the earliest work on the assessment of piping potential wasperformed by Bligh (1910, 1913), who developed an empirical re-lationship between piping potential and the shortest ow path lengthbeneath a water-retaining structure. Lane (1935) later recognized adistinction between ow along the base of a structure, vertical owalong vertical barriers, and ow through granular media and modiedBlighs work in developing the weighted-creep-ratio method. Lanesempirical method also took into account the varied erosion resistanceof different soil types.

Sellmeijer and various coinvestigators from Delft Hydraulicsand Delft Geotechnics Laboratories (Delft) in Netherlands (e.g., deWit et al. 1981; Weijers and Sellmeijer 1993; Technical AdvisoryCommittee on Flood Defences 1999) performed ume tests of up totens of feet in length on clean, ne- to medium-grained sands to

1Graduate Research Assistant, Dept. of Civil and Environmental Engi-neering, Utah State Univ., Logan, UT 84322. E-mail:[email protected]

2Assistant Professor, Dept. of Civil and Environmental Engineering,Utah State Univ., Logan, UT 84322 (corresponding author). E-mail: [email protected]

Note. This manuscript was submitted on June 11, 2013; approved onJanuary 31, 2014; published online on March 7, 2014. Discussion periodopen until August 7, 2014; separate discussions must be submitted forindividual papers. This paper is part of the Journal of Geotechnical andGeoenvironmental Engineering, ASCE, ISSN 1090-0241/04014017(12)/$25.00.

ASCE 04014017-1 J. Geotech. Geoenviron. Eng.

J. Geotech. Geoenviron. Eng.

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model the seepage of water below a structure. The water owedthrough the sand beneath an impermeable barrier and exited througha slot in the top of the downstream portion of the ume (modelinga ditch or defect in an impervious layer). Tests were performed byslowly increasing the upstream hydraulic head and observing whenand how piping erosion initiated and progressed. Based on these testresults, Sellmeijer and Koenders (1991; Koenders and Sellmeijer1992) developed a mathematical model for piping based predom-inantly on the hydraulic conductivity and the D70 of the piping soil(the sieve size where 70% of the soil by weight is ner).

Schmertmann (2000) also carried out ume tests at theUniversityof Florida (UF) to investigate piping using a ume that initiatedpiping along a sloped soil surface. Schmertmanns tests were per-formed using a variety of clean sands spanning a range of uniformitycoefcientsCu (ranging from 1.5 to 6.1). Using the results of the UFand Delft ume tests, Schmertmann showed that the average gra-dients across the ume required to cause piping erosion were stronglycorrelated with the uniformity coefcient of the sand. Using the resultsof the UF andDelft tests, Schmertmann also developed a procedure forcalculating the no-lter factor of safety against piping that took intoaccount the geometry of the ow seepage region, the hydraulic con-ductivity, and the uniformity coefcient of the eroding soil.

The Delft andUF ume tests indicated that the critical gradient insand is a function of grain size and the uniformity of the sand inaddition to the unit weight. However, because of the nonuniformgeometry of the seepage area and complex ow paths at the seepage

exit points, it is difcult to accurately measure hydraulic gradientsand other seepage parameters at the exit points. Thus the true criticalgradient as a fundamental soil property cannot be assessed accu-rately. This limits the usefulness of the research results to applica-tions having similar geometries and uniform sand throughout theprole.

Several researchers have correlated piping potential with otherparameters in addition to the soils unit weight. Lane (1935) em-pirically correlated the different piping resistances of soils by soiltype and incorporated this into his weighted-creep-ratio analysismethod. As mentioned earlier, Schmertmann (2000) correlated theuniformity coefcient of clean sands with the average gradient inume tests. Tomlinson and Vaid (2000) performed tests to inves-tigate the effects of grain size ratio (between parent soil and a pro-spective ltering material), conning pressure, and seepage forces onthe potential for erosion of soil to occur through the lter material.Several researchers (Khilar et al. 1985; Ojha et al. 2001a, b) havedeveloped theoretical relationships for critical gradient based on theporosity and hydraulic conductivity of the soils.

Laboratory tests have been performed by past researchers to assessthe hydraulic conditions necessary to initiate various forms of internalerosion. Skempton and Brogan (1994) used an upward-ow per-meameter to assess the critical gradient required to cause the erosionof sand grains from a gravel matrix, i.e., modeling the suffusionmechanism. Chang and Zhang (2011, 2013) developed a stress-controlled downward-ow erosion device to perform suffusion tests

Fig. 1. Schematic of sand-boil formation near a levee illustrating effects of concentrated seepage ow and soil arching

Fig. 2. Comparison of upward hydraulic gradients calculated using current methods versus observed seepage and erosion [data from U.S. ArmyWaterways Experimentation Station (1956) and USACE (2005)]



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on gap-graded soils. Li and Fannin (2013) used the results of labo-ratory tests performed by several researchers to calibrate a capillary-tube model for assessing whether sand gradations are susceptible tosuffusion. The pipingmechanismwas studied byRichards and Reddy(2010, 2012), who investigated the effects of stress state and exit-faceshape on critical gradient using a true triaxial load cell. The horizontaland vertical critical gradients to initiate piping also were studied byFujisawa et al. (2013) using two different laboratory testing devices.

Purpose

The purpose of this investigation is to evaluate the mechanismsassociated with the initiation of piping in sandy soils through ob-servation of simple laboratory models. The models were conductedusing a laboratory apparatus designed and constructed specicallyfor this study. The device imposes a uniform hydraulic gradientthrough a soil sample without converging or diverging ow con-ditions so that the hydraulic regime within the sampler (pressuresand gradients) can be easily assessed throughout the test, and thecritical hydraulic conditions necessary to start the initiation pipingprocess can be assessed. The study looked at a variety of soils so thatthe effects of various soil parameters on piping initiation and pro-gression could be assessed.

The primary objective of this study was to provide fundamentalunderstanding of the piping phenomenon and critical hydraulicconditions needed to initiate piping. Eventually, the study and con-tinued research are expected to provide sufcient information to de-velop practical solutions for assessing piping potential in sandy soilsthat account for soil properties, complex ow conditions, and exit-face conditions.

Testing Apparatus

A testing apparatus was designed and constructed to conduct ex-periments to measure the hydraulic conditions (pressures and gra-dients) in a soil sample during the development of piping undervertical ow (horizontal exit face) conditions. A schematic illus-tration of the apparatus is presented in Fig. 3. The general concept ofthe device is to apply a uniform hydraulic gradient through a soilsample so that the basic mechanisms of piping initiation can beobserved. A brief description of the device is provided in the re-mainder of this section. A detailed description of the device isavailable in Fleshman (2012) and Fleshman and Rice (2013).

The soil sample is retained in a rigid-walled Plexiglas sampleholder that is sealed in a vertical position between two pressure cells.The water pressure is increased in the lower pressure cell to imposea uniform vertical hydraulic gradient upward though the sample.The pressure is slowly increased in the lower pressure cell as pore-pressure and ow-volume data are collected from within the soilsample, and the behavior of the soil is noted and video recorded.Because the water ows perpendicular to the exit face througha uniform soil cross section, the issues experienced in previousstudies by others in determining the magnitude of the exit gradientresulting from the asymmetric convergence of seepage ow at theexit location are avoided.

The differential head across the sample is controlled by tworeservoirs, the high-head and low-head reservoirs connected to thehigh-head and low-head pressure cells, respectively (Fig. 3). Inaddition to controlling the differential head, the reservoirs are ca-pable of applying a backpressure to the pressure cells. The back-pressure assists in the saturation process by forcing gas bubbles intosolution.

The soil sample holder is a 12:73 5:1-cm (53 2-in:) cylinder-shaped Plexiglas mold. A screen at the base of the cylinder retainsthe soil while allowing water to ow freely through the soil sample.A Plexiglas disk and rubber gasket around the midpoint of thesample holder are used to bolt and seal the holder between thepressure cells so that all water passing between the cells owsthrough the sample. The inside of the sample holder is coated withsilicone gel that serves a dual purpose. First, it provides a frictionalinterface between the soils and the sample holder. Second, becausethe sand grains indent into the silicon, it prevents a preferred seepagepath along the edges of the sample that would occur as a result oflarger interstitial voids caused by a lack of interlocking with thesmooth Plexiglas surface.

Three pore-pressure measurement ports are located at the centerof the sample at distances of 1.9, 5.7, and 9.5 cm (0.75, 2.25, and3.75 in.) below the top of the sample holder. The ports are denotedPPA, PPB, and PPC, respectively, as shown in Fig. 3. The portsconsist of 0.3-cm (0.125-in.) tubes with ltered ends to prevent soilinow. The port tubes are connected to differential pressuretransducers installed between the port and the low-head pressurecell. The total differential head between the pressure cells (and thusthe total differential head across the sample) is also measured.

The apparatus includes an automated instrumentation and data-collection system designed to make precise measurements of owthrough the sample and hydraulic head at various locations withinthe sample. The hydraulic-head measurements are made using fourValidyne DP15-26 differential pressure transducers (Validyne En-gineering, Northridge, California). Three transducers are connectedbetween the three ports in the sample holder and the pressure portin the low-head pressure cell (upper cell). The fourth transducer isconnected between the high- and low-head pressure cells to measurethe total differential head across the sample. The ow is measuredwith a Kobold magnetic-ux owmeter (Kobold, Pittsburgh, Penn-sylvania). The data are collected with a data logger and can be dis-played in real time during the test on a dedicated computer screen. Avideo taken of each test is linked to the data through a digital counterthat visually displays the time since the start of data collection in theview window of the video. This system allows observations of soil be-havior made in the video to be linked precisely with the collected data.

Testing Procedure

The following procedure was used to performed tests using theapparatus described earlier: Soils were placed in the sample holder in 1.2-cm (0.5-in.) lifts.

Each lift was densied by vibrating the soil with sharp blows onthe side of the holder using a metal rod.

The sample and sample holder were sealed between the low- andhigh-head pressure cells using bolts and a rubber gasket.

The sample was deaired by ushing with carbon dioxide, ap-plying a partial vacuum, and saturating the sample from the topdown with deaired water while maintaining the vacuum in thepressure cells. After the sample and pressure cells were com-pletely lled, a backpressure of 103 kPa (15 psi) was applied tothe entire system.

Starting with zero differential head, the head in the high-head pres-sure cell (beneath the sample) was gradually increased until the rstmovement of sand grains was observed. Once movement wasobserved, the head increase was halted, and the sample was allowedto reach equilibrium. For the remainder of the test, the differentialhead was increased in small increments of 2.5 cm (#1 in:). Aftereach increment, the sample was again allowed to reach equilibrium(heave progression stopped and boils no longer growing).



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The test progressed until the sample completely failed, removinga large portion of the soil from the sample holder.

Soils Tested

Tests were performed on a variety of sandy soils. A summary of keyproperties of the soils tested is presented in Table 1. Grain sizedistribution curves for the soils are presented in Fig. 4. Ottawa 2030and graded sands conforming toASTMC778-03 (ASTM2003) (well-rounded silica sands) were tested. To investigate the effect of grainshape, specimens of angular silica sand were prepared to the samegradations as the Ottawa 2030 and graded sands. Specimens ofa uniform No. 16 sieve size angular quartz sand and a uniform ne-grained (No. 100 sieve) garnet sand also were tested. The garnetsand has a much higher specic gravity than the quartz sand (3.87for garnet versus 2.64 for quartz).

Observed Behavior

Following each test, the video was carefully inspected to observestages in the development of piping failure.Whereas the general soilbehavior varied between tests, four stages of piping developmentwere identied to describe the progression of the failure: (1) rstvisible movement, (2) heave progression, (3) boil formation, and (4)total heave. Details of these stages and interpretations of the mecha-nisms occurring during each stage are presented in subsequent para-graphs. Further evidence supporting these interpretations will bepresented in the discussions of data interpretation later in this paper.

The rst visible movement is a slight heave or rockingmovementof individual sand grains along the exit face. This movement isdifcult to detect and often requires repeated viewing of the portionof the video where movement rst occurs. This stage is attributed tothe sand grains along the free face of the sample reaching a state ofincipient motion as the forces imposed by the seeping water become

Fig. 3. Schematic illustration of testing apparatus (1 psi 5 6.895 kPa 5 0.006895 MPa)

Table 1. Summary of Soil Types Tested

Soil typeNo. oftests run

Specicgravity Gs

Coef. ofunif. Cu

Fric.angle f

Ave. dry unitwt. (/cu ft)

Initial voidratio eo

Terzaghi criticalgradient gb=gw

Average measured gradient

First visiblemovement (Stage 1)

First sand boil(Stage 3)

Total heave(Stage 4)

Ottawa 2030 sand 17 2.64 1 35 106 0.55 1.06 1.32 1.65 1.95Ottawa Graded sand 13 2.64 2 35 108 0.53 1.07 1.40 1.60 2.12Angular 2030 sand 13 2.64 1 37 94 0.75 0.93 1.47 2.24 2.72Angular graded sand 11 2.64 2 38 96 0.72 0.96 1.38 1.93 2.99No. 100 garnet sand 4 3.87 1.5 39 128 0.89 1.52 1.73 1.76 2.89



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equal to the forces retaining the soil grains. While movement isoccurring with the individual grains, there is little overall movement(heaving) of the exit face. The second stage is characterized byprogressive heaving of the exit face. This stage is attributed to for-mation of a zone of loosened sand grains that increases in thicknessby progressing downward through the sample as the hydraulicgradient is increased. The loosening of the sand increases the voidratio, resulting in a decrease in seepage velocity through the soil. Thereduced velocity results in lower viscous shear forces applied tothe sand grains. Thus, as the loosened zone increases in thickness,the reduced viscous shear forces allowmore of the weight of the soilgrains to be applied to the lower portions of the sample. In this way,a state of equilibrium is achieved with the increasing hydraulicgradient across the sample.

The third stage is formation of one or several sand boils on theexit face. Sand boils develop when a preferential seepage pathwayforms through the upper portion of the sample as a result of loos-ening and rearrangement of the grains during progressive heaving.The preferential seepage path relieves pressure from within the sam-ple, allowing the sample to reach equilibriumwithout further heaving.Sand boils did not form in every test, and their appearance seems to bea function of the random alignment of interstitial voids. In a few cases,the boil formation was the rst visible movement, whereas in othercases, a boil does not form before the test progresses to the nal stage.The second and third stages were generally observed to occur in-termittently within the test. As the differential head is increased, thedownward heave propagation is sometimes interrupted by the forma-tion of a sand boil. The pressure relief from the boils temporarily arreststhe downward progression of the soil heave until the boil collapses.

The downward progression of heave generally continues until theheave mounding at the top of the sample reaches an unstable con-guration and begins to slough off to the sides of the sample holder.The sloughing removes the pressure of the overlying soils, and thefourth stage, total heave, occurs as the entire sample heaves upward.

A summary of the test results for the different soil types is pre-sented in Table 1. For each soil type tested, the number of testsperformed and the average total gradients across the entire sample atwhich Stages 1, 3, and 4 (rst visible movement, boil formation, andtotal heave) were observed are presented in Table 1. For comparison,the critical gradient calculated by Eq. (1) is also included in Table 1.

Effect of Soil Properties

Figs. 5(ac) present plots of the sample unit weights versus thegradients where rst visible movement (Stage 1), boil formation

(Stage 3), and total heave (Stage 4) were observed, respectively.Each plot also contains a line representing the critical gradientscalculated using Eq. (1) and the unit weight of the soil specimen. Therst observation to be made from Fig. 5 is that the gradients for allthree stages of the failure fall well above the line representingEq. (1).This again is a result of the sample being retained by the friction,withthe silicon-coated sides forcing the sample to fail by intergranularmechanisms rather than the heave mechanism.

The variation in the test results observed in the plots of Fig. 5is the result of superposition of the effects of a number of soilparameters on the critical gradient, including unit weight, gradation,grain size, and grain shape. The obvious trends are the correlationswith unit weight, where if one considers the lower bound of valuesfor each soil type, there is a general trend of increasing gradient withunit weight. However, superimposed on the unit-weight correlationsare the effects of the other parameters, the most notable being thebehavior of the angular sands. In the Stage 1 (rst movement) plot,the effect is small, and the gradients for the angular soils are onlyslightly above the trend of the other soils. In Stage 3 (boil formation),the results are varied, with the lowest gradients for uniform angularsoils being in line with the unit-weight trend of the other soils, andthe remaining gradients varying up to double the trend line. In Stage4 (total heave), nearly all the gradients for angular soils are con-siderably above the density trend line.

The authors believe that the variation in the angular soils justdescribed is the result of interlocking of grains and increased frictionangle. In Stage 1, the movement is occurring in the upper layer ofgrains, and thus granular interlocking is of minor importance. Asa result, the Stage 1 gradients of the angular soils are close to thetrend of the other soils. In Stage 3, the development of sand boils isthought to depend on the random alignment of larger interstitialvoids in the loosening soil mass forming a channel of preferentialow. In soils with angular grains, the size and shape of interstitialvoids are much more varied than in soils with rounded grains. Asa result of this variation, there is a wider range of gradients at whichsufcient alignment of large interstitial voids occurs to cause boilformation. In Stage 4, the variation in gradients for angular soils isdecreased, but nearly all the gradients are signicantly above theunit-weight trend line for the other soils. The authors believe that thistrend is a result of the increase in angle of internal friction thatincreases the soils bridging ability and also increases the inclinationthat the heave mound can achieve before starting to slough.

The effect of soil gradation is also apparent in Stage 4, where, onaverage, the graded soils have slightly higher gradients. This trend isapparent in both the Ottawa sands and the angular sands. Also ofnote is the behavior of the garnet sands with 2% by weight kaoliniteclay added. The addition of the clay inhibits the densication of thesoil and also resulted in Stage 1 critical gradients that were notablylower than the unit-weight trend for the other soils. The reason forthis is unclear but likely the result of the clay affecting the interstitialow paths or the intergranular behavior of the soil.

Data Analysis

The data collected from the differential pressure sensors and duringeach test were analyzed and compared with the video recordings.Initially, the raw data are plotted versus elapsed time during the test,as shown in Fig. 6 for a test on graded Ottawa sand. Each plotincludes four sets of data: (1) the total differential head across thesample and (2) differential head between pore-pressure ports at 1.91,5.715, and 9.53 cm (0.75, 2.25, and 3.75 in.) below the top of thesample and the upper reservoir (DhA, DhB, and DhC, respectively).The various dashed and dotted vertical lines in Fig. 6 represent the

Fig. 4. Grains size-distribution curves for soils tested



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Fig. 5. Plots of soil unit weight versus critical gradient to cause (a) rst visible movement (Stage 1); (b) rst boil formation (Stage 3); (c) total heave(Stage 4) for various soils tested (1 pcf 5 16.02 kg/m3)



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times at which the various stages of failure progression wereobserved in the corresponding video. Fig. 6 shows the porepressure at all the port locations increasing until the rst movementoccurs, where the pressure at the uppermost port (DhA) levels off.After more time and differential head increase, the pore pressure atDhB also levels off.

To assist in their interpretation, the differential head data (DhA,DhB, and DhC) were normalized with respect to the differential headthat would be expected if the hydraulic gradient remained constantthroughout the sample for the duration of the test using

DhN DhLtDHLs (2)

whereDhN 5 normalized differential head value; Dh5 differentialhead between the sensor and the low-head reservoir (DhA, DhB, orDhC); DH 5 total differential head across the sample; Lt 5 totalheight of the sample; andLs5 distance from the top of the sampler tothe sensor. Thus, for Sensor PPA, the following equation would beapplied to normalize the data:

DhN-A DhA5:0 in:DH0:75 in: (3)

whereDhN-A5 normalized differential head value at Sensor PPA, 1.9cm (0.75 in.)5 distance from the top of the sampler to Sensor PPA;and 12.7 cm (5.0 in.) 5 total height of the sample. Similar normal-ization was performed for DhB and DhC. The resulting values areplotted in Fig. 7.

Except for variation fromdata scatter, the values forDhN-A,DhN-B,and DhN-C hover around a value of 1.0 until the time when the rstvisible movement (Stage 1) occurs. After rst visible movement,normalized values begin to deviate below a value of 1.0. This de-viation is most pronounced in DhN-A but is soon followed by DhN-Band later by DhN-C. The deviation is believed to be the result ofa decrease in ow resistance (increased hydraulic conductivity) thatresults from the loosening of the surface soil that occurs in Stage 2(i.e., an increase in void ratio). With the ow resistance loweredin the upper portion of the sample, the head drop is concentrated inthe lower portions, and the head drops across the upper portions ofthe sample are proportionally less than the overall differential pres-sure. Further development of the heave and associated downward

Fig. 6. Test pore-pressure and ow data plotted versus time for test on graded Ottawa sand (1 inch 5 25.4 mm)

Fig. 7. Normalized pore-pressure data plotted versus time for test on graded Ottawa sand



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progression of the loosened zone is reected in the continued devia-tions of DhN-B and DhN-C.

The development of sand boils is evident in the normalized plotof DhN-A in Fig. 7, where sudden drops are observed as each boilforms. The sand boils act as vertical drains, further decreasing thevertical ow resistance in the vicinity of the boil. The locations of theboils relative to the PPA port are also evident in the data. The rstand third boils were located near the PPA port, whereas the secondboilwas located near the side of the sample and consequently resultedin a smaller drop. The rise inDhN-A that occurred between the secondand third boils appears to be the result of plugging of the rst boil.

Comparison with Numerical Analysis

As described previously, the downward progression of a zone ofloosened soil (heave progression) is attributed to be the soil samples

response to an increasing hydraulic gradient. To corroborate thistheory, nite-element (FE) seepage analyses were performed tomodel the effects of the loosening soil. Fig. 8 presents several FEmodels designed to model the downward progression of the heavezone in a model consisting of Ottawa 2030 sand. Fig. 8(a) rep-resents the sample at the start of the test, when the entire sample is ata uniformdensity. Figs. 8(be) represent the sample at various stagesof progressive heave observed at specic times in the video. Thelocations and shapes of the upper boundaries of Figs. 8(be) weredetermined from the videos. The loosened zone in the models wasassumed to have a void ratio similar to that measured in the sampleholder following completion of the test. Thus, byknowing the amountof heave Dx and assuming that the loosened void ratio of the soilin the disturbed zone is the same as the disturbed void ratiomeasuredat the end of the test eL, the depth to the bottomof the loosened zone xcan be calculated using

Fig. 8. FE models and results for modeling downward progression of heaved zone (1 inch 5 25.4 mm; 1 foot 5 0.3048 m)



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x 1 eL1 eo x Dx (4)

where eo 5 original void ratio of the undisturbed test specimen.This equation estimates the depth x down to which the soil wouldhave to loosen to have expanded above the top of the soil sampleholder a distance Dx. It should be noted that Eq. (4) assumes thatthe heave is a two-dimensional phenomenon, whereas there areactually three-dimensional (3D) aspects of the heave because ofsloping edges of the heave zone and doming of the heave in thenal phases of the test. The effect of the 3D aspects is small in theearly stages of the heave but increases as the doming develops inthe latter stages. Therefore, the authors have selected Dx valuesfor the analysis to reect the average height of the heave rather thanthe maximum height. It is also acknowledged that the assumptionof a uniform void ratio throughout the loosened zone is likely asimplication of actual conditions. A gradual decrease with depthacross the loosened zone may occur as a result of increasing over-burden pressures, and the change from the original void ratio to theloosened state likely occurs over a zone of nite yet unknownthickness.

The hydraulic conductivities of the soils used in the testing attheir original densities were measured prior to testing and conrmedin the early stages of the tests with the owmeter measurements anddifferential heads. The hydraulic conductivities of the loosed soilswere estimated based on the loosened void ratio and the followingequation proposed by Kozeny (1927):

KLKo

e3L

1 eLe3o

1 eo(5)

where KL 5 loosened hydraulic conductivity; Ko 5 original hy-draulic conductivity; eL 5 loosened void ratio; and eo 5 originalvoid ratio. The measured original (dense) void ratios and hydraulicconductivities (eo andKo) for theOttawa 2030 and graded sands arepresented in Table 2, along with the measured loose void ratios eLand hydraulic conductivities KL calculated using Eq. (5).

The upper boundary condition for each model was dened asa zero-pressure boundary. The bottom boundary conditions weredened as constant-head boundaries, and the constant head valueswere selected tomodel with the differential pressuremeasured acrossthe sample coinciding with the time the respective heave at the top ofthe sample was noted in the video. The sides of the model were no-ow boundaries.

The graphic representations of the results of the analyses arepresented along with the respective models in Fig. 8. It is clear fromFig. 8 that very little head loss occurs in the loosened zone, wherethe hydraulic conductivity is approximately three times that in theundisturbed sand. A plot comparing differential heads at the threeinternal sensor locations (PPA, PPB, and PPC) is presented in Fig. 9.The horizontal axis in Fig. 9 represents the total differential headacross the sample. The vertical axis represents the differential headsbetween the sensor locations and the top of the sample. Plots are

Table 2. Measured and Calculated Void Ratios and Hydraulic Conductivities of 2030 and Graded Ottawa Sand

MaterialMeasured densevoid ratio eo

Measured loosevoid ratio eL

Measured dense sandhydraulic conductivity Ko

Calculated loose sandhydraulic conductivity KL

cm=s ft=s cm=s ft=s

2030 Ottawa sand 0.54 0.84 2:83 1021 9:33 1023 8:93 1024 3:03 1022

Graded Ottawa sand 0.52 0.80 5:03 1022 1:63 1023 1:63 1021 5:33 1023

Fig. 9. Plot comparing measured pore pressures at sensor locations PPA, PPB, and PPC versus results of FE models (1 inch 5 25.4 mm)



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presented for the following: (1) observed differential heads duringtesting, (2) differential heads calculated in the FEM analyses de-scribed earlier, and (3) differential heads calculated in FEM analysesthat assume constant hydraulic conductivity throughout the sample[i.e., similar to the model in Fig. 8(a) with varying constant headsalong the bottom boundary]. For all three internal sensors, the ob-served values correspond well with the values calculated from theFEM models presented in Fig. 8. The observed values also deviatefrom the uniform hydraulic conductivity model values by increasinglylarger amounts as the test progresses. These observations supportthe previously described process of a downward-progressing zoneof loosened soil.

Discussion

Mechanics of Piping Initiation

As described earlier, the sequence of initiation of the piping processobserved in the laboratory tests consists of four observable stages:(1) rst visible movement, (2) heave progression, (3) boil formation,and (4) total heave. The mechanics of this progression can be ex-plained as the soil structure reacting to the increasing hydraulic gra-dient and ow by adjusting its structure with a zone of decreaseddensity in conjunction with preferred seepage channels (sand boils).Thesemechanismswill be examined by considering the interaction ofthe various forces acting on the soil grains as the soil structure reactsto the increasing hydraulic gradient.

Consider the forces acting on the darker-shaded sand grain inFig. 10, which depicts a grain at the exit face of a test sample. Asa vertical hydraulic gradient is imposed on the sample, the forcesacting on the grain include (1) the weight of the grain W , (2) thebuoyant force B, (3) the seepage force S, (4) normal N and shear Fforces at intergrain contacts, and (5) the viscous shear forces fromthe seepingwater Sv. Theweight and buoyant forces remain constantthroughout the test. The intergranular forces will vary as the otherforces on the grain change, increasing or decreasing dependingon the orientation of the grain contact. The seepage force is the resultof the hydraulic gradient across the grain. If the ow is upward, as inthe laboratory tests presented in this paper, the seepage force is theresulting higher hydraulic heads below the grain than above the grainand is proportional to the hydraulic gradient acting across the grain.Themagnitudes of the seepage forces are a function of the size of theinterstitial voids and the velocity of the water seeping through thevoids. As it seeps through a void, the water ows at a maximumvelocity at the center of the void and decreases to near zero adjacent

to the void. According toNavier-Stokes theory, themagnitude of theviscous shear imposed on the grain increases not only as the averagevelocity through the void increases but also as the distance from themaximumvelocity to the grain surface decreases. Thus, as the size ofthe void increases, not only does the velocity of the seeping waterdecrease but, given a larger void, the shear transfer from the waterto the grain also decreases because of the greater distance to themaximum ow velocity.

Initiation of the initial movement of piping development (the rststage described previously) occurs when the seepage force and theviscous shear forces reach the magnitude of the retaining forces(buoyant weight and intergranular forces) on the soil grains at theexit face. At this point, the surface grains are in a state of incipientmovement and begin to move with increasing hydraulic gradient.However, their movement increases the size of the surrounding in-terstitial voids, allowing the velocity to decrease in both the seepagewater and the hydraulic gradient across the grain. As a result, theviscous shear forces and seepage forces decrease, and the grainsreach a state of equilibrium after a small movement or rotation.

As the hydraulic gradient across the sample is again increased,the surface grains move until a maximum void ratio is achieved.Additional increases in the gradient reduces the downward force ofthe upper grains on the next layer of underlying grains, allowingthem to loosen until they have reached a state of equilibrium. Thisprocess continues with increasing gradient across the sample as theloosened zone increases in thickness and the exit face of the sampleprogressively heaves (the second stage).

In some of the tests, the heave progression just described istemporarily interrupted by the formation of a sand boil (the thirdstage). In the tests performed, sand boils formwhen there is a randomalignment of large interstitial voids in the near-surface soil structure,thus forming a preferential low-resistance pathway for seepingwater.The pathway acts similar to a relief well, allowing water from withinthe sample to escape. With the water owing out, the preferentialpathway pressure from increased gradients is relievedwithout furtherprogression of the heave. In graded soils, the pathway may be largeenough to allow the smaller portion of the gradation to be removedfrom the soil matrix and deposited at the surface in the sand boil. Theremoval of the ne grains increases the hydraulic conductivity of thesoil surrounding the preferential pathway, thus increasing the ef-fectiveness of the pathway in providing drainage to the interior of thesample. Sand boils were observed to collapse with increased hy-draulic gradients. This collapse is likely the result of their drainagecapacity being exceeded and the continuation of heave progressiondisturbing the alignment of voids in the preferential pathway.

As long as the heaved zone remains effectively on top of thesample, the process of progressively achieving equilibrium can bemaintained as the remaining downward force of the upper grainscontinues to act on the lower grains. However, when the sides of theheaved mound exceed a stable inclination, sloughing of the sides ofthe heavemoundwill occur. This sloughing removes the overburdenof the loosened zone and prevents equilibrium from being achieved.At this point, the progression of total heave (fourth stage) occursrapidly, as observed in the tests.

Application to Field Conditions

The observed behavior of the soils in the laboratory models can betranslated to expected behavior in the eld. Consider the congu-ration in Fig. 11(a), consisting of a low-permeability layer of silt andclay (often referred to as a blanket layer) overlying a layer of higher-permeability sand. An irregularly shaped defect exists in the blanketlayer. Although the defect is admittedly an odd shape to be found innature, the shape is convenient for the purposes of this discussion.

Fig. 10. Schematic illustration of forces acting on a grain of sand atexit face of soil sample



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The seepage ow in the model is from left to right, as would beimposed by the ow conditions depicted in Fig. 1. As the water riseson the left side of Fig. 1, the differential head imposes increasinghydraulic gradients at the base of the defect in Fig. 11(a). When thegradients reach a critical level, the initial-movement stage identiedin the laboratory models will occur at the base of the defect. Increas-ing differential head will increase the gradients, and the progressive-heave stage will occur, forming a zone of loosened soil below thedefect and lling the lower portion of the defect with similarly loos-ened soil, as depicted in Fig. 11(b). The boil-formation stage also mayoccur intermittently with the progressive-heave stage, as observed insome of the laboratory models. The loosened zone around the base ofthe defect, having higher hydraulic conductivity than the surroundingsoil, will allow more ow to enter the defect. This ow increase,combined with increased ow from increasing differential head, mayincrease the ow velocity in the upper portion of the defect to thepoint where detached soil particles are able to be carried to the groundsurface in uid suspension (i.e., Stokes law phenomenon), as shown inFig. 11(c). Once out of the defect, the sand particles are deposited on theground surface, forming a sand boil. With removal of sand particlesfrom the ow path, the loosened zone can increase in size and prog-ress toward the source of the seepage, further decreasing the seepageresistance and progressing toward a piping failure.

Summary and Conclusions

This paper discusses the results of laboratory modeling designed toidentify and study the mechanisms involved with the initiation ofpiping erosion in sandy soils. The modeling was performed usinga laboratory apparatus designed to measure critical hydraulic con-ditions for the initiation of piping in sandy soils and observe themechanisms associated with the initiation of piping. Several dif-ferent soils were tested in the research to assess the effects of soilindex properties on the critical hydraulic conditions needed to ini-tiate piping. The test results indicated the following: (1) soils withhigher specic gravity showed greater piping resistance, (2) angularsoils showed greater piping resistance, and (3) graded soils showedgreater piping resistance. Hydraulic gradients needed to initiatepiping measured in this research were higher than those indicated bycommonly used relationships (i.e., Terzaghi 1922; Terzaghi andPeck 1948).

Four stages of piping initiation development were identied fromobservations of soil behavior during testing: (1) rst visible move-ment, (2) heave progression, (3) boil formation, and (4) total heave.The four stages represent several mechanisms that occur as the soilreacts to increasing gradients. Stages 1 and 4 represent the start andcompletion of the piping initiation process in the sample. Stages 2

and 3 (heave progression and boil formation) represent means bywhich pore pressure is dissipated from the soil structure to maintainequilibrium with increasing hydraulic gradients.

FE seepage analyses were performed to compare the observedlaboratory results with a theoretical assessment of the downward-heave-progression mechanism. The analyses modeled a downwardprogression of a zone of loosened soil. The hydraulic conductivity ofthe loosened soil was modeled by theoretically adjusting the hy-draulic conductivity of the undisturbed soil to account for the ob-served increase in void ratio. The results of the analysis matchedwell with the observed behavior.

A hypothetical example of how the stages of piping initiationobserved in the laboratory models can take place in a eld conditionwas presented. This example shows how the observed laboratorybehavior can be formulated into a new model for the initiation andprogression of piping in earth structures such as dams and levees.It is anticipated that with further research, the hydraulic conditionsneeded to initiate and sustain the identied stages of piping initiationcan be quantied, and a useful tool for predicting the initiation andprogression of piping in earth structures can be developed.

Acknowledgments

This material is based on work supported by the National ScienceFoundation (NSF) under Grant CMMI 1131518. Any opinions,ndings, and conclusions or recommendations expressed in this ma-terial are those of the authors and not necessarily the views of NSF.

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