experimental study of the grain-flow, fluid-mud transition...

[The Journal of Geology, 2001, volume 109, p. 427–447] � 2001 by The University of Chicago. All rights reserved. 0022-1376/2001/10904-0002$01.00

427

Experimental Study of the Grain-Flow, Fluid-MudTransition in Debris Flows

Jeffrey D. Parsons,1 Kelin X. Whipple, and Alessandro Simoni2

Department of Earth, Atmospheric, and Planetary Sciences, Massachusetts Instituteof Technology, Cambridge, Massachusetts 02139, U.S.A.

(e-mail: [email protected])

A B S T R A C T

We have performed a series of laboratory experiments that clarify the nature of the transition between fluid-mud andgrain-flow behavior. The surface velocity structure and the speed of the nose of debris flows in channels with semi-circular cross sections were measured with several cameras and visual tracers, while the mass flow rate was recordedusing a load cell at the exit chamber. Other rheological tests were used to calculate independently the yield strengthand matrix viscosity of the debris-flow mixture. Shear rates were varied by nearly an order of magnitude for eachmixture by changing the channel radius and slope. Shear rates were significantly higher than expected (6–55 s�1),given the modest slopes examined (10.7�–15.2�). The large values were primarily a result of the concentration of shearinto narrow bands between a central nondeforming plug and the sidewall. As a result, the shear rate of interest wascalculated by using the width of the shear band and the plug velocity, as opposed to the flow depth and front velocity.The slurries exhibited predominantly fluid-mud behavior with finite yield strength and shear-thinning rheologies inthe debris-flow body, while frictional behavior was often observed at the front, or snout. The addition of sand orsmall amounts of clay tended to make the body of the flows behave in a more Bingham-like fashion (i.e., closer toa linear viscous flow for shear stresses exceeding the yield stress). The addition of sand also tended to accentuate thefrictional behavior at the snout. Transition to frictional grain-flow behavior occurred first at the front, for body frictionnumbers on the order of 100. Similar behavior has been observed in an allied field site in the Italian Alps. In theexperiments, it was hypothesized that the snout-grain-flow transition was a result of concentration of the coarsestmaterial at the flow front, reduced shear near the snout, and loss of matrix from the snout to the bed. Regardless ofthe frictional effects at the snout, flow resistance in the body was nearly always regulated by yield-stress and shear-thinning properties, with no discernible boundary slip, despite volumetric sand contents in excess of 50%.

Introduction

Debris flows, gravity-driven masses of poorly sortedrocks, clay, and organic material, are of fundamen-tal societal importance as a result of the intermit-tent havoc they produce in mountainous commu-nities throughout the world (Costa 1984). Becauseof these pressing issues, considerable work has con-centrated on the dynamics of these flows. Recentreviews (Coussot and Meunier 1996; Iverson 1997b)exhaustively describe the current state of knowl-edge in this field. Both reviews divide previousdebris-flow research into two distinct categories.The first, based upon the pioneering work of John-

Manuscript received July 19, 2000; accepted March 5, 2001.1 Current address: School of Oceanography, University of

Washington, 106 MSB, Seattle, Washington 98195-7940.2 Dipartimento di Scienze della Terra e Geo-Ambientali,

Universita di Bologna, Via Zamboni, 67, 40127 Bologna, Italy.

son (1965) and Yano and Daido (1965), assumes thatdebris-flow material behaves as a continuum withan intrinsic yield strength and viscosity. However,these quantities cannot be easily derived from ma-terial properties (e.g., grain-size distribution, watercontent, etc.). Despite this limitation, models basedupon the underlying principles of yield-stress fluidshave been effective at predicting runout in flowsthat lack a significant amount of gravel and boul-ders (Whipple and Dunne 1992; Schwab et al. 1996;Whipple 1997; Huang and Garcıa 1999).

The other path of study has been grounded in themechanics of granular media. Classic research onunimodal grain flows (Bagnold 1954; Savage 1984)has motivated more recent studies that have at-tempted to alter grain-flow constitutive equationsto account for a poorly sorted grain-size distribu-

428 J . D . P A R S O N S E T A L .

tion and/or the presence of pore fluids (Takahashi1981; Suwa 1988; Iverson 1997a, 1997b; to nameonly a few). Grain-flow models, though moregrounded in the physics of grain-grain and grain-fluid interactions than the largely phenomenolog-ical yield-stress models, are complex and often de-pendent on parameters not easily estimatedwithout extensive and intrusive measurements(e.g., matrix permeability, pore-water pressure,etc.). Because both of these “models” (and the el-egant marriage proposed and advocated by Iverson1997b) are theoretical constructs, they have theiradvantages and disadvantages. Moreover, ratherthan simply two distinct models for the same phe-nomenon, the grain-flow and fluid-mud models aremost clearly applicable to distinct types of debrisflow. Much experimental data demonstrates thatsilt-clay slurries are well described by fluid-mudnon-Newtonian rheologies (e.g., O’Brien and Julien1988; Major and Pierson 1992; Coussot and Piau1995). Conversely, recent experimental studies offines-poor gravel and sand mixtures have clearlydemonstrated that frictional grain-flow models arebest applied to these types of flows (e.g., Iverson1997b; Major 1997, 2000). Many natural debrisflows have grain-size distributions intermediate be-tween these well-studied cases. Laboratory exper-iments provide a way to determine the range ofapplicability of each model. Most interesting to usare the situations that stretch the approximationspresent in each of these models (e.g., flows wherepore fluid rheology is heavily influenced by finesbut where sand in the dominant material in theslurry).

As a result, we have attempted to clarify the tran-sition from a friction-dominated grain flow to yield-stress-fluid flow by gradually increasing the silt-clay content of a predominantly sandy slurry.Frictional flows are dominated by grain-grain in-teractions that are strongly modulated by elevateddynamic pore pressures. Yield-strength flows be-have as a fluid-mechanical continuum that can bedescribed by a relatively simple constitutive law(e.g., related to a viscosity and a yield strength, inthe case of a Bingham material). Our study has beenmotivated by an ongoing, comprehensive, obser-vational study in the Italian Alps (Simoni 1998;Berti et al. 1999). The Acquabona debris-flow chan-nel in the Alps exhibits the grain-fluid transitionas fine material (silt, extracted from a marl) iseroded from the downstream reach of the channel.The fine material acts to lubricate the flow, in-creasing runout and initiating what has been in-terpreted to be yield-strength fluid behavior (Bertiet al. 1999).

Rheology of slurries near the frictional fluid tran-sition in sand-dominated debris flows has been ex-plored before (Fairchild 1985; Major and Pierson1992; Coussot and Piau 1995). However, these stud-ies measured rheological parameters in idealizedgeometries (i.e., viscometers of varying complex-ity). Though their data have been useful in obtain-ing rheologic properties for natural materials, theycannot comment on how shear in free-surface flowsdistributes itself and how this affects flow resis-tance and the appearance of the debris flow and itsdeposit.

Limited work on more natural, free-surface flowsalso has been performed. These experiments havediffered dramatically, depending on the approach.Small-scale devices have typically used predomi-nantly muddy slurries, with little to no sand(Schmeeckle 1992; Coussot 1994), while larger ex-periments (Iverson and LaHusen 1993; Iverson1997a; Major 1997) have typically used materialthat lacked a significant silt or clay component.Our experiments and analyses rigorously examinethe granular-fluid transition in sandy, but fines-richslurries (like earlier studies: Major and Pierson1992; Coussot and Piau 1995) in a more natural,free-surface geometry. Because of the spatial vari-ability of shear rate, we will separately focus ontwo different portions of the flow: the snout andthe quasi-steady body.

Experimental Setup and Procedure

Our experiments were performed in a 10-m longflume in the Experimental Sedimentology and Geo-morphology Laboratory at MIT. Each experimentconsisted of several runs of the same material, inorder to study a single slurry mixture under a va-riety of conditions (i.e., channel slope and width).The facility (fig. 1) consists of a supply tank (6 mabove the laboratory floor) that feeds one of twosemicircular channels roughened with a fixed(glued), well-sorted sand ( mm). The supplyD p 150

tank has a valve at its base that opens from the topof the tank. The mixture is guided to the appro-priate channel by canvas tubing. The channel slopecan vary from 10.7� to 15.2�. The slurry was main-tained in a well-mixed condition until just beforeeach run with a mixer drill inserted into the tank.(Tests that confirmed homogeneity in the supplytank are discussed in the final section of theanalysis.)

Monitoring the flow consisted of two parts. First,surface velocity profiles were obtained with twocamcorders at 5 and 8 m down the channel. Blackbeads that “floated” on the debris-flow surface were

Journal of Geology G R A I N - F L O W , F L U I D - M U D T R A N S I T I O N 429

Figure 1. Schematic of the experimental facility

used as tracers. More than 50 beads were laid downalong a flow-perpendicular line at a time. Typically,10 lines were laid down per experimental run, eventhough run times were often less than a minutelong. Lines were chosen for analysis depending onthe extent to which the channel was full. Becauseof the large quantity of material required to fill the10-m long channel (nearly 500 kg), the flow wasonly bankfull for the entire length for a few sec-onds. In the clay-rich experiments, only two lineswere observed during bankfull flow. As a result,measurement errors in these experiments (experi-ments 6 and 7) were large. In all of the other ex-periments, however, the velocity was well resolvedand assessment of error was straightforward, withrespect to both precision and accuracy (assumed tobe equivalent to repeatability).

Digitized video taken during the experiments al-lowed for measurement of the displacement ofbeads between frames (1/30 s for standard video).The distances were measured in pixels, whichcould be related to length with a photographed rulerusing image-processing software. More than 20 ve-locity measurements could be obtained along thechannel cross section with this technique. Errorsin precision and repeatability (from one line to thenext) were small and reflected in the error esti-mates of the plug velocity in table 1.

Mass flow rate of the slurry out of the channelwas measured using a load cell affixed to a sus-pended hopper at the base. As the mix poured intothe suspended hopper, the weight increased and theanalog data from the load cell was transferred tothe computer via an A/D board. The A/D boarddigitized the data at a rate of 4 Hz. Even in theshortest-lived experiments, steady flow was main-tained for 2–3 s, making 4 Hz more than sufficientfor a mass-flow measurement. Error based on the

standard deviation of the mean-flow rate duringsteady-flow periods is shown along with the mean-flow results in table 1.

Grain-size distributions (fig. 2) in the experi-ments were based on field studies in the Acquabonachannel, an active debris-flow channel in the Ital-ian Alps (Berti et al. 1999). The Acquabona channelhas been monitored for several years, and numerousdebris flows have been observed during this time(Genevois et al. 1999). Fines are incorporated as theflows run through a marl section. As a result, theflow becomes fines-laden (silt-clay contents in ex-cess of 25%) and exhibits fluid-like behavior (e.g.,no slip at the sidewall) while the front remainsgranular. Describing the rheologic transition in thisparticular field area was one of the goals of theexperiments.

To simulate the extremely wide range (nearlyfour orders of magnitude) of grain sizes present inour mixtures (fig. 2), material for the experimentscame from various sources. Note that the system-atic variation in grain-size distribution of the ex-perimental mixtures is achieved primarily by sub-stituting sand for silt. Clay content is heldconstant at 2.5% by weight of the solids. The finematerial (silt and finest sand) used was obtainedfrom U.S. Silica in Ottawa, Ill., while the coarsematerial was a washed concrete sand (relativelyround alluvium) purchased from a local concretesupplier. Clay (kaolinite) was also obtained fromthe same concrete supplier. Kaolinite is not anactive clay (requires less water, binds less strongly,etc.), particularly compared to other commonclays (e.g., bentonite). The dominant portion ofthe material in the finer mixtures, however, con-sisted of the silts obtained from U.S. Silica. Thesesilts are derived from crushed silica fragments andare highly angular, similar to the landslide ma-terial examined by Berti et al. (1999) and Genevoiset al. (1999). The debris flows observed by theseresearchers contained clasts up to meter scale.Only the fraction of material finer than 5 mm wassimulated in our experiments. In addition, our ex-periments involve flow depths about one order ofmagnitude smaller than typical debris flows. Theramifications of these limitations are elaboratedupon in “Discussion.”

To obtain homogeneous, well-mixed slurrieswithout sedimentation problems in the mixer, weadded water sequentially (usually in 10-kg amounts)to 20–30 kg of fine material (clays first, then silt)mixing thoroughly with a mixer blade attached to ahand drill at each step. Sand was then added incre-mentally in a large mortar mixer with a smallamount of additional water. The full debris mixture

430 J . D . P A R S O N S E T A L .

Table 1. Experimental Conditions

Experiment Material w R Slope (v)Snouteffect? Up Usnout Q Rpp (∼Rcr)

1a F 16.8 .073 10.7 None .24 (8.3) .22 (1.8) .00189 (1.8) .0397 (13)1b .073 15.2 None 1.17 (10.2) .87 (1.0) .00692 (1.3) .0295 (30)1c .05 15.2 Some .26 (7.8) .16 (1.7) .00061 (.4) .0322 (16)2a MF 14.8 .073 10.7 None .83 (4.8) .57 (.9) .00391 (.6) .0366 (19)2b .073 13.7 None 1.69 (2.3) 1.22 (.7) .00988 (3.7) .0327 (28)2c .05 13.7 Some .30 (8.3) .16 (.3) .00096 (.4) .0321 (13)3a MC 13.8 .073 12.2 Strong .65 (9.6) .45 (1.5) .00448 (1.6) .0409 (9.1)3b .073 15.2 Strong 1.30 (9.0) 1.03 (2.6) .00888 (5.1) .0314 (24)4a C 13.9 .073 15.2 Strong .41 (32) .30 (2.5) .00275 (15) .0545 (30)5a M 14.2 .073 12.2 Strong .94 (16) .61 (.7) .00554 (1.2) .0375 (15)5a2 .073 (wet) 12.2 Strong 1.02 (12) .77 (.7) .00649 (3.6) .0422 (21)5b .05 15.2 Strong .26 (9.0) .15 (1.4) .00081 (1.8) .0343 (18)5b2 .05 (wet) 15.2 Strong .27 (9.5) .22 (6.3) .00076 (1.0) .0326 (20)6a MC � 2 15.1 .073 12.2 Some 1.02 (25) 1.10 (.8) .00573 (1.7) .0401 (6.9)6b .073 15.2 Some 1.86 (6.7) 1.19 (.7) .00963 (1.2) .0330 (21)6c .05 15.2 Strong .23 (8.0) .08 (.9) .00026 (2.1) .0318 (25)7a MC � 3 17 .073 10.7 Some .91 (15) .99 (2.0) .00600 (4.8) .0371 (25)7b .073 15.2 None 2.45 (4.5) 1.79 (1.3) .01137 (5.9) .0304 (30)7c .05 15.2 Strong .57 (12) .36 (2.5) .00210 (1.4) .0311 (16)8a F 17.6 .073 10.7 Some .40 (8.7) .32 (3.6) .00200 (2.0) .0396 (18)8b .073 12.2 None .42 (2.8) .29 (2.7) .00227 (.3) .0346 (12)8c .073 13.7 None 1.06 (3.3) .43 (1.8) .00499 (2.7) .0302 (33)8d .05 13.7 Strong .16 (1.8) .10 (.9) .00031 (1.9) .0259 (15)8e .05 15.2 Strong .16 (1.9) .11 (1.9) .00047 (1.1) .0238 (23)9a CMC 14.4 .05 15.2 Strong,

stoppedNA NA NA NA

9b .05 15.2 Strong,stopped

NA NA NA NA

10 M 13.7 .05, .073 13.7 Strong,stopped

NA NA NA NA

Note. Material abbreviations correspond to the grain-size distributions found in figure 2. The “�” on experiments 6 and 7 indicatesthe percentage by mass of added clay (in addition to the 2.5% present in all experiments). “Water content” (w) is the percentage ofmass of water divided by the total mass of the slurry. “Wet” indicates a thin layer of wet material left on by a previous run (in thepipe radius column). Slope is in degrees. “Stopped” in the snout-effect column means that the flow was arrested before it reachedthe tailbox (and load-cell). The Rpp column is the observed plug radius, which is a close approximation to the actual plug thicknessRc. The subtle difference is discussed in “Analysis.” Plug and snout velocities, flow discharges, and plug radii are all in meter-kilogram-seconds, with percentage error in parentheses. Error is representative of both precision and accuracy, which is determinedfrom deviations in multiple measurements. “NA” indicates not applicable or not measured.

was kept well mixed in the mortar mixer until im-mediately before each experimental run. Though awell-mixed state is not reflective of the initial stagesof failure and conversion into a debris flow (Iverson1997b), it is representative of the state of the fluidin distal reaches of debris-flow runout in channelsand on fan surfaces where these flows generally pre-sent the greatest hazard (e.g., Costa 1984). Moreover,the flows observed by Berti et al. (1999) were in awell-mixed state where the grain-fluid transitionoccurred.

Experimental Results

Experimental conditions for the flows are shownin table 1; symbols are defined in table 2. All of theslurries had essentially the same density, varyingbetween 2100 and 2300 kg m�3. In all of the ex-periments, a high-velocity, unsheared core, or plug,

occupied a significant portion of the center of thechannel, with a rapidly sheared section between itand the sidewall. All flows were laminar. Thesefluid-like flows appeared to reach a steady state,particularly in the body, within the first few metersof the channel. Steady state flow was verified bythe synchronization of multiple cameras and theload-cell measurements. There was also no observ-able basal or sidewall slip except where frictionallylocked snouts formed in experiments with thecoarser mixtures and lower boundary shearstresses. Where frictional snouts either did notform or had not formed yet, lack of basal slip causeda conveyor-belt-like flow at the front. Conveyor-belt behavior has been seen previously by other re-searchers studying subaerial mudflows (e.g., Li etal. 1983; Mohrig et al. 1998). All of these featurescan be seen from a sequence in figure 3.

In some experiments, frictionally locked snouts


Figure 2. Grain-size distributions of all debris flowsstudied in the experiments. The field grain-size distri-butions, with material 15 mm removed, are taken fromBerti et al. (1999). Table 2. List of Symbols

Symbol Definition

D50 Mean grain diameter (L)err Subscript that denotes measurement error

of a particular quantity (in percent)g Gravitational acceleration (L T�2)h Flow depth (L)K Linear coefficient in Herschel-Bulkley

modeln Exponent in Herschel-Bulkley modelNBAG Bagnold numberNf Friction numberNSAV Savage numberQ Volumetric flow rate (L3 T�1)r Radial direction (L)ref Subscript that denotes reference valueR Channel radius (L)Rcr Nondeforming plug radius (L)Rpp Apparent plug, or pseudoplug, thickness

(L)Terr Total average error used in minimization

routineU Streamwise velocityUp Plug velocity (L/T)URMSx Root-mean-square uncertainty calculated

in the parameter xvs Volumetric solids concentrationd Grain diameter in dimensionless number

calculations (L)g Shear rate (1/T)m Matrix viscosity (ML�1 T�1)v Channel slope, in degreesr Overall density, 2100–2300 kg/m3

rs Density of solids, 2650 kg/m3

rf Density of interstitial fluid (estimatedfrom fines content and bulk density)

to Yield strength (ML�1 T�2)tb Bed shear stress (ML�1 T�2)trx Shear stress acting in the down-channel

direction

formed and tended to impede flow runout (as seenin boulder- and gravel-rich debris flows in the field:Suwa and Okuda 1983; Whipple 1994; and in large-scale flume experiments: Iverson 1997b; Major1997). These frictional snouts effectively formeddams that moved by basal sliding without internaldeformation unless by faulting (fig. 4, last frame).These dams were pushed forward by the pressureof the more fluid and rapidly moving body of theflow, which ponded behind the snout, causing localdepths to increase and producing the characteristicbulbous shape of the snout. These frozen snoutswould grow from the front backwards as additionalmaterial was incorporated into the snout from be-hind. In some runs this “snout effect” was so pro-nounced that the snout eventually grew in size tothe point that the pressure from behind was insuf-ficient to propel it forward (fig. 4). Beyond thispoint, any continued discharge of material from thesupply tank was forced over the bank. The “snouteffect” was so strong with the coarsest mixture (fig.2) that only in the run in which the slurry wasconfined in the largest channel on the steepest in-cline did the flow traverse the length of the flumewithout being arrested by the snout (experiment4A; table 1).

It is important to note, however, that in allcases—even those with a pronounced snout ef-fect—the more rapidly sheared body of the flowremained fluid-like with no observable boundaryslip. Thus, it appears that our experimental flowsvaried from macroviscous (no snout effect) to fric-

tional (e.g., Iverson 1997b). The onset of frictionalbehavior appeared to be favored by coarser debrismixtures and lower boundary shear stresses (table1), qualitatively consistent with the dimensionalanalysis presented by Iverson (1997b). A quantita-tive assessment of flow regimes and an analysis ofthe rheology of the rapidly sheared body of theflows are presented in “Discussion.”

In addition to the results from the flume exper-iments, several other tests were performed on theslurry mixtures. Depositional board tests were per-formed to assess the yield strength of the variousslurries. In these tests, a board (roughened in a sim-ilar manner to the channels in the flume) was setat three prescribed slopes (at approximately 8�, 10�,and 12�). The expression of Johnson (1970), t po

, where to is the effective yield stress,t p rgh sin vb

tb is the basal shear stress, g is the gravitationalacceleration, h is the flow depth (in this case, the

432 J . D . P A R S O N S E T A L .

Figure 3. Sequence of frames illustrating smooth, well-behaved debris flow. The first two frames indicate the“conveyor belt” of material circulating at the front (i.e., the tracers traveling to the snout are subsequently buried).Later frames illustrate the no-slip behavior at the sidewalls and the significant plug in the center of the channel. Theframes shown were taken approximately 1 s apart during experiment 2 (for experimental conditions, see table 1). Thepipe shown is 0.075 m in radius.

thickness of a rapidly formed deposit), and v is thebed slope, was used to estimate the effective yieldstress of each mix. After the slurry was pouredquickly out over most of the board, the depositfroze en masse, and the depth was measured in sev-eral locations (two to four) with a ruler (accuracy,1 mm). The deposits on the depositional board werethin, tabular, and lobate, as expected for a visco-plastic material. Thickness variations were gener-ally less than 10% away from the periphery of thedeposit. More significantly, average deposit thick-

ness was found to be inversely proportional to sinv

( in all cases), such that estimated yield2R ≥ 0.96strengths were constant (!10% variation from themean) over the range of slopes used. This findingimplies that the constant yield strength model isboth relevant and accurate. Mean values and 1j

errors (%) are given in table 3. Estimated yieldstrengths also varied in a consistent manner, risingas the mix became coarser.

Viscosities of the “matrix” component of the de-bris mixtures were measured with a Brookfield


Figure 4. Sequence of frames illustrating arresting snout (experiment 4C). Time between the first frame and thesecond is approximately 3 s, while the third frame is 15 s after the second. The pipe shown is the small pipe (0.05m in radius).

Model LVF Dial Viscometer (an adjustable, cylin-drical viscometer). We assumed that the matrixconsisted of all of the material that was silt andclay sized (i.e., mm). We also assumed thatD ! 63it contained all of the water that was present in thebulk mix. Because some water will bind to sand

grains, our matrix viscosity estimates will be con-servative lower bounds. A range of water contentswas examined for each matrix. Note that, becausethe percentage of clay in the total mixture was heldconstant, the relative abundance of clay in the ma-trix varies systematically, becoming greater in the

434 J . D . P A R S O N S E T A L .

Table 3. Results of the Tilting Board and ViscometerTests

Experiment(mix)

to

(Pa) r2mmatrix

(Pa-s)

1 (fine) 54 (4) .99 1.22 (medium fine) 55 (3) .98 .93 (medium coarse) 98 (2) 1 .44 (coarse) 113 (2) .97 .065 (medium) 67 (5) .99 .46 (medium coarse �

2% clay) 121 (3) .97 .57 (medium coarse �

3% clay) 73 (8) .96 .4

Note. The r2 values for the yield strength are those for thelinear relationship of Johnson (1970), , wheret p t p rgh sin vo b

to is the effective yield stress, tb is the basal shear stress, g isthe gravitational acceleration, h is the flow depth (in this case,the thickness of a rapidly-formed deposit), and v is the bed slope.Matrix viscosity measurements are reflective of interpolationsbetween values measured separately. The 1j variations of yieldstrengths in parentheses are in Pa. Error in matrix viscositymeasurements is high and can be considered roughly one orderof magnitude. Units are all meter-kilogram-seconds.

Figure 5. Comparison of various empirical relation-ships with the data obtained in this study. “OJ (1988)”refers to O’Brien and Julien (1988). The Major and Pierson(1992) relationship is for their material !63 mm (i.e., siltand clay only). Thomas (1965) is the relationship usedby Iverson (1997b), and Kang and Zhang (1980) representsthe relationship for a poorly sorted silt.

coarser mixtures. For each matrix composition, asthe water content was increased, measured viscos-ities decreased exponentially. This observation isconsistent with many previous studies (fig. 5). Be-cause the water content of the total mix could notbe prescribed exactly beforehand, the values in ta-ble 3 were interpolated from the data in figure 5.The only exception was for the coarsest mix (ex-periment 4), where nearly all of the material wassand. In this case, the viscosity had to be extrap-olated because of the very dilute nature of the ma-trix in the coarse debris slurry. However, the as-sumption that none of the water was bound to sandgrains is probably poor.

As can be seen in figure 5, our matrix viscosityestimates are in good agreement with other studies.In all cases, except the study by Schmeeckle (1992),decreasing clay contents are characterized by (1)lower viscosities for a given water content and (2)an increased sensitivity to water content (i.e., theslope of the lines on the semilog plot steepen withlower clay contents). In both these respects, ourmatrix slurries are intermediate between the rela-tively clay-rich slurries of O’Brien and Julien (1988)and the clay-poor slurries of Major and Pierson(1992). The more clay-rich matrix of the coarsemixture approximates the 5%–7% clay data ofO’Brien and Julien (1988). Similarly, the matrix ofthe fine mixture is approaching the relation givenby Major and Pierson (1992) for their clay-poor,fines-only sample (!63 mm; fig. 5). This degree ofconcurrence gives us confidence in the viscosityestimates obtained with the Brookfield viscometer.

As a matter of speculation, the well-sorted, veryfine-grained nature of the silts used by Schmeeckle(1992), which included a considerable fraction ofangular, clay-sized (∼1 mm) silica fragments, mayexplain the unusual low sensitivity to water con-tent in this clay-mineral-free material. Finally, it isnotable that the empirical relation given by Tho-mas (1965) for suspensions of uniform sphericalparticles grossly underpredicts the viscosity (2–3orders of magnitude) of slurries of poorly sorted andangular natural debris. The underprediction isgreatest for slurries containing even small amountsof clay.

Analysis

Dimensional Analysis of Flow Regime. There arethree sources of impedance to motion in theseflows: collisional, frictional, and viscous. Depend-ing on the strength of each of these forces, the flowwill evolve differently. Iverson (1997b) formulatedand summarized the three dimensionless variablesthat describe the relationship between these threeeffects. He also presented preliminary constraintson the magnitudes at which these dimensionlessparameters transition from one force being domi-nant over the other. The mathematical expressions


describing each of these parameters are (Iverson1997b) the Bagnold number (the ratio of collisionalto viscous forces)

2v r d gssN p , (1a)BAG ( )1 � v ms

the Savage number (the ratio of collisional to fric-tional forces

2 2r d gsN p , (1b)SAV (r � r )gh tan fs f

and the friction number (the ratio of frictional toviscous forces)

v (r � r )gh tan fs fsN p , (1c)f (1 � v )gms

where g denotes the shear rate, rs the clast density(2.6 kg m�3 for quartz, the material used), rf theestimated interstitial fluid density, d the meangrain size (table 1), the mean volume fraction ofvs

solids (related to the water content via the sub-merged specific gravity of the clasts; see table 1), m

the viscosity of the interstitial fluid (table 3), h theflow depth (table 1), f the angle of internal friction(assumed to be 42�; Simoni 1998), and g the grav-itational acceleration (9.81 m s�1). According toavailable experimental constraints (albeit largelyrestricted to experiments with unimodal sphericalparticles), collisional forces dominate over viscousforces for , collisional forces dominateN 1 200BAG

over frictional forces for , and frictionalN 1 0.1SAV

forces dominate over viscous forces for N 1 2000f

(Bagnold 1954; Savage and Hutter 1989; Iverson1997b).

Following Iverson (1997b), the interstitial fluiddensity was estimated by assuming the entire massof silt and clay (and no sand) contributed to theinterstitial fluid. That is, if the sand content was100%, the interstitial fluid density would be thedensity of water, while if there were no sand andonly fines, the interstitial fluid density would beequal to the bulk density.

All of these quantities were either measured orestimated directly. The only exception is the shearrate g, which has to be calculated. Assessments ofnatural debris flows typically estimate g by divid-ing the snout or plug velocity by the flow depth(e.g., Phillips and Davies 1991; Iverson 1997b). Pre-vious rheological work (Major and Pierson 1992;Coussot and Piau 1995) has constrained the valueof g through the use of constructed geometries. Be-cause of the direct flow visualization in our exper-

iments, we were able to use the shear rate defini-tion that regulates runout in a free-surface flow.From our observations, the relevant shear rate isdefined by the ratio of the plug velocity and theshear width (the distance between the plug and thesidewall). Because the plug does not participate inthe shearing process, it should not be included inthe calculation. The shear width was defined bythe distance to the sidewall where the measuredvelocity profile was “indistinguishable” from theplug speed. In the next section, the difference be-tween this “pseudoplug” and an actual rheologicalplug (i.e., where shear stress is less than the ma-terial yield strength) will be discussed at length. Acomparison was made (table 4) of these two differ-ent methods for obtaining the shear rate, along withthe calculations of the various dimensionless pa-rameters. The value we propose presents consid-erably larger values of the shear rate than the tra-ditional method. Flow depth and snout velocity are,however, probably more representative of the con-ditions at the snout, where the entire cross sectionis deformed and the fluid velocities are smaller.

Regardless of definition of the shear rate, dimen-sional analysis using the critical Bagnold, Savage,and friction numbers places our flows either in theviscous regime or near the transition from viscousto frictional regimes (table 4). Body friction num-bers (Nf1) predict viscous behavior for all except thecoarsest mixture (experiment 4), which has a fric-tion number near the threshold value. Snout fric-tion numbers (Nf2) predict important frictional ef-fects for the medium, medium-coarse, and coarsedebris mixtures, at least in configurations withlower boundary shear stresses (gentler flume slopesand smaller channel radii). For the coarsest mix-ture—which failed to traverse the length of theflume except when run down the larger channel setat the steepest inclination (experiment 4A)—thesnout friction number is well into the frictionalrange. Contrary to the speculations of Iverson(1997b) about the grain-size characteristics of flowslikely to exhibit macroviscous behavior, most ofour flows were predominantly sandy with low wa-ter contents. We believe there are our two causesfor the deviation from previous analyses. First, theinterstitial viscosities of our slurries (table 3) areconsiderably higher than some previous estimates(Thomas 1965; Schmeeckle 1992) but not all(O’Brien and Julien 1988; fig. 5). The high viscosi-ties are most likely a result of the poorly sorted,highly angular makeup of the constituent silts andthe presence of a minor but nonnegligible amountof clay. Second, the relevant shear rates in our free-surface flows were considerably higher than the 1–5

436 J . D . P A R S O N S E T A L .

Figure 6. Diagram illustrating Bingham, shear-thin-ning, and shear-thickening behavior.

Table 4. Comparison of Different Shear Rate Defini-tions and Their Resulting Friction Numbers

Experimentrun g1 g2 Nf1 Nf2 NBAG NSAV

1A 6.8 2.9 164 380 .002 7.1E-061B 25.7 11.6 43 96 .007 1.0E-041C 14.6 3.2 51 232 .004 4.9E-052A 21.6 7.6 89 253 .028 2.3E-042B 40.0 16.3 48 118 .052 7.9E-042C 16.8 3.2 76 401 .022 2.1E-043A 19.1 6.0 271 862 .107 3.2E-043B 29.8 13.7 173 377 .168 7.9E-044A 20.0 4.0 1868 9338 1.672 7.9E-045A 25.1 8.1 190 587 .095 3.9E-045A2 31.1 10.3 153 465 .117 5.9E-045B 16.6 3.0 192 1061 .063 2.5E-045B2 15.5 4.4 205 723 .059 2.2E-046A 29.2 14.7 127 254 .118 7.5E-046B 44.3 15.9 84 235 .179 1.7E-036C 12.6 1.6 196 1552 .051 2.1E-047A 24.0 13.2 168 306 .106 5.1E-047B 54.9 23.9 74 169 .241 2.7E-037C 30.2 7.2 89 374 .133 1.2E-038A 11.3 4.3 118 312 .003 2.0E-058B 10.4 3.9 128 344 .003 1.7E-058C 23.7 5.7 56 232 .007 8.6E-058D 6.6 2.0 134 444 .002 1.0E-058E 6.1 2.2 145 403 .002 8.6E-06

Note. Indices indicate the two different shear definitions dis-cussed in the text. They are (1) traditional estimate: snout ve-locity and flow depth, (2) proposed value: plug velocity and shearwidth. Savage and Bagnold numbers are calculated with theshear rate defined by the shear width and plug velocity. Onlyexperiments where flow discharge was obtained are shown (i.e.,snout-stopping flows were not included).

s�1 range that has been argued by some to be rel-evant to debris-flow runout in channels and on fansurfaces (O’Brien and Julien 1988; Phillips and Da-vies 1991; Major and Pierson 1992).

Rheology of the Debris-Flow Snout. As describedqualitatively earlier, frictional effects were ob-served at the front or snout of many of the exper-imental flows. Because of the increased frictionnumber there (Nf2, defined by the snout velocityand flow depth at the snout) and other sorting ef-fects to be discussed below, the flow transformedfrom fluid to frictional behavior from the snoutbackward. This flow transition could be seen qual-itatively in “strong-snout-effect” runs (seen in table1) as a freezing or interlocking in a large region nearthe snout (that moves by basal sliding), while someruns simply appeared to be slowed near the snoutand the conveyor belt action near the front wasreduced (“some snout effect”). In the most fluid-like flows (“no snout effect”; table 1), no frictionaleffects were observed anywhere.

Dividing the runs into these three categories, acritical friction number can be postulated. All butone of the strong-snout-effect runs have body fric-

tion numbers in excess of 130, and all but two havesnout friction numbers above 400. Neither bodynor snout friction numbers of the no-snout-effectand some-snout-effect runs are statistically sepa-rable. However, the onset of some frictional be-havior appears to occur at body friction numbersof ∼100 and snout friction numbers of ∼250 (table4). The threshold value (∼100) is considerably lowerthan the value (∼2000) obtained by Iverson (1997b)from a combination of more idealized experiments(Bagnold 1954; Savage and Hutter 1989). Althoughthe large error in the matrix viscosity estimate(conservatively up to an order of magnitude, despiteour agreement with previously published esti-mates; fig. 5) makes definitive calculations of atransition friction number impossible, the transi-tion friction number does appear (within experi-mental error) to be significantly smaller than thepreviously accepted estimate. Perhaps more im-portant is the observation that the transition to fric-tional behavior appears to be restricted to theslowly deforming snout region and occurs in flowsthat otherwise behave in a macroviscous manner.Thus, for many transitional flows the relative im-portance of fluid rheology and the frictional behav-ior of the snout may be difficult to assess.

Rheology of the Quasi-Steady Debris-Flow Body.Because of the no-slip behavior at the sidewall andthe particular combination of dimensionless pa-rameters in our flows, it was readily apparent thatthe bodies of the flows, particularly in the shearingregion, were predominantly fluid-like. Considera-ble work has concentrated on the rheology of fluidsthat have a significant sand component. Early stud-


ies (O’Brien and Julien 1988; Phillips and Davies1991) demonstrated the strong dependence of fines(silt-clay) content and water content. They alsodemonstrated that rheology was strongly depen-dent on shear rate and postulated that low shearrates ( s�1) were most relevant to natural de-g ! 10bris flows. In later work, Coussot and Piau (1995)used a field rheometer on Alpine debris-flow ma-terials, quite similar to those simulated here, toexamine the utility of the Herschel-Bulkley model.The Herschel-Bulkley model is a generalized for-mulation of continuum behavior in a yield-stressfluid. Figure 6 illustrates the difference between thevarious models discussed. Coussot and Piau (1995)found that their samples, sieved at 2 cm, possessedrelatively high yield strengths (100–400 Pa) and ex-hibited strongly shear-thinning behavior (n p

–0.35). In other experiments, Major and Pierson0.15(1992) found shear-thinning behavior ( –0.9)n p 0.3for silt/clay-dominated slurries and Bingham be-havior (approximately ) for highly shearedn p 1( s�1) sandy slurries.g 1 5

Following earlier work (Major and Pierson 1992;Coussot and Piau 1995), we characterized our flowsusing the general Herschel-Bulkley model. The der-ivation of characteristics (plug velocity, etc.) forHerschel-Bulkley fluids in semicircular channelshas been presented before (e.g., appendix in Mohriget al. 1999). However, Mohrig et al. (1999) did notexploit the analysis for the assessment of postyieldproperties but only for an estimation of the yieldstrength. The applicability of a constant yield-strength model to the experimental slurries wasdemonstrated by the tilting board analysis (table 3).It will be independently verified below.

We begin with the general Herschel-Bulkleymodel for non-Newtonian fluids in steady, uniformopen channel flow of semicircular cross section:

n

dut � t p K ; t ≥ t , (2a)x o x o( )dr

1t p rgr sin v, (2b)x 2

where tx denotes shear stress acting in the down-channel direction (x), to is the yield stress, K is alinear coefficient, which for Bingham behavior( ) corresponds to a viscosity, u is the down-n p 1stream velocity, r is the radial direction ( atr p 0the channel axis and at the wall), r is ther p Rbulk density, g is the gravitational acceleration, v

is the channel slope, and n is a positive constant.A nondeforming plug region forms wherever t ≤x

(or ) (Johnson 1965). The variable Rcr is de-t r ≤ Ro cr

fined by

2toR p . (3)crrg sin v

Using equations (2b) and (3), a nondimensional plugradius may be written

R tcr op , (4)R tb

where tb is the boundary shear stress (at ).r p RIntegrating equations (2) once and applying a no-slip boundary condition gives relations for thesteady, uniform, radial velocity profile,

1/n(t /K) RbU(r) p1 � 1/n

1�1/n 1�1/n# [(1 � t /t ) � (r/R � t /t ) ], (5a)o b o b

1/n(t /K) Rb 1�1/nU p (1 p t /t ) , (5b)p o b1 � 1/n

where Up is the plug velocity. Integrating equation(5) in r and around the arc of the semicircular chan-nel section gives a relation for flow discharge (Q):

1/n 3(t /K) pRbQ p1 � 1/n

1�1/n 2�1/n(1 � t /t ) (1 � t /t )o b o b# � (6)[ 2 2 � 1/n

3�1/n(1 � t/t)� .](2 � 1/n)(3 � 1/n)

Thus, the problem involves three equations ([4],[5b], [6]) and three unknown rheological properties(to, K, n). Nondeforming plug radius Rcr, plug ve-locity Up, and flow discharge Q of our experimentscan be found with error estimates in table 1. It ispossible to calculate all of these rheological prop-erties with entirely nonintrusive measurements.Because of the remote nature of the measurements,the analysis herein could be extended to in siturheological examination of field-scale flows, if theproper location was chosen (i.e., a muddy, laminarflow in a nearly semicircular channel).

A comparison of flow discharge (measured at theflume exit) and surface velocity data affords a pre-liminary test of the hypothesis that the quasi-steady stage of the experimental flows (i.e., well

438 J . D . P A R S O N S E T A L .

Figure 7. Relationship between relative bed shear stressand relative plug thickness for each mix examined (alongwith experimental error bars). Solid line represents thatexpected for constant yield strength behavior (eq. [4]).The dashed line is reflective of the general trend expectedfrom a frictionally dominated flow.

behind the frictional snout for transitional flows)could be well described as homogeneous fluids withnon-Newtonian rheology. The velocity field of alaminar, homogeneous fluid in a channel with asemicircular cross section is expected to be axisym-metric (e.g., Johnson 1965; eqq. [2]–[6]). Frictionalgrain flows by comparison will not exhibit axisym-metric velocity fields because of the increased nor-mal forces in the deepest part of the channel. Thus,a radial integration of the surface velocity profileshould match measured discharges if and only ifthe material is behaving as a homogeneous fluid.In all experiments, integration of the velocity re-produced the independently measured flow dis-charge within the accumulated error of the surfacevelocity measurements (i.e., 20%). Although thisprovides some measure of support to the applica-tion of a homogeneous-fluid rheology, the test isnot a strong one; at the limited depths and rapidshear rates of our experimental flows the deviationfrom axisymmetry in frictional grain flows may notbe large. A more convincing test is whether con-stant values of (to, K, n) can be found that explainall the experimental data over the full range of flowconditions tested, including the tilting board testsfor material yield strength.

We begin by testing the validity of the constantyield strength assumption based on observed plugthickness as a function of imposed basal shearstress. The test is critically important because, asIverson (1997b) and others have pointed out, theexistence of a nondeforming plug does not neces-sarily imply the existence of a finite yield strength;any number of granular flow models without a plas-tic yield strength predict nondeforming plugs in theright circumstances. Equation (4) can be rewrittenin a nondimensional form that allows us to testthis assumption directly. Normalizing both sidesof equation (4) by a reference value gives therelation

R /R t /t tcr o b brefp p , (7)(R /R) (t /t ) tcr ref o b ref b

where the second equals sign is true if and only ifthe yield strength is constant over the range of flowconditions tested. Equation (7) predicts normalizedplug thickness to decrease monotonically with in-creasing normalized boundary shear stress. For allruns in a given experiment (e.g., experiment8A–8E), we take the reference value to be that mea-sured for the run with the lowest boundary shearstress (e.g., experiment 8A). The normalized plugthickness data for all runs collapses to a singlecurve that is well predicted by equation (7) (fig. 7).

Granular flows are expected to have the oppositebehavior, because it is the shear band width that isexpected to remain constant with channel radiusfor granular flows (Savage 1984; Haff 1986). Thisimplies that normalized plug thickness would in-crease rapidly with channel radius, as illustratedschematically on figure 7. As can be seen in thefigure, all but one of the runs agree with a constantyield strength model within experimental error. Al-though our discussion of expected plug thicknessvariations for a granular material is highly simpli-fied, there is no experimental basis to reject theconstant yield strength assumption.

Most significant to our analysis was the deter-mination of the postyield properties (K, n). Becauseequations (4), (5b), and (6) could be solved for (to,K, n) for each experimental run, the properties ofeach mix were overdetermined (as the result of thethree to five runs per mixture). The solution of theequations is therefore a minimization problem. Tofind best-fit combinations of rheological parame-ters, we seek to minimize the residuals betweenmeasured and estimated values of the measuredvariables (Rcr, Up, Q) for each experiment. Esti-mated values of Rcr, Up, Q were computed fromequations (4), (5b), and (6), respectively.

The root-mean-square residual error for eachmeasured quantity (URMSQ, , ) forURMS URMSU Rp cr

each run in a given experiment was calculated fora wide range of realistic parameter values (i.e.,


Figure 8. Velocity profile obtained from experiment 1Cillustrating pseudoplug, estimated plug thickness, andthe errors associated with measurement. Solid circlesrepresent individually measured velocities, while theline was obtained from equation (5a), using the rheolog-ical parameters in table 5. The results shown are typicalof all of the clay-poor experiments. The estimated Rcr

was obtained from the minimization analysis and is alsoapproximately the lower bound of Rcr examined in equa-tions (8)–(10).

, , ). Because mea-1 ! t ! 200 0.1 ! n ! 2 0.1 ! K ! 50o

surement error varied greatly depending on thequantity examined, the residual errors wereweighted accordingly in the minimization scheme.The weighting was done in a linear manner, ac-cording to

URMS /R � URMS /R � URMSQ cr U cr Rerr p err crT p , (8)err Q/R � U /R � 1cr p crerr err err

where URMSQ, , are the residualURMS URMSU Rp cr

errors of the worst run in each experiment for eachquantity. The total error Terr is the parameter thatwas ultimately minimized in the search routine.

The analysis is complicated somewhat becausethe measurement error in the plug thickness Rcr isalso a function of n. As , the apparent plugn r 0thickness Rpp will be an increasingly poor estimateof the actual plug thickness because low rates ofdeformation expected in the interior of the flow forshear-thinning materials cannot be resolved withinthe error in our velocity measurements. Theseslowly deforming areas outside the rheologic plugwould therefore be included in the observed “pseu-doplug” radius Rpp. Figure 8 illustrates this effectalong with the definition of the pseudoplug for avelocity profile obtained from experiment 1C. Thepseudoplug thickness is the actual parameter mea-sured and reported in table 1. However, we can es-timate the error in Rcr, in terms of the error in thevelocity measurements (the Up error in table 1 isreflective of both precision and repeatability). Thedifference between the pseudoplug thickness Rpp

and the rheologic plug thickness Rcr depends di-rectly on the velocity measurement error. The mea-sured pseudoplug will extend to the point that thedifference between local flow velocity U(Rpp) andthe plug velocity Up is equal to or greater than themeasurement error Uerr, which is defined as

U � U(R )p ppU p . (9)err Up

Similarly, the pseudoplug thickness error is definedas . Substituting equationsR p (R � R ) RZpp pp cr crerrcalc

(5a) and (5b) for U(Rpp) and Up in equation (9), re-spectively, and solving for yields an expres-Rpperrcalc

sion for the pseudoplug error in terms of n and thevelocity measurement error Uerr:

R n/(1�n)R p � 1 U . (10)pp errerrcalc ( )Rcr

Only for strong shear-thinning rheologies ( )n ! 0.5

will be large. Because error in the origi-Rpperrcalc

nal measurement of Rpp is significant (typically10%–20%), only in experiments 1 and 5 were theerrors due to the “pseudoplug effect” larger than theinitial measurement error (table 1). In these twocases, we replaced the error calculated from equation(10) in our minimization scheme for the measurederror in Rpp reported in table 1.

Using the method above, the in situ rheologicalparameters were calculated along with an estima-tion of their uncertainty (table 4). The Herschel-Bulkley model was found to perform well. Plug ve-locities, flow discharges, and plug thicknessespredicted with best-fit Herschel-Bulkley parame-ters satisfactorily explain all experimental data (fig.9). Trends in the estimated rheological parametersas a function of grain-size distribution, in both ex-ternal (tilting-board) and in situ (flume experi-ments), were quite evident. In both the tilting-board measurements and the in situ calculations,yield strengths increased with increasing coarsematerial and clay content. The yield strength es-timates derived by these independent methods alsoagree remarkably well (fig. 10). In situ rheologicalparameters indicated other trends as well. For in-stance, shear thinning became increasingly domi-

440 J . D . P A R S O N S E T A L .

Figure 9. Evaluation of the performance of the Her-schel-Bulkley model. a, Comparison of calculated dis-charges (eq. [6]) using best-fit rheological parameters (ta-ble 5) to measured values (table 1). b, Comparison of thecalculated plug velocities (eq. [5b]), using the best-fit rhe-ological parameters (table 5) to measured values (table1).

Figure 10. Comparison of the tilting-board yieldstrengths (table 3) with the channelized values obtainedfrom the Heschel-Bulkley minimization routine (table 4).

nant as the mixes became fines-dominated, whilethe addition of extremely small amounts (1%–3%)of clay made the flows nearly Bingham. All of thesequalitative trends were observed by earlier rheo-metric work, though our flows were generally lessshear thinning. The reduction in shear-thinning be-havior (particularly as compared to Coussot andPiau 1995) was possibly a result of the high sandcontents in our experimental slurries, consistentwith the data and analysis of sand-rich slurries pre-sented by Major and Pierson (1992).

For the purpose of comparison, the minimizationroutine was also adapted to assess the performanceof the Bingham ( ) model, by simply remov-n p 1ing n as a free variable. The Bingham assumptionis common in many modeling applications (e.g.,

Whipple 1997; Huang and Garcıa 1999), and it isuseful to quantify the error incurred by its appli-cation to our experimental flows. This analysis hasthe side benefit of providing best-fit estimates of aBingham viscosity for the bulk debris mixtures forcomparison to matrix viscosity estimates. The re-sults in table 6 demonstrate that, aside from theclayey experiments, viscosities were in excess of 1Pa-s. These viscosities are surprisingly close to(given the high sand contents), but somewhat largerthan, the matrix viscosity measurements (table 3).As explained below, a systematic overestimate ofyield strength in the case of the Bingham fits re-sulted in an artificial reduction in the best-fit Bing-ham viscosities. Nonetheless, some combination ofloss of water from the matrix slurry to adhesion tofine sand particles and participation of some frac-tion of the sandy component in the bulk viscosityare probably responsible for the greater viscosity ofthe bulk mixtures.

Though the Bingham model did not perform aswell as the more general Herschel-Bulkley model(compare residual errors in tables 5, 6), the errorswere not significantly larger. The largest deviationsin the Bingham model appear to be in the assess-ment of the yield strength. The least-squares rou-tine favored the discharge and plug velocity data(the most accurate measurements) and passed mostof the miss-fit of the Bingham model to the as-sessment of the yield strength (tables 5, 6). As aresult, the tilting-board tests of yield strengthagreed well with Herschel-Bulkley calculations butnot with the Bingham numbers. The exaggerated


Table 5. Yield-strength rheologic parameters for the non-snout-stopped experiments

Experiment (mix)to

(Pa)K

(Pa-s)1/n n URMSRcrURMSUp URMSQ

1 (fine) 55 22.5 .45 3.7 6.6 .52 (medium-fine) 60 8.8 .60 1.7 .4 1.13 (medium-coarse) 70 7.1 .70 4.2 1.1 .85 (medium) 70 15.8 .43 3.2 .3 .56 (medium-coarse � 2% added clay) 125 .5 1.08 23 22 3.47 (medium-coarse � 3% added clay) 75 .5 1.25 1.0 1.8 .78 (fine) 43 31 .43 2.5 2.0 2.5

Note. Uncertainties (in percent) are the root-mean-square differences between the calculated and observed parameters (Rcr, Up,Q) using the selected parameter set (to, K, n) in equations (4), (5b), and (6).

yield strengths also caused the calculated in situviscosities to be artificially low, masking the par-ticipation of sand in the viscosity. Regardless, theerrors were small (only slightly greater than mea-surement error) and will only be important if therheological parameters are used over a large (greaterthan an order of magnitude) range of the basal shearstress.

In summary, all of the experimental data ob-tained from the quasi steady flow away from theinfluence of any frictional snout are consistentwith a non-Newtonian fluid rheology, similar tothe results of Coussot and Piau (1995) and Majorand Pierson (1992) (for s�1). Again, this is notg 1 5surprising considering the friction numbers ex-amined, given our estimates of matrix viscosity.Although we have not evaluated whether the fric-tional debris-flow model due to Iverson (1997b)could be modified to explain our experimental data(by accounting for the high viscosity and finitestrength of the interstitial fluid), the best interpre-tation, given available data, is that our experimen-tal flows acted as homogeneous non-Newtonianfluids. Postyield behavior was typically shear thin-ning for clay-poor flows typical of the Italian fieldsite ( –0.7), while the clay-rich experimentsn p 0.4exhibited near-Bingham characteristics. Most in-teresting is that most of these experiments had sandcontents well in excess (150%) of previously pro-posed limits for macroviscous behavior at strainrates relevant to debris-flow runout in channels andon fan surfaces (20%; Major and Pierson 1992). Thefluid-like behavior we observed is a result of therelatively high viscosity of the interstitial fluids(silt and clay slurries) and the concentration ofshear into narrow bands that helps sustain highshear rates during debris-flow runout.

Discussion

Transition to Frictional Behavior: Snout Dynamics.Many of the flows exhibited a thick snout near the

front of the flow. As discussed above, only above athreshold body friction number ( ) did theN 1 100f1

onset of frictional behavior in the snout becomepronounced and significantly influence flow run-out. We noticed from the first experiments thatthese frictionally locked snouts appeared drier andtended to have a greater portion of the largest clasts.This result was similar to the observations seen inthe field by Genevois et al. (1999) and many otherresearchers (Suwa 1988; Iverson 1997a, 1997b, toname only a few). It is clear, however, that thelower fluid pressures documented in the snouts offines-poor experimental debris flows by Iverson(1997b)—and used to explain snout formation inthat case—cannot explain the frictional behavior ofthe snouts in our experimental flows. The con-veyor-belt motion at the flow front preceding fric-tional lock-up guarantees that pore fluids reach thesnout with the elevated pore pressures associatedwith the rapidly shearing and liquefied body of theflows. Given the silt and clay contents of our flows,elevated pore fluid pressures will only dissipateover timescales several orders of magnitude greaterthat the duration of the experiments (Major 2000).Some other mechanism(s) must be responsible forthe onset of frictional behavior in our experiments.

These early observations prompted an experi-ment (experiment 10) where a snout was allowedto form and to arrest the flow. The deposit wassampled immediately following deposition for bothwater content and grain-size distribution. The re-sults are shown along with the deposit depth profile(fig. 11). The water content dropped by nearly a halfof a percent (error 0.1%), while the coarsest ma-terial increased systematically (error 0.3%) towardthe leading edge of the snout. These measurementsare not entirely independent. The addition of coarsematerial will increase the contribution of solids,decreasing the water content. Regardless, experi-ment 10 agreed with earlier, less systematic mea-surements that indicated that the water contentdropped almost a percentage point in a similar flow.

442 J . D . P A R S O N S E T A L .

Table 6. Rheologic Parameters if Bingham Behavior ( ) Is Assumedn p 1

Experiment(mix)

to

(Pa)m

(Pa-s) URMSRcrURMSUp URMSQ

1 (fine) 98 1.92 12 6.6 .82 (medium fine) 80 1.48 1.8 .6 1.83 (medium coarse) 90 1.75 6.9 1.4 25 (medium) 14 .99 7.3 .7 .56 (medium coarse � 2% added clay) 124 .71 23 21 3.67 (medium coarse � 3% added clay) 68 1.5 .8 1.2 1.18 (fine) 77 4.1 8.4 7.1 3.7

Note. Uncertainties were calculated as in table 4.

There are undoubtedly many effects that a drier,coarser snout will have on the dimensionless pa-rameters regulating the flow. However, the effectsto the friction number Nf are most important toour particular flow regime. It can be seen in theformulation of Nf that the only way these two var-iables directly affect the value is through the vol-ume of solids . It will also indirectly affect thevs

viscosity and the interstitial fluid density. How-ever, both the lower water content and coarser ma-terial will raise the volume of solids, raising Nf bya factor of , a nonlinear quantity. With thev /(1 � v )s s

increase of Nf, enhanced frictional interactions willdecelerate the flow, decreasing shear, and furtherincreasing Nf. Because water contents are small al-ready (sometimes !15%), this positive feedbackshould be strong. Final locking of the flow also willbe enhanced by the yield strength of the matrixbecause as the flow decelerates, local (grain-scale)shear stresses may drop below the matrix yieldstrength. During this entire process, the fluid be-hind the head should behave normally, experienc-ing a lower friction number. Flow in this regionwill ultimately back up behind the slower front andpush the frictionally locked snout ahead as a mov-ing dam that translates by boundary slip and oc-casionally by failure along discreet planes (fig. 4).Figure 12 is a schematic that describes this process.

Traditional theories describing snout develop-ment (e.g., Bagnold 1968; Takahashi 1980) have re-lied on granular effects to generate sorting of thelargest clasts. Kinetic sieving and/or dispersivepressure are thought to float large clasts to the flowsurface where velocities are largest so that theseclasts are rapidly carried to the snout. In our ex-tremely low Savage-number experiments, however,dispersive pressure will be negligible. Other work(Suwa 1988) has questioned the kinetic-sieving par-adigm by insisting that the momentum of the larg-est particles carries them to the front of debris flowsas the slope decreases. Though this mechanism isnot appropriate to our constant flows, it does point

out the possible importance of dynamic processes.Savage (1989) has pointed out that the kinetic siev-ing effect will have the further influence of trappingcoarser particles at the snout while finer particleswill be recirculated back into the body of the debrisflow. In addition to this effect, a similar “fines-stripping” process may have contributed to the seg-regation of drier, coarser material into the snoutsof our experimental flows: the fine-grained matrixslurry tends to be preferentially trapped in the dry,rough bed of the flume. This process may effec-tively strip fines and water from the snout region.A similar process has been observed in the field atthe Jiang-Jia gully in China (Li et al. 1983).

Before further discussing the mechanisms bywhich coarse grains may be concentrated at thefront of our experimental flows, it is first importantto assess whether dynamic processes are indeed re-sponsible. Because settling and stratification in thesource tank could have had the effect of imposinga drier, coarser snout at the inflow, we performedan experiment to address this possibility specifi-cally. To estimate the effect of settling in the supplytank, experiment 10 was performed to assesswhether a snout would form after the material inthe bottom half of the supply tank has run out (inthe other channel). We sampled the material fromthe bottom half of the supply tank for grain sizeand water content during runout directly at the out-flow. Four samples were obtained, including theinitial release of material from the very bottom ofthe supply tank. The four samples obtained indi-cated variations of 0.1% in water content and 0.3%in the percentage of material coarser than 1 mm.We attributed these nonsystematic variations tomeasurement error. Recent work (Major 2000) hasconfirmed that settling is slow to occur in poorlysorted debris flows, particularly with the relativelyhigh silt and clay contents of our debris mixtures.In an exhaustive series of experiments, Major (2000)found that elevated pore pressures in poorly sortedslurries remained high for tens of minutes. More-


Figure 11. Depth profile of snout-arrested flow (experiment 11). The first number indicates the water content (inpercent) obtained, while the second number indicates the percent (by mass) of material greater than a millimeter indiameter. Numbers are placed where each sample was obtained. Snout values were obtained at the tip of flow (i.e.,distance upstream equals 0).

over, even with all of the debris from the lower halfof the supply tank removed and sampled, we founda vigorous snout effect, as strong as any previousexperiment (note that the data presented in fig. 10comes from this experiment). Therefore, it wouldappear that the sorting and drying observed in fig-ure 10 is indeed the result of some sort of dynamicprocess.

As mentioned above, stripping of fines from theleading edge of the flow and sequestering them inthe dry, rough bed of the flume may have contrib-uted to snout development. In fact, a rough cal-culation indicates that if dry walls were completelycovered with matrix (to a depth of the wall rough-ness, 1 mm), all of the fine material and water couldbe removed from the snout in the first few metersof the channel, regardless of slurry composition.Therefore, two different experiments (5 and 9) wereperformed to investigate this effect. In these ex-periments, a given debris mixture was run downthe same channel twice: once when the channelwas dry, next when it was covered with a severalmm thick layer of debris flow material (left overfrom the first run). In experiment 5 (medium grain-size distribution and moderate to strong snout de-velopment), snout speeds were slowed (see table 1)by 10%–20% when the channel boundary was dry,but there was no change in either the shape of ve-locity profiles observed in the body of the flow orthe plug speed. Even though the “snout effect” wasnot enough to arrest the flow front in experiment5, stripping of fines and water as the flow traverses

a dry boundary does appear to enhance snoutdevelopment.

A second experiment using a very coarse-grainedmixture that developed a pronounced frictionalsnout that arrested the flow in the upper part ofthe channel (experiment 9), was influenced onlyslightly by the change in boundary condition. Thefirst flow, which was run out over a dry bed, wasarrested after only 0.9 m, while the second run,which flowed over an entirely mud-covered bed,ran out 1.3 m. Unfortunately, these flows advancedtoo short a distance down the flume to allow us tocompare snout speeds. In addition, most of the dif-ference in runout distance was likely controlled bythe placement of support brackets along the chan-nel. The support brackets only impede overbankflow. With very pronounced snout development,this blockage of overbanking flow sometimescaused flows to become arrested by effectivelycausing a sudden increase in volume of the fric-tionally locked part of the flow as the snout passedunder the support bracket. Experiment 9A with thedry bed did not make it through the first supportbracket at 0.9 m down flume. Experiment 9B withthe wet bed made it through the first bracket butnot the second. Therefore, it is difficult to evenqualitatively assess the effect of the dry bed on thiscoarse-grained flow.

Regardless of the mechanism, sorting and localfrictional interlocking of the snout region com-monly occurred in flows where the body of the flowexhibited macroviscous, fluid-rheology behavior. In

444 J . D . P A R S O N S E T A L .

Figure 12. Schematic of the relative friction numbersas time progress in a snout-affected flow. The diagramillustrates the hypothetical path that the two frictionnumbers (body and snout) will proceed through withtime. Notes illustrate hypothetical physical processes oc-curring at various times.

Figure 13. Schematic of the process hypothesized tooccur in a frictional-snout, yield-strength-body debrisflow. The final stage illustrates a series of clast piles,typical of those found by Whipple and Dunne (1992) andWhipple (1994).

natural flows, the dams formed in this parameterregime (transitional between viscous and frictional)may often be pushed aside or bypassed as the bulkof the debris flows overbank (e.g., Suwa and Okuda1983; Whipple and Dunne 1992; Whipple 1994). Aninteresting question, then, is whether and how fasta frictional snout is again formed by either kinetic-sieving or fluid-mechanical sorting. Additional ex-periments were performed where the snout wasphysically removed (by hand) from the channel dur-ing runout. The results indicated that the snoutreformed quite rapidly (within a few meters), fur-ther supporting our interpretation that snout for-mation is a dynamic process. Figure 13 schemati-cally illustrates the process described above andhow it would extend to previous field observations(Whipple 1994). The deposits of such flows wouldhave strong frictional signatures; however, the rel-ative roles of frictional snout dynamics and fluidrheology in controlling flow runout and depositionrates and patterns are not yet clear.

Scale Effects and Experimental Limitations. Theexperimental facility used is considerably smaller

than field-scale debris flows and some laboratoryexperiments (Iverson and LaHusen 1993; Iverson1997b; Major 1997). The variables we measured andanalyzed are by no means scale independent. Forexample, the yield strengths we report are morethan enough to control dynamics in our flume butmake up only a small (!1%) percentage of the re-sistance in flow depths similar to Berti et al. (1999).The grain-size distribution has also been truncatedto only material smaller than 5 mm. In addition,


experimental flow depths are about an order ofmagnitude less than typical debris flow depths. Inshort, many of the measured parameters cannot bedirectly related to field-scale flows.

However, the dimensionless variables and theconclusions based upon them are relevant to thephysics of natural flows. The transition we describeshould occur at roughly the same friction numberin natural environments, when similar dimension-less representations are compared. Concentrationof shear within narrow bands along channel bankscan be seen in the observations of Berti et al. (1999).These higher shear rates will impact the rheologyof the resisting layer (i.e., the material within theshear width). In fact, friction numbers in the lowerreaches of Acquabona channel were approximately300, very near the transition point investigatedherein. Finally, the high interstitial viscosities re-ported herein will also be present in many naturalflows, as natural debris flows commonly contain atleast 10%–15% silt and clay by dry weight. Indeed,the viscosity relevant to the macroscopic frictionnumber could be larger than the “matrix” viscosityused here, depending on the contribution of sandto the viscosity. Though these effects will not beimportant to all debris flows, many will be affected.In such flows, runout will be in part regulated byfluid rheology, even though they may exhibit somecharacteristics of granular behavior (e.g., a granularsnout). Fast storm-induced flows that run throughclayey or silty reaches (e.g., Berti et al. 1999), non-hydroplaning submarine debris flows, and fines-dominated lahars are just a few examples.

Summary and Conclusions

The transition from fluid-mud to grain-flow behav-ior is quite complicated and occurred at considerablylower friction numbers than expected from previousexperimental constraints (Iverson 1997b). Frictionalinteractions were observed to occur at the snout offlows when body friction numbers were as low as100. Despite the frictional interactions at the front,the bodies of all experiments remained fluid and canbe best described by a non-Newtonian (shear thin-ning) fluid rheology including a finite, constant yieldstrength. Analysis suggested that the in situ rheol-ogy of our mixtures was moderately shear-thinning( ). With increases in clay and sand con-0.4 ! n ! 0.7tent, rheology tended to be more Bingham-like (napproximately unity). Effects of clay addition wereparticularly pronounced.

The relevant shear rates in all our experimentsexceeded 5 s�1, and most surpassed 20 s�1, even

though our slopes were relatively mild (10�–15�).Hypotheses set forth by earlier work (O’Brien andJulien 1988; Phillips and Davies 1991; Iverson1997b) have suggested that shear rates greater than5–10 s�1 are unusual and irrelevant. These conclu-sions, however, were based on the assumption thatshear is distributed evenly throughout the flow.Shear concentrated considerably at the flow mar-gins in all our experiments. Low shear rates (!5 s�1)did occur locally in the snout and the nondeformingplug. In some cases (beyond a roughly defined crit-ical body friction number of 100), these low shearrates and a suite of dynamic sorting and strippingmechanisms together caused frictional interlock-ing of the flow front. In a few experiments with thecoarser debris mixtures, the damming effect ofthese frictional snouts caused the entire flow toarrest in the flume but only after the frictionalsnout was pushed a considerable distance by thefluid pressure building from upstream.

The in situ rheological results agree with earlierstudies (Major and Pierson 1992; Coussot and Piau1995), that observed shear-thinning or Binghamfluid behavior of natural debris flow mixtures(without a significant gravel component) for shearrates greater than 5 s�1. Phillips and Davies (1991)and Major and Pierson (1992), however, reportedvery high instantaneous shear stresses in sand- andgravel-rich slurries, which they attributed to tran-sient formation of clusters and chains of granularmaterial. This onset of frictional behavior wastaken to indicate a breakdown of the fluid rheologyassumption at the strain rates relevant to debrisflow runout in hazard zones for flows with greaterthan 20% sand. However, we observed fluid rheo-logical behavior in free-surface flows with sandcontents in excess of 50% (by volume) under flowconditions relevant to debris-flow runout. In part,this is because shear concentration in narrow bandssustained high shear rates in all of our experiments.In addition, it is possible that free-surface flows areless sensitive to the formation of transient grainclusters and chains because these granular clustersare much less likely to become trapped betweensolid boundaries than they are in co-axial or cone-and-plate viscometers.

The transition to frictional behavior in our free-surface experiments occurred only at the flow frontwhere lower shear rates and a suite of dynamic sort-ing and stripping mechanisms together caused thefrictional interlocking of the flow front. Settlingand stratification in the supply tank were defini-tively ruled out as potential causes of the coarserand drier snouts. Further, we have demonstratedthat dynamic sorting mechanisms (e.g., kinetic

446 J . D . P A R S O N S E T A L .

sieving) acting alone were not sufficient to triggerthe rapid formation and re-formation of frictionalsnouts. We postulate that the dynamic concentra-tion of coarser material at the flow front increasesthe local friction number, thus inhibiting internaldeformation and triggering a series of positive feed-backs that quickly result in a wholesale frictionalinterlocking of the snout region. Despite limita-tions of the experimental set up in regards to themaximum size of clasts and the magnitude of nor-mal stresses developed in shallow experimentalflows, we anticipate that the macroviscous to fric-tional transition in field-scale debris flows probablyoccurs via a similar suite of mechanisms and oughtto occur at approximately the same friction num-ber. In our view the greatest obstacle to translationof experimental results to field scale lies in deter-mining the appropriate values of the representativegrain size d and the “fluid” viscosity m in the non-

dimensional scaling numbers used to gauge flowregime.

A C K N O W L E D G M E N T S

This research was financially supported by MIT andChevron. A. Simoni’s stay at MIT was kindly spon-sored by CNR-GNDCI (National Research Councilof Italy) within the CNR-MIT Cooperation on Cli-mate Change and Hydrogeological Disasters in theMediterranean Area program. We thank G. Parkerand D. Mohrig for helping develop the experimentaltechnique and J. Southard for his advice and do-nating the shell of the flume for the experiments.Also thanks to S. DiBenedetto, N. Snyder, B. Lyons,and M. Hendricks for their assistance in performingthe experiments and C. Mei for the use of his vis-cometer. The manuscript benefited from careful re-views by P. Coussot, L. Pratson, and two anony-mous reviewers.

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