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Experimental modelling of debris flow behaviourusing a geotechnical centrifuge

Elisabeth T. Bowman, Jan Laue, Bernd Imre, and Sarah M. Springman

Abstract: Physical modelling of debris flows has been carried out in the geotechnical drum centrifuge at ETH Zurich. Anew apparatus to model debris flows in the centrifuge is described. The apparatus permits the final reach of a typical de-bris flow to be modelled within the centrifuge, with unconsolidated material flowing down a slope to deposit as a fanaround the drum. Experiments are described for both fixed base conditions and erodible bases. Tests to examine the verifi-cation (modelling) of models show that debris flow behaviour is governed mainly by friction and consolidation processes,although some resolution is required between flow behaviour downslope and flow arrest during runout. The results arecompared with bulk parameters determined for field-scale debris flows. It is found that some important flow mechanisms,such as contact-dominated behaviour and high pore pressures, are developed that are closer to those developed at field-scale than tests conducted at 1g. Velocity profiles for erodible beds are compared with a semi-empirical expression derivedfor experimental debris flows at 1g. Normalized velocity profiles are found to be in agreement; however, absolute veloc-ities differ from those predicted. Scaling, the limitations of the apparatus, and potential for future work are discussed.

Key words: Debris flow, physical modelling, centrifuge, erosion.

Resume : Une modelisation physique des ecoulements de debris a ete effectuee avec une centrifuge geotechnique a baril aETH Zurich. Un nouvel appareil servant a modeliser les ecoulements de debris dans la centrifuge est decrit. Cet appareilpermet de modeliser a l’aide de la centrifuge l’etendue finale d’un ecoulement de debris typique, en considerant l’ecou-lement de materiaux non consolides descendant d’une pente et se deposant en eventail autour du baril. Des experiencessont decrites pour des conditions avec la base fixe et avec la base erodable. Les essais effectues dans le but de valider lesmodeles ont demontre que le comportement des ecoulements de debris est gere principalement par la friction et les proces-sus de consolidation, malgre qu’il manque certaines informations entre le comportement de l’ecoulement en descente depente et l’arret de l’ecoulement. Les resultats sont compares aux parametres globaux determines pour des ecoulements dedebris a l’echelle reelle. Il a ete observe que des mecanismes importants d’ecoulements sont developpes, tels les comporte-ments domines par le contact et les pressions interstitielles elevees; ceux-ci etant plus pres de ceux developpes a l’echelledu terrain de ceux developpes durant les essais a 1g. Les profils de vitesse pour des lits erodables sont compares a une ex-pression semi-empirique derivee pour des ecoulements de debris experimentaux a 1g. Les profils de vitesse normalizesconcordent, cependant les vitesses absolues different de celles predites. Une discussion est presentee portant sur les effetsechelle, les limites de l’appareil et les possibilites de travaux futurs.

Mots-cles : ecoulement de debris, modelisation physique, centrifuge, erosion.

[Traduit par la Redaction]

IntroductionDebris flows are a highly unpredictable hazard in areas of

mountainous terrain and high runoff. They are one of themost frequent mass movement processes, constituting high-speed gravity-driven mixtures of soil, rock, and water(Hungr et al. 2001). Often originating in steep mountain gul-lies, they can travel over long distances and generate signifi-cant impact forces, causing damage to infrastructure and

loss of life. Mechanically, debris flows are particularly com-plex because they have a large range of clast sizes, fromboulders through to silt, which tend to segregate duringdownslope motion. This alters the material behaviour intime and space. In addition, debris flows have a propensityto erode and deposit material as they travel, rendering theirboundary conditions rather indeterminate. The investigationof this phenomenon via centrifuge testing is the focus ofthis study.

In this paper, it is hypothesized that certain aspects of thebehaviour of debris flows — in particular, erosion and en-trainment — are gravity and drainage path dependent. Thatis, the drained strength of the bed over which a debris flowtravels is a function of the effective stress applied to it,while its undrained behaviour is a function of both the pathlength and soil permeability. Geotechnical centrifuge testingoffers the possibility of examining the failure of the bed andits entrainment as a debris flow passes over it by modellingstresses and diffusional–inertial times at approximately pro-totype values.

Received 20 May 2008. Accepted 27 November 2009. Publishedon the NRC Research Press Web site at cgj.nrc.ca on 21 June2010.

E.T. Bowman.1 Department of Civil and Natural ResourcesEngineering, University of Canterbury, Christchurch, NewZealand.J. Laue, B. Imre, and S.M. Springman. Institute forGeotechnical Engineering, ETH Zurich, Switzerland.

1Corresponding author (e-mail:[email protected]).

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Can. Geotech. J. 47: 742–762 (2010) doi:10.1139/T09-141 Published by NRC Research Press

Growth of debris flows by entrainmentThe magnitude of a debris flow can vary widely, even

during the course of a single event because it may grow byeroding and entraining material in its path, while it may alsodiminish in size as a result of deposition. There are numer-ous examples of debris flows in different geological settingsthat are known to have entrained large volumes in their flowpath. The 1990 Tsing Shan debris flow in Hong Kong beganfrom an initial failure volume of 355 m3 and led, via en-trainment of colluvium and weathered bedrock, to a total de-bris flow volume of 19 000 m3 (Chan et al. 1991; King1996) — a greater than 50-fold increase in volume. Jakobet al. (1997) reported on two contrasting large debris flowsin British Columbia that occurred in a similar geological set-ting in colluvial soils, where one entrained approximatelythree times its initial volume (from 22 000 to 63 000 m3),while the other entrained approximately 16 times its initialvolume (from 3000 to 50 000 m3). In their back-analysis oferosional debris flows, Chen et al. (2006) selected a repre-sentative debris flow from over 200 that occurred in 2000in Bianzone, Italy, for analysis. This debris flow, originatingin well-graded silty sand and gravels, grew from an initialvolume of 266 to 4084 m3 — a 16-fold increase.

Flows that are enlarged due to entrainment of eroded mate-rial along their paths travel further than if no erosion took place(Benda and Cundy 1990; Fannin and Wise 2001) and increasetheir destructive potential; hence, understanding debris flowhazards requires an understanding of erosion mechanisms.

Erosion is thought to occur chiefly in the vertical direc-tion (Davies et al. 1991; Rickenmann et al. 2003) and alsomay be accompanied by collapse of the sidewalls as toe sup-port is eroded (Hungr et al. 2005). The erosion process canoccur via several mechanisms, as listed below in order of in-creasing depth of influence:

(1) Single particle erosion of loose material (Takahashi1991; Armanini and Gregoretti 2000).

(2) Scour and knickpoint erosion–migration (Davies et al.1992; Tognacca and Bezzola 1997; Rombi et al. 2006).

(3) Drained shearing of the bed (Anderson and Sitar 1995).(4) Undrained shearing of the bed (Hutchinson and Bhandari

1971; Wang et al. 2003).The first two items in the list are processes that affect the

surface or near-surface of the bed, where stresses are rela-tively low. The third and fourth items, however, can occurat greater bed depths and are dependent on the state of thesoil, its relative saturation, and the overall stress level ap-plied, as discussed later.

Physical modelling of debris flowsPhysical modelling allows boundaries to be defined and

particular perturbations to be input to a model situation,without preconditioning the outcome. The small-scale mod-elling of debris flows is therefore a useful tool in elucidatingparticular aspects of their mechanics. Considerable physicalmodel research on debris flows has been conducted, despitetheir apparent mechanical complexity at field scale. On afundamental level, laboratory studies have been instigatedto examine, for example, the role of solid fraction and fluidviscosity on runout of debris flows (Tognacca and Minor2000), the effect of particle size on runout and erosion by

debris flows (Egashira et al. 2001), and the influence of bedtopography, saturation, and density on overall runout behav-iour (Chau et al. 2000; Rombi et al. 2006).

There are some drawbacks with the extrapolation ofsmall-scale model behaviour to field-scale debris flow proc-esses. Scaling issues that pertain to laboratory flows overfixed beds have been discussed previously by Iverson(1997) and Iverson and Denlinger (2001), where in sum-mary, they state that by pure virtue of their size, small-scalelaboratory flows do not necessarily develop the key dynam-ics of field-scale debris flows — in particular, segregation ofparticle sizes and high mobility. To answer this, Iverson andhis co-workers conducted a number of large-scale modelsusing a 90 m long flume of fixed bed and fixed angle, whichran out onto a horizontal surface. Basal stresses and porepressures were measured during the flow downslope. Segre-gation of particle sizes was observed during flow and run-out, which appeared to agree well with field observations(e.g., McArdell et al. (2007)). However, these elements ofbehaviour have also been observed in carefully preparedsmall laboratory flume tests albeit at a smaller scale (e.g.,Wang and Sassa 2006; Bowman and Sanvitale 2009), sug-gesting that a judicious selection of material properties canobviate the necessity of testing at very large scale for manyobservable debris flow processes, particularly where bounda-ries are fixed and defined.

In contrast to this, attempts to model erosion by debrisflows have generally been hampered both by the unknownboundary conditions present in some test arrangements,which are particularly difficult to control in large-scale tests,and by an inability to capture some important features suchas the stress state of soil that influences soil behaviour at asmall scale. As a result, the physical modelling of erosionby debris flows has received little attention, and hence it isdiscussed in some detail here.

Physical modelling of erosion andentrainment by debris flows

This section discusses the necessary conditions required tomodel the different processes by which debris flows mayerode and entrain material.

Single-particle erosion and knickpoint migrationIt is notable that single-particle erosion, scour, and knick-

point erosion–migration are processes that have been exam-ined in some detail previously using laboratory-scale flumemodels (Takahashi 1991; Davies et al. 1992; Tognacca andBezzola 1997; Armanini and Gregoretti 2000; Rombi et al.2006). Such processes largely behave according to fluid me-chanics principles, as it is the action of water on a solidbody that causes movement of discrete particles. Accord-ingly, small-scale modelling appears adequate to investigatethese processes. The removal of large quantities of bed ma-terial as seen in the likes of Tsing Shan (King 1996), how-ever, suggests that the deeper seated processes of drainedand undrained shearing of soil may be involved in somehighly erosive flows.

Drained shearing of the bedThe stress applied by and hence thickness of a debris flow

Bowman et al. 743

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has a direct bearing on the deformation and effectivestrength of the soil beneath it and therefore on its tendencyto erode. During drained shearing of soil, an increase in con-fining stress causes a reduction in soil dilatancy (Bolton1986), which can lead to soil contraction even if it is rela-tively densely compacted (Vesic and Clough 1968). Further-more, the rotation of the stress field in the bed as a transientload passes may also lead to soil contraction (Symes et al.1988; Anderson and Sitar 1995). A contractive soil mobi-lizes a lower frictional strength than a dilative soil until thecritical state is reached (Schofield and Wroth 1968).

This means that laboratory-scale model flows at 1g do notproduce the same mean stress increase in the bed as largerfield-scale flows (the prototype), so the soil in a model bedwill behave as if it is relatively stronger than soil in a bed atthe prototype scale. For example, the typical vertical thick-ness of a large debris flow is of the order of 10 m, whilethat of a flow produced in a laboratory model may be ofthe order of 10 mm, representing a three order-of-magnitudereduction in normal basal stress (approximately 100 kPa ver-sus 0.1 kPa for saturated soil, respectively). Sture et al.(1998) conducted triaxial tests on sand at extremely lowstress levels of around 0.05 kPa and showed dilation anglesof around 308 above the critical state, compared with typicalvalues of less than 88 above critical state for tests conductedabove 35 kPa (Ponce and Bell 1971). This difference couldresult in an approximate doubling of the shear strength ofthe soil at model scale compared with the field, resulting insignificantly lower erosion rates at model scale than arerealistic and hence, leading to underprediction of the mobi-lized mass of debris.

Undrained shearing of the bedUndrained shearing of a saturated soil bed can occur dur-

ing the high-speed loading by a debris flow (Wang et al.2003) if there is not enough time for diffusion of pore waterto occur. That is, the loading may be too fast for drainage totake place from a saturated substrate, leading to pore pres-sure generation and loss in effective stress and resulting infailure at depth.

Using the approximation of one-dimensional consolida-tion, the time, t, for water to begin draining from the baseof a saturated substrate loaded by a passing debris flow isdefined as

½1� t ¼ H2

12D

where H is the thickness of the flow normal to the bed (as-suming one-way drainage) and

½2� D ¼ kEs

rfg

where D is the coefficient of consolidation (also referred toas hydraulic diffusivity), k is Darcy’s permeability, Es is thestiffness modulus, rf is the density of the fluid, and g isEarth’s gravitational acceleration. Hence, for a 1 m thicklayer of clean sand (permeability k = 10–3 m/s) overlying animpermeable stratum, eq. [1] equates to approximately 1 s;for a 2 m thick layer, eq. [1] equates to approximately 4 s,and so on. For more typical soils of lower permeability (e.g.,

silty sand or well-graded soil containing some clay), thetime taken will be 10–1000 times greater. As shown inFig. 1, for a short-duration field-scale debris flow travellingover a saturated substrate, the loading is likely to be largelyundrained. In Fig. 1a, scenario A considers a thick and (or)low permeability stratum where loading by a passing debrisflow will occur in an undrained manner with an increase inpore pressure (clear arrowheads) within the substrate redu-cing the effective stress, and little or no drainage by the endof the flow. The superimposed isochrone profile remains lar-gely rectangular throughout debris flow, denoting that anyincrease in pressure is taken by the pore water. A relativelysmall amount of drainage may occur in the upper regions ofthe saturated strata after a particularly long duration of load-ing, as shown. In Fig. 1b, scenario B considers a thin and(or) high permeability stratum where loading by a passingdebris flow leads to time-dependent drainage of the substratevia an increase in hydraulic gradient. This leads to waterflow out of and compression of the substrate. The superim-posed isochrones, which are initially assumed to be rectan-gular, gradually follow an approximately parabolic shape asthe debris flow proceeds.

Undrained behaviour is difficult to achieve using small,short, and relatively thin laboratory flows of relatively highpermeability at 1g. That is, for a typical laboratory-scalemodel debris flow bed comprised of a 20 mm thickness ofsaturated clean sand, diffusion of pore pressure will occurin approximately 400 ms, far more quickly than the time forthe overriding flow to pass. To mitigate this problem, itseems possible to increase the fluid viscosity or decreasethe particle size; however, these approaches induce viscouseffects — eliminating particle segregation and resulting inmud-type grain flows rather than debris flow–type behaviour(Bowman and Sanvitale 2009).

Modelling erosion and entrainment in acentrifuge

Due to the effects of stress level, substrate thickness, andpermeability, small-scale geotechnical models tested atEarth’s gravity are not generally adequate for simulatingdrained and undrained mechanisms of bed erosion by debrisflows. Geotechnical centrifuge modelling involves testing asoil model of 1/N scale, where N is the scale factor, under acentrifugal acceleration of N times Earth’s gravity — i.e.,Ng. This offers the possibility of examining these erosionprocesses by modelling at stresses that approximate proto-type values and by the careful selection of materials to rep-licate correct diffusional and inertial times.

This paper discusses experiments conducted using anewly developed debris flow apparatus, housed within ageotechnical centrifuge. The apparatus is designed to allowthe testing of small-scale debris flows over fixed and erodi-ble substrates at stresses relevant to typical prototype scale.Focus is given to discussing general centrifuge scaling lawsand how they may relate to the experiments. An interpreta-tion of the results, first in terms of nondimensional groupsconsidered important to debris flow mechanics and secondin terms of flow velocity profiles developed in comparisonto theoretical profiles, is also given.

744 Can. Geotech. J. Vol. 47, 2010


Centrifuge scaling principlesScaling principles have been developed for the geotechni-

cal centrifuge over a number of years for both static and dy-namic processes including seismically induced liquefaction,rockfall behaviour, fluid flow, and erosion (Schofield 1980;Craig et al. 1988; Chikatamarla et al. 2006; Garnier et al.2007). Debris flows are a new phenomenon to be tested ona centrifuge; however, much of this previous work can beused to elucidate reasonable scaling laws for this case.

Debris flows are observed to occur in an agitated state;however, this should not be confused with fluid turbulence,as defined by the pore Reynolds number, Re,

½3� Re ¼ rfVd

m

where V is taken to be the Darcian velocity, d is the meanparticle size, and m is the dynamic viscosity of the fluid(Goodings 1984). The upper limit of Re for laminar flow isfound to be between 1 and 10; hence, within a debris flow,the flow will be laminar as a result of the high concentrationof particles (Hungr et al. 1984; Iverson 2005) and small par-ticle size. Note that Goodings (1984) stated that, for soil inwhich pore pressures are able to develop for any appreciableperiod of time, turbulent flow will not be possible due to thesmall size of the pores. This is fortuitous, as Goodings(1982, 1984) also shows that centrifuge scaling laws for la-minar and turbulent flows are in conflict — with laminarflow scaling following Darcian–conventional consolidationlaws and turbulent flow requiring similitude of Froude scal-

ing. As Goodings states, ‘‘this conflict is entirely acceptableprovided a given centrifuge model involves either laminar orturbulent flow, but not both’’ (Goodings 1984).

Table 1 gives a summary of scaling principles as used ingeotechnical engineering relevant to this study (laws for tur-bulent flow are included for interest only). In general, thestress felt by a 1/N scale model may be increased to proto-type stress level by applying N times the Earth’s gravity tothe model through centrifugal acceleration. For static model-ling conditions, this means that, for example, the stress ex-perienced at the base of a 20 mm thick bed at a scale factorof N = 50 will be the same as that at the base of a 1 m thickprototype, with concomitant stress–strain behaviour.

Debris flows are clearly dynamic processes and, in thisresearch, the correct dynamic modelling of debris flows inthe centrifuge was hypothesized to be governed by similarprinciples to those used for dynamic simulation of liquefac-tion phenomena (Schofield 1980; Craig et al. 1988). That is,whereas saturated soil may be maintained in a liquefied stateduring a seismic event due to ground shaking and vibration,the interior of a debris flow consists of saturated materialmaintained in a liquefied state by continuous compressionand extension, vibration, and shearing as it moves down-slope under the force of gravity.

For dynamic inertial-diffusion events, the centrifuge mod-elling of both inertial effects (which scale with 1/N) and dif-fusional effects (which scale with 1/N2) must be resolved sothat pore pressures do not diffuse N times too rapidly com-pared with the gross deformation developed over the sametime period. This matching of time scales may be achievedby the use of one of two methods. The prototype pore fluid(assumed to be water) may be replaced with a fluid with aviscosity N times higher than water — this lengthens thetime for diffusion–consolidation by N2 and inertia by N inthe model, resulting in the same overall time for these proc-esses as the prototype with water. Alternatively, particle sizecan be scaled, following for example Hazen’s rule for uni-formly graded sands (Hazen 1892), such that k / d2

10, wherek is permeability (in m/s) and d10 is the largest particle sizeof the smallest 10% of the particles by mass (in mm). UsingHazen’s rule to achieve a reduction in permeability by a fac-tor N, the d10 particle size of the model soil should be N1/2

times smaller than the prototype (Kutter 1995). Note thatHazen’s rule is generally applied to uniformly graded soilswith particle sizes less than 3 mm. The empirical rule as-sumes that the intrinsic permeability of the soil, K (in m2),may be altered without changing the structure (particle orvoid shape and distribution) of the soil.

This paper describes experiments where either a viscouspore fluid — a combination of water and glycerine — isused or the entire particle grading curve is shifted by N1/2

scaling. In the latter case, the entire particle-size distributionis downscaled using soil of the same origin to ensure appli-cation of Hazen’s rule.

The ‘‘modelling of models’’ (Schofield 1980) is employedto check the validity of the scaling laws described. Model-ling of models is the process whereby models of differentscale or different combinations of soil–fluid properties aretested at appropriate accelerations corresponding to thesame prototype. The process provides a helpful internal

Fig. 1. Sketch of undrained versus partially drained loading of sa-turated substrates, with pore pressure isochrone profiles within thebed superimposed. (a) Scenario A, field event with stratum of lowpermeability and large thickness; (b) scenario B, laboratory eventwith stratum of low permeability and small thickness.

Bowman et al. 745


check on the validity of expected centrifuge scaling laws —the results of such tests are discussed later.

Interpretation of results

Nondimensional groupsMass movements of all types (slow landslides, debris

flows, rock avalanches) have been classified previously ac-cording to flow ‘‘regimes’’ based on hypothesized differen-ces in internal load, momentum transfer, and energydissipation mechanisms that govern each type. In attemptingto place bounds on the behaviour of debris flows and othertypes of mass movement, Iverson (1997) and Iverson andDenlinger (2001) described a series of nondimensionalgroups relevant to particular mechanical processes. Flowsthat fall within a range of stated values for each group areconsidered to behave within a particular mass movement re-gime.

Iverson and Denlinger (2001) have argued previously thatsmall laboratory-scale debris flows cannot capture essentialdebris flow behaviour because the use of small flumes andcorrespondingly small particle sizes causes the flows to falloutside the true debris flow regime. Modelling on the centri-fuge at enhanced g, however, allows laboratory-scale flowsto exist within regimes beyond those usually possible atsmall scale. The results of some of the centrifuge modeltests are compared with published dimensionless group val-ues of ‘‘typical’’ flows in this paper. The dimensionlessgroups are listed in the ‘‘Results’’ section, with a brief ex-planation of their relevance and specific values attributed inparticular tests.

Vertical velocity profilesAs discussed earlier, while there is some debate regarding

the ability of model-scale flows to capture the mechanics oflarge-scale debris flows entirely, there exists a reasonablebody of work undertaken at laboratory scale. The value ofthese tests lies in their ability to specify and control theboundary conditions of individual scenarios and in allowingdetailed observations to be made by the use of (often) trans-parent flow margins. Takahashi and co-workers (Takahashi1980; Takahashi 1991; Takahashi et al. 1997) have carriedout particularly extensive testing of coarser and finer-grained flows and have identified three flow regimes:‘‘viscous,’’ ‘‘macroviscous,’’ and ‘‘stoney.’’ For stoney de-bris flows, they undertook laboratory experiments using rel-

atively uniform materials flowing over erodible beds, andused the results of these experiments and those of others toderive a semi-empirical relationship for such flows (Taka-hashi 1991).

The velocity profiles developed in two experiments con-ducted on the centrifuge are compared with Takahashi’s(1991) equation and a discussion is made regarding its moreuniversal applicability beyond the narrow range of condi-tions for which it was originally proposed.

ApparatusExperiments were carried out using the ETH Zurich Geo-

technical Drum Centrifuge in Switzerland. This centrifugehas a maximum working radius of 1.1 m, a maximum de-sign acceleration of 440g, and a maximum load carrying ca-pacity of 2000 kg (Springman et al. 2001).

The debris flow apparatus is designed as a 160 mm widevariable-slope flume (Figs. 2, 3), which guides liquefied de-bris flow material from its head to the inner circumferenceof the centrifuge drum (Fig. 4). The types of flow discussedhere may be regarded as ‘‘unconfined’’ (Fannin and Wise2001) — with the flow width tending to be much greaterthan the flow depth. The drum circumference itself is usedas the runout zone, i.e., where the flow comes to rest. Theliquefied material has the potential to travel around the en-tire half-circumference (approximately 3 m) before being ar-rested by a barrier. While the runout zone is itselfimpermeable, three 10 mm diameter holes are located every432 mm along the circumference of the drum. These holesallow fluid to be removed at the edges of the consolidatingdebris flow deposit, to be collected outside the rotating partsof the centrifuge. See Fig. 4 for a schematic cut-away planview of the channel and other components within the drumduring a test.

The main debris flow apparatus consists of three parts: achannel, a strut, and a curved support to spread load to thedrum. The 600 mm long and 160 mm wide (internal) alumi-nium slope is curved to follow the inner curvature of thedrum, such that at a slope angle of 08 it lies evenly alongthe drum circumference (drum radius is 1100 mm, while ra-dius to the head of the slope at 248 is 850 mm). This appa-ratus has been designed to withstand a working g-level, Ng,of 200g or 1960 m/s2. The channel has also been designedwith maximum flexibility of use in mind, such that in thefuture, flow constrictions and obstacles can be appliedwithin the channel width.

The back of the slope is supported by an aluminium strut,which bears onto the curved support against the drum wall.The strut–channel connection is hinged to enable differentslope angles to be selected up to a maximum of 368 by ad-justing the position and length of the strut. The sides of thechannel are polished aluminium on one side and Perspex onthe other. The aluminium channel wall is designed to hold anumber of pore pressure transducers (PPTs) for the measure-ment of pore pressure during the experimental debris flow.Corresponding pore pressure transducer (PPT) positions inthe base of the channel along the centreline and edge havebeen manufactured to enable base pore pressures to bemeasured across the width of the expected debris flows toinvestigate variations arising from fixed-bed and erodible-

Table 1. Scaling laws used in geotechnical centrifuge testing,based on Ng = ru2 (where r is the radius and u is the angular ve-locity).

ParameterPrototype(field)

Model(centrifuge)

Gravity acceleration g NgStress s s

Displacement x x/NAcceleration a aNTime (inertial) ti ti/NTime (laminar seepage, diffusional) td td/N2

Energy E E/N3

Time (turbulent seepage) tt tt/N



bed flows. Coarse sand particles glued to the base provide arough substrate; the smooth walls ensure relatively planestrain behaviour.

To allow for provision of the PPT wiring beneath the flatbase and to reduce the weight of the channel, the 3 mmthick base plate is ribbed with stiffeners running longitudi-nally and horizontally on the underside (Fig. 5). The con-tacts of the PPTs with the side and base plates are sealedby rubber O-rings. Ceramic filter plates with high air-entryvalues are placed between the PPT and base to enable dy-namic pore pressures to be recorded, while protecting thetransducers from direct contact with soil particles. ThePPTs are de-aired initially using a mixture of glycerine andwater, then they are calibrated and mounted on the chute.Thereafter, they are topped up periodically with water, usinga syringe (note, the glycerine does not evaporate and ishygroscopic).

The Perspex side of the channel allows a small, mono-chrome high-speed digital camera (500 frames per second(fps) at full scale of 240 pixels � 240 pixels) to observe an

elevation view of the flow during the test. Once installed atthe correct angle on the drum, the camera is positioned at acontrol point to view through the Perspex window (markedas a star in Fig. 4 and also shown in Fig. 6). Small markersare painted on the window to enable tracking of the flow forlater image analysis. The placement and the brightness ofthe lighting are critical to the production of high-speed im-ages, both in terms of maximizing the frame rate and thedepth of field. The result is that lighting is one of the majorchallenges for the success of these experiments. The flow islit by a close array of eight light-emitting diodes (LEDs)with a power of 5 W and a typical luminous flux of 120 lmeach. The colour spectrum of the LEDs with a maximumspectral power at a wavelength of 505 nm is selected tomeet the wavelength spectra in which the high-speed digitalcamera is most sensitive. This small, lightweight lightingsystem is flexible enough to be mounted offset from thecamera lens to reduce glare from the Perspex window(Fig. 6).

The unconsolidated debris flow material is introduced ‘‘in

Fig. 2. Photograph of debris flow flume. Scale: supporting strut is 240 mm long from centre to centre of the fixing bolts.

Fig. 3. Photograph looking from base of flume to the crest.

Bowman et al. 747


flight’’ to the channel by a flexible tube. The tube extendsfrom the central axis of the centrifuge, where material is de-livered via a funnel, and is guided by an actuator on the cen-trifuge tool plate to the head of the channel, where it exits toflow outward under centrifugal acceleration, down the slope(Weber et al. 2006). This system allows the material to beprepared and maintained as a slurry external to the drum (inwhich it would otherwise consolidate during spin-up). Themaximum prototype particle size that may be used in thesedebris flow experiments is approximately 3.5 mm, whichwould scale to 350 mm at 100g (N = 100), representative ofthe larger particles in many typical flows (Iverson 1997).The maximum size is controlled by the narrowest internalpoint of constriction in the tube (where the internal diameteris 20 mm). That is, for particles larger than 1/6th of this di-ameter, mechanical arching, comparable to the silo effect asfound by Janssen (1895), may occur with resulting blockageof the tube (Nedderman 1992).

Fixed bed tests

MaterialsTable 2 gives details of seven tests over fixed (nonerod-

ible) substrates. Test nomenclature is as follows. T followedby a number is a simple test identifier. Tests are then de-scribed in terms of their material constituents as ‘‘fwg’’ for‘‘fine, well graded’’ or ‘‘s’’ for ‘‘silt’’ in this series. The finalnumber indicates the viscosity of the fluid. The details ofthe tests, named T4_s_40, T5_s_1, T6_fwg_40, T7_fwg_40,T8_fwg_40, T9_fwg_20, and T17_fwg_10, are discussed be-low.

In each of the tests, 2.5 kg of dry solids were mixed witha specified fluid quantity (see Table 2). The materials usedfor tests denoted ‘‘fwg’’ were a relatively well-graded finesandy silt (maximum and minimum void ratios emax = 0.682and emin = 0.296, respectively; specific gravity, Gs = 2.74;uniformity coefficient, CU = d60/d10 = 18) mixed with a20 cP or 40 cP (1 centipoise (cP) = 1 mPa�s) glycerine–water pore fluid. The material used for the two tests denoted‘‘s’’ was a more uniformly graded silt (CU = 11) mixed witheither water or 40 cP glycerine–water. The particle-size dis-tributions are given in Fig. 7. In the tests reported here, theaverage particle size tends to the measurable grain-sizelimit. These fine materials were chosen to facilitate compar-ison with previous research on well-constrained laboratoryflows and to contrast with a preliminary set of tests thatwere designed to examine the workings of the apparatus(Bowman et al. 2006) where coarser-grained materials(d50 = 0.7 mm) were used.

Tests T4_s_40 and T5_s_1 (Table 1) demonstrate the ef-fect of altering fluid viscosity at a given g-level of 40g. Acomparison between results obtained for tests T6_fwg_40,T7_fwg_40, and T8_fwg_40, which were carried out at 40gwith 40 cP fluid, shows the typical effects of altering themoisture content of the flow. Tests T9_fwg_20 andT17_fwg_10 were undertaken using 20 cP fluid at 20g and10 cP fluid at 10g, respectively, to investigate modelling ofmodels (Schofield 1980) in terms of the velocity profile.They are comparable with test T8_fwg_40, which wasundertaken at the same moisture content, and represent the

Fig. 4. Plan cut-away schematic view of the debris flow channel within the drum centrifuge (only half of the drum shown). Note that grav-ity acts into page.

Fig. 5. Photograph looking at the back of the flume: (i) flume stif-feners; (ii) mounting of PPT; (iii) bored hole to transmit pore pres-sure to the PPT.



same prototype by reducing the fluid viscosity by the samefactor as the g-level.

ResultsParameters and results in terms of flow velocity between

PPTs and runout dimensions for each of the tests are givenin Table 1 and Figs. 8 and 9. The average speed of the satu-rated front of flow, u1, u2, and u3, was measured over threestretches of the channel using the first response of basalpore pressure transducers placed at four locations, PPT1,

PPT2, PPT3, and PPT4, which were 140, 140, and 70 mmapart, respectively, with the last being placed 140 mm fromthe lower end of the slope (for comparison, the camera wasplaced between PPT3 and PPT4; see Fig. 6). A typical porepressure response for a fixed bed from test T7_fwg_40, forthe stretch nearest the head of the channel (between PPT1and PPT2), is given in Fig. 10, along with the pore pressureresponse from test T11_fwg_40E for flows over an erodiblebed (discussed later).

Figure 6 shows a photograph of the runout zone of a test,

Fig. 6. Photo of debris flow channel and runout zone after a test (T16_fwg_20E): (i) camera, (ii) supply tube fixed to the actuator (shown inretracted position), and (iii) lighting. The positions of PPTs 1–4 are also indicated. Velocity u1 is taken as the average between PPT1 andPPT2, u2 between PPT2 and PPT3, and u3 between PPT3 and PPT4. View is oblique from central axis of drum at top of centrifuge towardsinner drum channel. Note that unconsolidated material sags in the direction of Earth’s gravity after centrifuge spin down.

Table 2. Parameters and results for fixed bed tests T4_s_40, T5_s_1, T6_fwg_40, T7_fwg_40, T8_fwg_40, and T9_fwg_20 and erodiblebed tests T11_fwg_40E and T16_fwg_20E.

Results

Initial conditions Mean velocity (m/s) Runout (cm)

Test name

Flowmoisturecontent,w (%)

Meanparticlesize, d(mm)

Fluidviscosity,m (cP)

Bed moist-ure con-tent, wb

(%)Nominalg-level, N u1 u2 u3

Max.length

Max.width

T4_s_40 49 0.026 40 — 40 0.124 0.114 0.106 60 45T5_s_1 49 0.026 1 — 40 1.56 7.00 3.50 93 43T6_fwg_40 49 0.054 40 — 40 0.875 0.933 0.875 97 48T7_fwg_40 36 0.054 40 — 40 0.116 0.101 0.093 70 44T8_fwg_40 33 0.054 40 — 40 0.068 0.059 0.049 50 42T9_fwg_20 33 0.054 20 — 20 0.067 0.058 0.046 60 34T17_fwg_10 33 0.054 10 — 10 — — — 80 25T11_fwg_40E 36 0.054 40 25 40 0.130 0.108 0.069 60 51T16_fwg_20E 36 0.054 20 25 20 0.117 0.26* 0.26* 80 42

Note: 1 cP = 1 mPa�s.*Third PPT reading was unreliable; hence, an average reading over both u2 and u3 has been taken between the second and fourth PPTs.

Bowman et al. 749


which was still unconsolidated after centrifuge spin-down.Note that there is always a component of 1g due to Earth’sgravity in the lateral direction to the flow, which, under highcentrifugal acceleration, can be usually ignored (Craig et al.1988). However, after spin-down of the centrifuge, unconso-lidated material will sag in this lateral direction, as shown.

Comparison of velocity results from the PPTs with thatfrom the high-speed camera was made where possible,although with the very thin flow thicknesses of the fixedbed tests this was not an easy task. Only for testsT6_fwg_40 and T7_fwg_40 are results clear enough to de-termine a velocity near the window. The results forT6_fwg_40 were 1.67 m/s at the head reducing to 0.305 m/s later in the flow for data taken from the top of the flow,compared with u3 of 0.875 m/s from the PPTs at the base.For T7_fwg_40, the single clear result obtained is 0.164 m/s near the top of the flow at the head, compared with0.093 m/s for u3. The results of data obtained from thePPTs and from the camera are in reasonable agreement be-cause the top velocity is greater than the basal slip velocitydue to increased shearing towards the top (Takahashi 1991).In addition, elevated pore pressures are usually found to oc-cur behind the unsaturated head of a developing granular de-bris flow (Iverson 1997), so an exact match between thesaturation front and the head of a debris flow is unlikely.

Influence of moisture contentFigures 8a and 9a show the results of tests in model scale

carried out on the same materials (soil type and fluid viscos-ity) but with different moisture contents. For testsT6_fwg_40 through T8_fwg_40 (Table 1), the runout showsa clear decrease (hence, reduced flow mobility) with de-creasing moisture content, as expected. For example,T6_fwg_40 with a moisture content of 49% has a runoutthat is almost twice as long (as measured from the end ofthe channel) as T8_fwg_40 with a moisture content of 33%,as well as marginally greater lateral spread.

Modelling of models of velocity profileComparison of tests T8_fwg_40, T9_fwg_20, and

T17_fwg_10, as shown in Figs. 8b and 9b, allows modellingof models for velocity to examine the influence of keepingthe ratio of Ng to the fluid viscosity constant. Note thatT17_fwg test flow had a significant component of g (i.e.,10%) in the lateral direction to the flow. This resulted inthe flow sagging laterally and the leading edge missing thePPTs in the centre of the channel. The velocity results deter-mined from the PPTs were therefore inaccurate and are notreported.

Tests T8_fwg_40 and T9_fwg_20 show very similar meanvelocities at all stages of the flow (Fig. 8b). The overall areaof runout at the end of all tests is also very similar; how-ever, the lower viscosity, lower Ng, flows appeared to gen-erate somewhat longer and thinner deposits (Fig. 9b). Theresults of tests on flows over erodible beds (tests T11 andT16, discussed later) also show the same behaviour — i.e.,very similar velocity profiles for tests conducted with differ-ent viscosity fluids and g-level, but slightly longer and thin-ner final deposits for the less viscous flows. It should benoted that the T17_fwg_10 flow was somewhat confined toone side of the channel (i.e., it did not spread across the fullwidth as for tests T8_fwg_40 and T9_fwg_20). This mayhave led to a greater runout length, relative to width, in ad-dition to such effects of viscosity as are discussed below.

There are two different mechanisms involving energy dis-sipation that may be responsible for the differing runout be-haviour of the model flows, which may be consideredinterparticle and fluid-particle energy dissipation mecha-nisms, respectively.

The interparticle dissipation mechanism involves momenttransfer and friction between particles and at flow margins.For tests of the same prototype undertaken at different g-levels and using a different viscosity fluid, to produce thesame consolidation behaviour during flows that have other-wise developed the same velocity during downslope motion,the degree of interparticle energy dissipation will be differ-ent during runout and deposition. This is because they willexperience different frictional resistance due to the g-effectover the flat runout zone, where the downward driving forceis removed. Hence, the creation of similitude during down-slope motion of flows under different g-levels will result indifferences during flow arrest, i.e., different degrees of run-out. The fluid–particle dissipation mechanism relates to theinfluence of viscous damping within the flow, as understoodfrom the dynamic behaviour of soils. While the primaryform of energy dissipation during dynamic shearing relatesto the soil skeleton, the energy loss within pore fluids willbe different in model flows of different viscosity. This is be-cause the dynamic damping ratio of a soil mixture that usesa higher viscosity fluid is, in general, higher due to greaterviscous losses as the fluid is forced to flow between themoving soil particles (Bolton and Wilson 1990; Ellis et al.2000), while fluid viscosity does not affect soil stiffness.For example, Bolton and Wilson (1990) found that, for avery viscous pore fluid (100 cP), the damping ratio of cycli-cally strained specimens was significant, resulting in a three-fold increase in hysteretic soil damping compared withwater-saturated or dry specimens.

During the downslope motion of liquefied debris, the ef-fect of fluids of different viscosities will not be seen becausethe behaviour is dominated by large strains and energy in-

Fig. 7. The particle-size distributions (PSDs) for the soils used inthe tests. Two materials were used, denoted ‘‘fwg’’ and ‘‘s’’. For alltests except T5_s_1, the model and prototype particle-size distribu-tion (PSD) is the same due to the matching of fluid viscosity to theg-level (i.e., by a factor ‘‘N’’). For test T5_s_1, the prototype PSDis larger by a factor of (40)1/2, assuming consolidation scaling.



Fig. 8. Mean velocity versus distance from the end of the slope. (a) Influence of initial moisture content for tests on the same materials (T6at w = 49%, T7 at w = 36%, T8 at w = 49%); (b) modelling of models (T8 at N = 40 with m = 40 cP, T9 at N = 20 with m = 20 cP);(c) influence of particle-size distribution for tests at the same N = 40 (T4 silt with m = 40 cP, T5 silt with m = 1 cP, T6 fine well gradedwith m = 40 cP).

Bowman et al. 751


Fig. 9. Runout length and width. (a) Influence of initial moisture content for tests on the same materials (T6 at w = 49%, T7 at w = 36%,T8 at w = 49%); (b) modelling of models (T8 at N = 40 with m = 40 cP, T9 at N = 20 with m = 20 cP, T17 at N = 10 with m = 10 cP);(c) influence of particle-size distribution for tests at same N = 40 (T4 silt with m = 40 cP, T5 silt with m = 1 cP, T6 fine well graded withm = 40 cP).



put — equivalent to a ‘‘forced vibration’’ phase of a dynamicresponse in which viscous damping is relatively small com-pared with the hysteretic damping of the soil skeleton due tononlinearity of the soil stress–strain behaviour. This situationchanges when the flow reaches a flat runout zone, during a‘‘free vibration’’ episode without the presence of a drivingforce and where flow is coming to a halt. Here, the greaterdamping of the more viscous fluid comes into play to slowdown the material and dissipate energy faster. Further testsare needed to investigate the phenomena described above.

Influence of particle size and fluid viscosityFor tests carried out with different fluid viscosities,

T4_s_40 and T5_s_1, the influence of viscosity on flowspeed is clear, with the 40 times higher viscosity fluid re-sulting in an approximately 35 times lower velocity, takenas an average between PPT1 and PPT4 (Fig. 8). It shouldbe noted that the trend in the change in velocity over thechannel length for test T5_s_1 was very different from othertests, resulting in a particularly large peak in velocity in themiddle stretch (u2 in Table 1), which may have been the re-sult of a temporary block in the delivery tube. However, theoverall runout area for test T5_s_1 is slightly less than thatof T6_fwg_40, which was carried out at the same moisturecontent, but with a factor N higher fluid viscosity. This maybe explained by different rates of consolidation between thetests. The effective particle-size distribution for T5_s_1 wasshifted to the right by N1/2 (assuming diffusional scaling) inFig. 7 (i.e., effectively larger particles were modelled thanfor T6_fwg_40, particularly at d10 size), which should havealso contributed to somewhat faster consolidation and hence,a shorter runout, as found.

Nondimensional groupsAs discussed above, Iverson (1997) and Iverson and Den-

linger (2001) described nondimensional groups that are re-garded as significant in debris flow research. Thesenondimensional groups are listed and defined below, with abrief explanation of their relevance.

Aspect ratio, 3 — The ratio of flow thickness to flowlength (measured from the head of the flow to theend). Aspect ratio may be regarded as a measure of theflow mobility — there should be no scale-dependencebetween model and field-scale flows (Iverson andDenlinger 2001).Savage number, NS — The ratio of the stresses gener-ated via grain collisions to stresses due to grain con-tacts. It is regarded as characterizing the flow regime(collision or contact dominated), with NS > 0.1, result-ing in a grain inertial regime where particle collisionsdominate the flow (Savage and Hutter 1989).Bagnold number, NB — The ratio of the stresses viagrain collisions to the viscous fluid stresses. NB < 40is regarded as a ‘‘macroviscous’’ regime, wherebyshear and normal stress are found to be proportional toshear rate; NB > 450 suggests a collision-dominated re-gime, where shear and normal stresses become propor-tional to the square of the shear rate (Bagnold 1954).Bagnold’s number examines the role of fluid stressesin highly sheared solid–fluid mixtures and explicitlyexcludes shear stresses generated from Coulomb fric-tion. Hence, it is most relevant to situations whereNS > 0.1; that is, where the flow is dominated by briefcollisions rather than enduring contacts.Quasi-Reynolds number, NR — Analogous to the Rey-nold’s number used in fluid mechanics, larger flowsare characterized by NR > 106, while smaller flowshave much lower values. Comparison with a momen-tum equation for debris flows (Iverson and Denlinger2001) suggests that viscous effects are more dominantin smaller flows.Fluidization number, NF — The ratio of the velocityscale for fluidization of the mass to the velocity scaleof particles falling within the flow. NF < 1 suggeststhat the solid and fluid phases remain linked, so thatvelocities and accelerations of the fluid relative to theadjacent solids are small, allowing the mass to be trea-ted mathematically as an aggregated mixture (Iverson

Fig. 10. Change in pore pressure recorded at PPT1 for two tests, T7_fwg_40 and T11_fwg_40E, on fixed and erodible beds, respectively.Note the start time is arbitrary.

Bowman et al. 753


and Denlinger 2001). For debris flows, it is typical thatNF � 1. This clearly does not preclude internal parti-cle segregation, which is a key feature of most debrisflows; however, a particularly low value of NF may im-ply relatively little segregation (i.e., mudflow) has ta-ken place.Pore pressure number, NP — The ratio of the time fordownslope motion to the timescale for pore pressure dif-fusion, normal to the flow direction. Field-scale debrisflows have NP � 1, implying that high pore pressureswithin the flow will persist for far longer than the time-scale for the flow itself (Iverson and Denlinger 2001).

The definitions of the aforementioned dimensionlessgroups and the associated parameters correspond to thosederived in Iverson and Denlinger (2001). Equations [4]–[9]listed below have been amended where necessary, replacingg with Ng

½4� 3 ¼ H

L

½5� NS ¼rs _g2d2

ðrs � rfÞNgH

½6� NB ¼C1=3

C�ð1=3Þ � C1=3

� �rs _gd2

m

½7� NR ¼rH

ffiffiffiffiffiffiffiffiffiNgL

pCm

½8� NF ¼K

m

C

ð1� CÞ ðrs � rfÞffiffiffiffiffiffiffiffiffiffiNg=L

p

½9� NP ¼D

ffiffiffiffiffiffiffiffiffiffiL=Ng

pH2

where L is the flow length, rs is the solid density, _g is theshear strain rate, C is the average solid fraction in flow, andC* is the maximum possible solid fraction in flow.

Two tests were selected to show the extremes of possibil-ities in terms of nondimensional groups that could beachieved with the apparatus configuration and materials de-scribed. Table 3 gives bulk parameters used to determinenondimensional group values as discussed for these twotests, T5_s_1 and T7_fwg_40.

Note that for the calculations, r is the weighted average ofrf and rs, and other definitions of symbols are given in Table 3.A few notes regarding the values given in Table 3 follow.

The ‘‘typical’’ grain diameter is taken to be the meanvalue, equal to d50, which is the typical approach used inpractice. However, the truly representative particle size interms of mechanical–hydraulic behaviour may err by an or-der of magnitude either way, in particular for more well-graded materials that are representative of debris flows(note that empirically, d10 governs seepage and consolida-tion behaviour, as shown by Hazen (1892), while larger par-ticles can act as a ‘‘brake’’ on the flow, reducing runout(Rombi et al. 2006)).

Fluid viscosity has been taken to be the actual viscosity ofthe fluid without the addition of fine particles. This differsfrom the calculations by Iverson (1997) and Iverson andDenlinger (2001) where the viscosity includes the effect ofadding fine particles, which can increase the effective vis-cosity of the fluid. The reason for taking a different ap-proach here is that, in the centrifuge, inertia can cause fineparticles to behave as N1/2 times larger. Hence, silt size par-ticles may not behave as part of the fluid phase, as for flowsat 1g. The overall result is that the effective viscosity maybe up to an order of magnitude greater than given here,although it is hard to quantify. The partitioning of particlesizes into a ‘‘fluid phase’’ and ‘‘solid phase’’ in the centri-fuge needs further investigation.

Darcy’s permeability is a function of intrinsic permeabil-ity K, as well as density r, Ng, and viscosity m, such that

½10� k ¼ KrNg

m

The hydraulic diffusivity, D, is assumed to relate directlyto Darcy’s permeability, k, flow mixture stiffness, Es, and g-level, Ng, by the conventional equation for one-dimensionalconsolidation of a static saturated soil as given in eq. [2], us-ing estimates for stiffness, Es, and intrinsic permeability, K,based on published values (Major 2000; Iverson and Denlin-ger 2001). However, due to the rapidly moving and chang-ing nature of the flowing material, D may be rather higherthan given by the above calculation (Iverson 1997; Major2000). In addition, such values will change with entrainment(as solid concentration, C, changes). Hence, there may bebetween one and two orders of magnitude difference in theeffective values for k and D.

Note that the more general term of ‘‘hydraulic diffusiv-ity,’’ D, is used here, rather than the more common term‘‘coefficient of consolidation,’’ as the diffusion process dur-ing flow is a combination of both sedimentation (i.e., whenthe particles are not in contact with each other) and consol-idation (i.e., when a contact network has been formed be-tween particles).

C*, the maximum value taken by C in the flow, is as-sumed to equal 0.6 (i.e., minimum porosity n = 0.4), as de-termined from the value for emax for fwg material for thetests described here. This contrasts with the estimated valueof 0.7 used elsewhere (Iverson and Denlinger 2001).

Finally, as shown in Fig. 7, the actual typical particle sizeof material used in test T5_s_1 is smaller than that oftest7_fwg_40; however, the ‘‘effective’’ particle size (scaledby N1/2) is larger. Similarly, Table 2 shows that the esti-mated Darcy’s permeability has a higher value for testT5_s_1 than for test7_fwg_40. Both of these points reflectthe different ratios of g-level to pore-fluid viscosity for thetwo tests, such that for test T7_fwg_40, a g-level, N, of 40is counterbalanced by a fluid viscosity, m, of 40 cP, whereasfor the same g-level of 40 in test T5_s_1, water with a vis-cosity of 1 cP is used, resulting in a larger effective particlesize for this test.

Comparison of field cases and experimental flowsFigure 11 shows a comparison of nondimensional group

data using eqs. [4]–[9], for the two tests given in Table 3,



T5_s_1 and T7_fwg_40 with two field cases; Yake Dake inJapan (Takahashi 1991; Iverson and Denlinger 2001) andOsceola in the USA (Iverson 1997; Vallance and Scott1997); as well as that from a typical laboratory-scale flow(Rombi et al. 2006) and a large-scale flume flow (Iversonand Denlinger 2001). The field cases have been chosen torepresent the approximate range of debris flow behaviour:Yake Dake is typical of a small to medium sized, coarse-grained debris flow (peak discharge 1.5� 102 m3/s), whileOsceola is typical of an extremely large muddy debris flow(peak discharge approximately 2.5� 106 m3/s).

The data show that the centrifuge tests can match particu-lar aspects of behaviour of large-scale flows, which are oth-erwise difficult to replicate at small scale at 1g. Inparticular, the centrifuge tests can reproduce relatively lowSavage numbers, NS, below 0.01, ensuring that the flowsare frictional rather than collision dominated (Savage andHutter 1989), as found mainly in 1g flume tests, where NStends to be of an order between 0.1 and 10.

Low values of NF ensure that the fluid within the flow ismoving relatively slowly with respect to the adjacent solids,simplifying mathematical understanding of the flow, whichcan then be treated as aggregated. The values of NF in thecentrifuge tests lay between the two field cases, whereasthere was greater variation of NF determined from 1g flumetests.

The influence of the pore pressure number, NP, is of morephysical importance: larger volume flows tend to have lowervalues of NP, due to high pore pressures persisting for longeras a result of longer drainage paths within the flowing mass.This results in larger flows having greater flow mobility

(compare Osceola with Yake Dake) — a key issue in pre-dicting the risk posed by these hazards. The value of NP inthe centrifuge tests, while not as low as those of the Osceolaflow, was lower than those of flume tests conducted at 1g.

While data from the centrifuge tests give lower values ofthe Bagnold number, NB, than both field and other experi-mental flows, this should only affect flows that alreadyhave a high Savage number (NS > 0.1), leading to an inertialflow regime. It is notable that both field and centrifugeflows develop low Savage numbers (contact dominated),whereas other experimental flows develop both high NS(> 0.1) and high NB (> 600) values, suggesting that colli-sions dominate flows over both contact and fluid stresses, inthese cases.

The gradually reducing slope angle of the curved channelarrangement discussed here (average 248) generally resultedin flows decelerating between the mid-section and the lowersection of the channel. Increasing the average slope anglewould increase average flow speeds at the control point, re-sulting in higher Savage and Bagnold numbers, NS and NB.respectively Also, the wide channel led to flows that wereparticularly unconfined and thin, resulting in relatively lowvalues for quasi-Reynold’s number, NR. Larger volumeflows tend to have higher values of NR, indicating that vis-cous effects are lessened compared with smaller volumeflows. This is an important issue in the modelling of debrisflows. Future tests, using a steeper and more confined chan-nel, should be able to address these issues by increasing theflow velocity (increasing NS and NB) and flow thickness andlength (increasing NR), although it should be noted that thevalue for NB is constrained to remain relatively low in future

Table 3. Parameters and resulting nondimensional groups for tests T7_fwg_40 and T4_s_1.

Typical centrifuge

Parameter or nondimensional group Symbol (units) T7_fwg_40 T5_s_1Initial moisture content (by weight) w (%) 33 49d50 (mean) grain diameter d (m) 0.000054 0.000026Maximum flow thickness H (m) 0.008 0.005Flow length L (m) 1.2 1.5Bulk velocity at camera position v (m/s) 0.10 4.0Shear strain rate (= v/H) _g (1/s) 12.5 800Solid density rs (kg/m3) 2740 2650Fluid density rf (kg/m3) 960 1000Fluid viscosity m (kg/(m/s)) 0.04 0.001Gravity acceleration Ng (m/s2) 400 400Intrinsic permeability* K (m2) 1� 10–12 1� 10–13

Mixture stiffness* Es (kg/(m/s2)) 1� 104 1� 104

Darcy’s permeability* k (m/s) 1� 10–5 4� 10–5

Hydraulic diffusivity or coefficient ofconsolidation*

D (m2/s) 3� 10–7 1� 10–6

Average solid fraction in flow (= 1 – n,where n is porosity)

C 0.51 0.44

Max. possible solid fraction in flow C* 0.6 0.6Aspect ratio 3 6.7� 10–3 3.3� 10–3

Savage number NS 3.8� 10–7 6� 10–4

Bagnold number NB 0.007 3.5Quasi-Reynolds number NR 5.3� 104 1.2� 105

Fluidization number NF 2.7� 10–7 6.7� 10–7

Pore pressure number NP 6.8� 10–4 7.7� 10–3

*Values are estimates, based on published data, and may err by a factor *10.

Bowman et al. 755


centrifuge work, as particle size and fluid viscosity are dom-inant in its expression.

Erodible bed tests

The nomenclature for the tests on erodible beds is thesame as that for the fixed beds, but with the addition of asuffix ‘‘E’’ for ‘‘erodible.’’ A total of four tests on erodiblebeds were carried out. Two tests, T11_fwg_40E andT16_fwg_20E, are reported in detail here (Table 2, lowersection). Profiles of the flows were recorded; the results arecompared with theoretical values according to Takahashi(1991) and Takahashi et al. (1997).

Preparation of erodible bedsErodible beds, 20 mm in thickness, were prepared in situ

to a moisture content of 24.5% (saturation ratio, Sr?1) witheither a 40 cP glycerine–water mixture (T11_fwg_40E) or a20 cP glycerine–water mixture (T16_fwg_20E). To reducethe variables involved, the same PSD was used in the bedas in the debris flow, although the moisture content was nec-essarily lower in the bed than the flow to ensure stabilityfollowing placement as a vertical layer on the curved flumebase in the channel under 1g conditions. In situ preparationallowed the channel, PPTs, and lighting to remain on thecentrifuge between tests, considerably reducing preparationand turnaround time.

To construct and maintain a vertical bed uniformly, four40 mm wide curved moulds were formed from polystyreneto match the curved shape of the bed, behind which fixedamounts of pre-mixed material were packed. The surface ofeach mould in contact with the soil was hardened with glueand sand to prevent absorption of fluid into the pores. Themoulds were placed at a fixed distance, ensuring a standardthickness and density of the bed, as it was built up in fourstrips. The relatively flexible nature of the polystyrenemoulds allowed them to be wedged together between thewalls after the bed was completed.

The relatively high fluid viscosity used in the beds re-ported here ensured that there was little migration of mois-ture through the bed at 1g before the test had begun. Thepacked moulds were removed from the bed just before eachtest and suction stresses maintained the bed vertically in thedrum until the centrifuge was spun up. Movement wasmonitored by a video camera placed at the head of the bed.No detectable movement of the bed was noted between re-moval of the moulds and spin-up to the working g-level forany test.

ResultsFigure 12 shows sequences of images taken by the high-

speed camera for one of two tests, T16_fwg_20E, as the ex-perimental flows progressed (test T11 being similar). Theslope angle at the location of the camera was approximately188 (Fig. 4) — note that the camera was also tilted at 188 sothat the flow appears to be horizontal in the figure. Parts (a)through (d) of Fig. 12 correspond to (a) before the debrisflow, (b) the arrival of the flow, (c) mid-way through theflow, and (d) the final frame after deposition and some con-solidation has taken place. Note that there is a clearly de-fined line in the final frame that demarcates the new layerof debris over the old. Taken in isolation, this may suggestthat the overriding flow remained separated from the bedbelow. However, the images taken during the experimentsshow that the bed beneath the flowing material did not re-main fixed, but was rather mobilized by, and entrained into,the flow during the test, such that the upper separate layer ofsoil also included some material eroded from the bed (thiscan be seen by comparing the first and last image taken —the separation line between previously mobilized and sta-tionary soil is lower than the original bed surface).

From web-cam images focussing on where the flow firstexited the nozzle at the top of the slope, it was noted thatthe flow spread out over the width of the channel initially,although the flow later constricted to follow an incisedchannel, approximately 20 mm wide, which meandered

Fig. 11. Comparison of values for nondimensional groups: aspect ratio, 3, Savage number, NS, Bagnold’s number, NB, quasi-Reynold’snumber, NR, fluidization number, NF, and pore pressure number, NP, for different flow types (USGS data from Iverson and Denlinger 2001).



down through the erodible bed to the end of the flume.More information can be found in Bowman et al. (2006).

Figure 10 shows the change in pore pressure for testT11_fwg_40E in comparison with T7_fwg_40, a test on afixed bed, but otherwise with the same inputs. The initialpore pressure response is slower in the erodible bed case,due to the transducer being located beneath a layer of unsa-turated soil. The subsequent pore pressure response inT11_fwg_40E indicates the extent of erosion of the bed upto a time of 90 s, where the change in pore pressure becamenegative as soil was eroded below the initial bed depth. Thiswas particularly influenced by the incised channel passingover the first and second PPT for this particular test (exami-nation of the bed after the test reinforced this view).

Figure 13 shows the runout length and width for the twoerodible bed tests against test T7_fwg_40, which was under-taken on a fixed bed with the same flow moisture content of36%. It is notable that while undertaken with the same fluidviscosity and same g-level, test T11_fwg_40E has a shorterrunout than T7_fwg_40. This suggests that the slightly unsa-turated bed removed some of the fluid from the flow, result-ing in runout more similar to that carried out at a lowermoisture flow content of 33% (see test T6_fwg_40). As forthe tests on fixed beds, a lower viscosity fluid coupled witha lower g-level (test T16_fwg_20) resulted in a slightly lon-ger runout compared with the equivalent prototype model oftest T11_fwg_11. There was minimal erosion in both testsbecause the flows spread thinly over the bed, except for thepreviously noted narrowly incised channel, which did notaccount for much additional debris volume in this case.

Figures 14 and 15 show velocity profiles of the two flowsfrom test T11_fwg_40E and T16_fwg_20E with depth. Fig-ure 14 gives absolute values of velocity, vz, against the flowdepth, z, while Fig. 15 gives velocity normalized by the sur-face velocity, vz/vH, and flow height, normalized by themaximum flow thickness, z/H. Solid points denote testT11_fwg_40E data, while open points denote testT16_fwg_20E data. The velocity profiles were determinedfrom four sequences of images during steady flow. Individ-ual patches of texture, corresponding to solid particles in theflow, were traced against the calibration grid of pointspainted on the Perspex window. There was little image tex-ture in the upper parts of the flow compared with the lower;hence, data is sparse for values of z/H > 0.5, except for theflow surface, where the migrating surface profile providedenough information to determine the flow velocity, vH. Interms of the flow depth, it should be noted that for erodiblebeds, flow thickness can be difficult to ascertain accurately,

even at 1g (Armanini et al. 2005). However, zones of move-ment and of no movement provide bounds on the probablelocation of z = 0, where vz = 0. For these tests, z = 0 wastaken as the mid-point between these bounds.

Comparison of velocity distributions with semi-empiricalvalues

Takahashi (1991) and Takahashi et al. (1997) determineda semi-empirical equation for mature ‘‘stoney’’ (coarse-grained) debris flows over erodible beds, which has beenamended here for tests carried out under Ng, such that, vz,the local velocity at a height above the bed, z, is

½11� vz ¼2A

153 1� z

H

� �5=2

� 5 1� z

H

� �3=2

þ 2

� � ffiffiffiffiffiffiffiffiffiffiNgH

p

where

½12� A ¼ 1

3

cosq

ai cosa

rs � rf

rs

� �1=2C� � C

C1=2

H

d

and

q is the slope angle (taken as 188 at the camera posi-tion);ai cosa is a semi-empirical term, assumed to equal0.035 (with ai = 0.042), based on the work of Bagnold(1954);C* is the solid fraction at the bed = (1–nmax), wherenmax is porosity when e = emax;C is the average solid fraction = (1 – n), for a moisturecontent w of 36% for these tests;Ng is gravitational acceleration (g in the original equa-tion proposed by Takahashi is replaced by Ng here).

As indicated by Fig. 15, the distribution of normalized ve-locity with normalized depth appears to be modelled well bythe corresponding eq. [13]

½13� vz

vH

¼ 1� 1

21� z

H

� �3=2

2þ 3z

H

� �

However, the absolute velocity determined from eq. [11]does not match the true distributions of velocity in the tests.The figure shows that the

ffiffiffiffiffiffiNg

pterm in the equation does

not lie well with the dynamic scaling employed in the cen-trifuge tests. Assuming a value for Ng of 370 m/s2 andai cosa = 0.035 at the camera position for testT11_fwg_40E, the computed surface velocity, vH is pre-dicted to be 8.9 m/s for a 7 mm thick flow, compared withan actual velocity of 0.4 m/s. Assuming an equivalent value

Fig. 12. Images of debris flow test progression for test T16_fwg_20E. Frame rate 730 fps; numbers refer to frame number. (a) Before arri-val; (b) during flow arrival; (c) mid flow; (d ) final image of deposit.

Bowman et al. 757


for Ng of 185 m/s2 and ai cosa = 0.035 for testT16_fwg_20E, the predicted surface velocity is 6.3 m/s fora 7 mm thick flow compared with a measured velocity ofapproximately 0.4 m/s. Hence, velocity is found not to de-pend on the g-level, as dynamic similarity has been em-ployed by altering the fluid viscosity. That is, in theempirical eqs. [11] and [12], there is no viscosity term(where applicable) to offset the enhanced acceleration pro-vided by the centrifuge, so that the velocities are predictedto be greater than under Earth’s gravitation.

There are several other reasons to expect discrepancies be-tween the results and the empirical expression determinedfrom tests conducted at 1g. With respect to the experimentalarrangement in the centrifuge, within the 2.2 m diameterdrum, there is a nonnegligible change in g-level from Ng =304 m/s2 at the head to Ng = 392 m/s2 at the base, due to the

change in radial position of the flow. Therefore, the measuredvalues incorporate the history of the actual g-level change,whereas eq. [11] does not. This complicates exact comparisonof both values, measured and calculated, although this can ac-count only for a discrepancy of up to 20%.

In the development of an earlier approximation to theerodible bed flow case, Takahashi (1980) noted that a largervalue for Bagnold’s ai than 0.042 was needed to fit the the-oretical relationship to the experimental data. He used ai =0.5 and 0.35 in his reported experiments on debris flow ero-sion over a saturated bed of uniform fine gravel. He sug-gested that uncertainty in the ai value could be attributableto variability in the saturation of the bed, with a less satu-rated bed drawing more fluid away from the flow and thus,slowing it down. Figure 12 supports this suggestion, in thatthe bed is mobilized gradually as the debris flow progresses

Fig. 13. Runout length and width. Modelling of models for erodible beds and comparison with an equivalent fixed-bed case (fixed test: T7at N = 40 with m = 40 cP; erodible tests: T11 at N = 40 with m = 40 cP, T16 at N = 20 with m = 20 cP).

Fig. 14. Flow height versus flow velocity at camera position, for two tests of flows over erodible beds at model scale. Test T11_fwg_40E,‘‘T11’’, was carried out at 40g with 40 cP pore fluid and T16_fwg_20E, ‘‘T16’’, at 20g with 20 cP pore fluid.



over it, which indicates that a saturation front is movingdownward from the flow into the bed.

Estimates of typical suctions developed in the beds of Ta-kahashi’s (1991) tests on coarse sands and fine gravels areof the order of 1 kPa, while that of the tests discussed hereare of the order of 100 kPa (the glycerine–water mix has asimilar surface tension to water, while the d10 particles areapproximately 100 times smaller than those used by Takaha-shi). This is likely to lead to differing behaviour in terms ofseepage into the bed. Furthermore, the tests reported by Ta-kahashi were carried out on relatively monodisperse (uni-formly graded — Cu & 1.2 to 3.0) particle sizes. It may bethat the effective particle diameter, which has been taken tobe equal to the d50 value here, as in his tests, is not the mostappropriate diameter to consider for well-graded flows.

Finally, and most importantly, there is a variable missingin eq. [11] to deal with the combined effects of changingviscosity and g-level. The experiments show that the effectof enhanced g-level is counteracted by the increased fluidviscosity as shown by the close agreement of the two tests.Therefore, it is suggested here that increased viscosity (ei-ther from the fluid or from the effect of incorporating fines)may also act to slow the flow even when the flow is not de-fined as ‘‘viscous’’ in nature (Takahashi 1991).

Considering the above, Fig. 16 shows that if in eq. [11] a g-level of 9.8 m/s2 (i.e., as for the Earth and considering that thecentrifuge acceleration is balanced by the higher viscosityfluid in both cases) is substituted for the enhanced value, thepredicted velocity is 1.6 m/s, which is closer to the true value,but is still four times faster than what actually occurred. How-ever, if a value of g = 9.8 m/s2 is used in combination withai cosa = 0.5 (i.e., taking into account effects of bed seepage),good agreement between the experimental velocities and Ta-kahashi’s (1991) formulae (eqs. [11], [12]) is found.

In conclusion, it appears that Takahashi’s (1991) semi-empirical equations for a stoney-debris flow can describe

motion of fine-graded flows in the centrifuge, if a combina-tion of enhanced g and viscosity is taken into account. Sim-ilar problems are encountered as those found by Takahashiin using Bagnold’s value with erodible beds. Further re-search is needed to clarify these issues.

DiscussionThe advantages and drawbacks of centrifuge modelling of

debris flows are discussed with reference to the data that hasbeen obtained so far.

Recent developments in high-speed digital photographyand lighting and sensors such as pore pressure transducersenable a similar range of data to be recorded on the centri-fuge as can be obtained in 1g tests, although there are limitsto the number of data channels that can be used at any onetime (at the time of this test series, eight dynamic channelscapable of logging at a frequency of 16 kHz and 32 that canlog at 1 Hz were available for measurements in the chan-nel). A drawback of the modelling arrangement is that therewas a limit to the size of particle that can be used(<3.5 mm) due to the nozzle delivery of the flow. The useof particle scaling can, to an extent, mitigate this problem,by increasing the g-level without a corresponding increasein fluid viscosity, so that larger ‘‘effective’’ particle sizesare obtained. A clear understanding of the particle-size dis-tribution from the silt–sand boundary downwards is impor-tant if this approach is to be used.

Unlike at prototype scale, in the centrifuge the debris flowmaterial experiences a nonconstant g-level as the flowmoves radially outward from the tip of the nozzle, downthe channel. That is, with an average channel slope of 248in this centrifuge, there is an approximately 20% increaseof g from the beginning of the channel to the end. The influ-ence of g-level change is quantifiable, however, although itdoes add a complicating element to attempting direct com-parison with data obtained at 1g.

Fig. 15. Normalized flow height against normalized flow velocity for two tests of flows over erodible beds (model scale) and the semi-empirical relationship proposed by Takahashi (1991) — eq. [13]. Test T11_fwg_40E, ‘‘T11,’’ was carried out at 40g with 40 cP pore fluidand T16_fwg_20E, ‘‘T16’’, at 20g with 20 cP pore fluid.

Bowman et al. 759


Additionally, a small reduction in N (due to the velocityof the flow) has not been accounted for in this analysis; thatis, the full equation for centrifuge modelling also includes aterm 2vru, where vr is the radial velocity of the point of in-terest in the model and u is the angular velocity at thatpoint. Again, however, these can be quantified. For example,with a mean velocity of the flow of 0.4 m/s for a slope of188, tangential acceleration (coriolis) accounts, at the cameraposition, for less than 2% of the radially generated g-level.Hence, for the suite of tests reported here, tangential accel-eration can be neglected for the entire experiment.

The relatively thin flowing layer for the fixed-bed testsreported herein precluded detailed examination of the veloc-ity of flow with depth. In the future, it will be possible toexamine deeper flows within a more confined channel, thusenabling velocity profiles to be obtained for fixed-bed ar-rangements as for the erodible bed tests.

For both fixed and erodible bed tests, it is notable that thevelocity as determined from inspection of the PPT data wasconsiderably lower than the surface velocity determinedfrom the image data, as the flowing material shearedthroughout its depth. The PPT data for the fixed bed testsgiven in Table 1 therefore represent a basal slip velocity.Velocity estimates given in Table 1 for the erodible bedtests may be somewhat in error because the pore pressureresponse depended on the local bed saturation condition,which was not exactly the same from point to point. Overall,however, average particle velocities at the surface werefound to be between two and six times greater than the ve-locity determined at the base, as recorded by PPT response.

ConclusionsThe modelling of debris flows within a drum centrifuge is

shown to offer many benefits to complement experimental

and field studies at 1g. The flow regimes achieved in thecentrifuge more closely match those of field-scale debrisflows in many respects, as indicated by closer matching ofdimensionless numbers that are required to ensure correctscaling of the mechanical processes involved.

The tests reported in this paper were designed to replicatelaboratory flows as closely as possible, to allow comparisonwith data developed from well-constrained experiments.Therefore, it is interesting to note that, although the centri-fuge flows appear to produce a better approximation ofreal-scale physical processes than 1g laboratory flows, asshown by dimensional scaling, the data also match empiricalformulae derived from small-scale 1g experiments well. Itmay be that testing in a centrifuge can therefore generateconfidence in testing at 1g for particular types of debrisflows even if the values of particular nondimensional groupswould suggest that some of the mechanisms are different be-tween the small and large scale.

The tests to examine ‘‘modelling of models’’ confirm thatit is possible to match flow velocities for downslope motionby matching an increase in Ng with an increase in fluid vis-cosity, suggesting that the consolidation process has a majorinfluence on flow behaviour. The differences in runoutlength (if not overall area, which was well matched) indicatehowever, that in coming to arrest, viscous influences cannotbe ignored entirely. Further work is needed to elucidatebounds on this behaviour.

Erosion events are particularly difficult to model at 1g. How-ever, the results of experiments on erodible beds in the centri-fuge show very similar shearing behaviour to that reported byothers for coarse-grained flows. In addition, the developmentof an incised channel with a width approximately six times themaximum grain diameter agrees with observations made offield-scale events (Davies et al. 1991). Together these resultssuggest that, with judicious selection of materials, many impor-

Fig. 16. Flow height versus flow velocity for the two tests in Fig. 15, with eq. [11] using different values for gravity acceleration, Ng in m/s2,and Bagnold’s dimensionless parameters ai cosa.



tant elements of debris flow behaviour can be modelled in ageotechnical drum centrifuge to complement the experimentaltechniques that are currently in common use.

AcknowledgementsThe authors wish to thank the Royal Academy of Engi-

neering, UK, which provided partial financial support for theresearch. The assistance of Markus Iten, Adrian Zweidler,Heinz Buschor, Ernst Bleiker, Dusan Bystricky, and MarcoSperl at the Institute for Geotechnical Engineering, ETH Zur-ich, is gratefully acknowledged. Finally, the authors wish tothank Dr. Misko Cubrinovski of the University of Canterburyfor helpful discussions on soil dynamic behaviour.

ReferencesAnderson, S.A., and Sitar, N. 1995. Analysis of rainfall-induced

debris flows. Journal of Geotechnical Engineering, 121(7): 544–552. doi:10.1061/(ASCE)0733-9410(1995)121:7(544).

Armanini, A., and Gregoretti, C. 2000. Triggering of debris-flowby overland flow: A comparison between theoretical and experi-mental results. In Proceedings of the 2nd International confer-ence on Debris Flow Hazards Mitigation: Mechanics, Predictionand Assessment, Taipei, Taiwan, 16–18 August 2000. Edited byG. Wieczorek and N.D. Naeser. A.A. Balkema, Rotterdam, theNetherlands. pp. 117–124.

Armanini, A., Capart, H., Fraccarollo, L., and Larcher, M. 2005.Rheological stratification in experimental free-surface flows ofgranular-liquid mixtures. Journal of Fluid Mechanics, 532: 269–319. doi:10.1017/S0022112005004283.

Bagnold, R.A. 1954. Experiments on a gravity-free dispersion oflarge solid spheres in a Newtonian fluid under shear. Proceedingsof the Royal Society of London. Series A: Mathematical and Phy-sical Sciences, 225(1160): 49–63. doi:10.1098/rspa.1954.0186.

Benda, L.E., and Cundy, T.W. 1990. Predicting deposition of deb-ris flows in mountain channels. Canadian Geotechnical Journal,27(4): 409–417. doi:10.1139/t90-057.

Bolton, M.D. 1986. The strength and dilatancy of sands. Geotech-nique, 36(1): 65–78. doi:10.1680/geot.1986.36.1.65.

Bolton, M.D., and Wilson, J.M.R. 1990. Soil stiffness and damp-ing. In Proceedings of the 1st European Conference on Struc-tural Dynamics, Bochum, Germany, 5–7 June 1990. Edited byO.T. Bruhns, H.L. Jessberger, A.N. Kounadis, W.B. Kraetzig,K. Meskouris, H.-J. Niemann, G. Schmidt, G.I. Schueller, andF. Stangenberger. A.A. Balkema, Rotterdam, the Netherlands.Vol. 1, pp. 209–216.

Bowman, E.T., and Sanvitale, N. 2009. The role of particle size inthe flow behaviour of saturated granular materials. In Proceed-ings of the 17th International Conference on Soil Mechanicsand Geotechnical Engineering, Alexandria, Egypt, 5–9 October2009. Edited by M. Hamza, S. Marawan, and Y. El-Mossallamy.IOS Press, Amsterdam, the Netherlands. Vol. 1, pp. 470–473.

Bowman, E.T., Laue, J., Imre, B., Zweidler, A., and Springman,S.M. 2006. Debris flows in a geotechnical centrifuge. In Pro-ceedings of the 6th International Conference on Physical Model-ling in Geotechnics, Kowloon, Hong Kong, 4–6 August 2006.Edited by C.W.W. Ng, L.M. Zhang, and Y.H. Wang. Taylor &Francis, London. Vol. 1, pp. 311–316.

Chan, Y.C., Lam, C.H., and Shum, W.L. 1991. The September 90Tsing Shan landslide: a factual report. Geotechnical EngineeringOffice, Hong Kong Government, Hong Kong. Technical NoteTN 4/91.

Chau, K.T., Chan, L.C.P., Luk, S.T., and Wai, W.H. 2000. Shapeof deposition fan and runout distance of debris-flow: Effects of

granular and water contents. In Proceedings of the 2nd Interna-tional Conference on Debris-flow Hazards Mitigation: Me-chanics Prediction and Assessment, Taipei, Taiwan, 16–18 August 2000. Edited by G. Wieczorek and N.D. Naeser.A.A. Balkema, Rotterdam, the Netherlands. pp. 387–395.

Chen, H., Crosta, G.B., and Lee, C.F. 2006. Erosional effects onrunout of fast landslides, debris flows and avalanches: a numer-ical investigation. Geotechnique, 56(5): 305–322. doi:10.1680/geot.2006.56.5.305.

Chikatamarla, R., Laue, J., and Springman, S.M. 2006. CentrifugeScaling laws for guided free fall events including rockfalls. Interna-tional Journal of Physical Modelling in Geotechnics, 6(2): 14–26.

Craig, W.H., James, R.G., and Schofield, A.N. 1988. Centrifuges insoil mechanics. A.A. Balkema, Rotterdam, the Netherlands.

Davies, T.R., Phillips, C.J., Pearce, A.J., and Bao, Z.X. 1991. Newaspects of debris flow behaviour. In Proceedings of the Japan–U.S. Workshop on Snow Avalanche, Landslide, Debris FlowPrediction and Control, Tsukuba, Japan, 30 September – 2 Octo-ber, 1991. Organizing Committee of the Japan–U.S. Workshopon Snow Avalanche, Landslide, Debris Flow Prediction andControl, Tsukuba, Japan. pp. 443–451.

Davies, T.R., Phillips, C.J., Pearce, A.J., and Zhang, X.B. 1992.Debris flow behaviour - an integrated approach. In Proceedingsof the Erosion, Debris Flows and Environment in Mountain Re-gions, Chengdu, China, 5–9 July 1992. Edited by D.E. Walling,T.R. Davies, and B. Hasholt. International Association of Hy-drological Sciences, Wallingford, UK. pp. 217–225.

Egashira, S., Honda, N., and Itoh, T. 2001. Experimental study onthe entrainment of bed material into debris flow. Physics andChemistry of the Earth, Part C: Solar, Terrestial, and PlanetaryScience, 26(9): 645–650. doi:10.1016/S1464-1917(01)00062-9.

Ellis, E.A., Soga, K., Bransby, M.F., and Sato, M. 2000. Resonantcolumn testing of sands with different viscosity pore fluids.Journal of Geotechnical and Geoenvironmental Engineering,126(1): 10–17. doi:10.1061/(ASCE)1090-0241(2000)126:1(10).

Fannin, R.J., and Wise, M.P. 2001. An empirical-statistical modelfor debris flow travel distance. Canadian Geotechnical Journal,38(5): 982–994. doi:10.1139/cgj-38-5-982.

Garnier, J., Gaudin, C., Springman, S.M., Culligan, P.J., Goodings,D., Konig, D., Kutter, B., Phillips, R., Randolph, M.F. andThorel, L. 2007. Catalogue of scaling laws and similitude ques-tions in geotechnical centrifuge modelling. International Journalon Physical Modelling in Geotechnics, 7(3): 1–24.

Goodings, D. 1984. Relationships for modelling water effects ingeotechnical centrifuge models. In Proceedings of the Sympo-sium on The Application of Centrifuge Modelling to Geotechni-cal Design, Manchester, UK, 16–18 April 1984. Balkema,Rotterdam, the Netherlands. pp. 1–23.

Goodings, D.J. 1982. Relationships for centrifugal modelling ofseepage and surface flow effects on embankment dams. Geo-technique, 32(2): 149–152. doi:10.1680/geot.1982.32.2.149.

Hazen, A. 1892. Some physical properties of sands and gravelswith special reference to their use in filtration. 24th Annual Re-port. Massachusetts State Board of Health, Boston, Mass. DocNo. 34, pp. 539–556.

Hungr, O., Morgan, G.C., and Kellerhals, R. 1984. Quantitativeanalysis of debris torrent hazards for design of remedial mea-sures. Canadian Geotechnical Journal, 21(4): 663–677. doi:10.1139/t84-073.

Hungr, O., Evans, S.G., Bovis, M.J., and Hutchinson, J.N. 2001. Areview of the classification of landslides of the flow type. Envir-onmental and Engineering Geoscience, 7(3): 221–238. doi:10.2113/gseegeosci.7.3.221.

Hungr, O., McDougall, S., and Bovis, M. 2005. Entrainment of ma-

Bowman et al. 761


terial by debris flows. In Debris-flow hazards and related phe-nomena. Edited by M. Jakob and O. Hungr. Praxis PublishingLtd., Chichester, UK. pp. 135–158.

Hutchinson, J.N., and Bhandari, R.K. 1971. Undrained loading, afundamental mechanism of mudflows and other mass movements.Geotechnique, 21(4): 353–358. doi:10.1680/geot.1971.21.4.353.

Iverson, R.M. 1997. The physics of debris flows. Reviews of Geo-physics, 35(3): 245–296. doi:10.1029/97RG00426.

Iverson, R. M. 2005. Debris-flow mechanics. In Debris-flow ha-zards and related phenomena. Edited by M. Jakob and O. Hungr.Praxis, Chichester, UK. pp. 105–134.

Iverson, R.M., and Denlinger, R.P. 2001. Flow of variably fluidizedgranular masses across three-dimensional terrain: 1. Coulombmixture theory. Journal of Geophysical Research, 106(B1):537–552. doi:10.1029/2000JB900329.

Jakob, M., Hungr, O., and Thomson, B. 1997. Two debris flows withanomalously high magnitude. In Proceedings of the 1st Interna-tional Conference on Debris-flow Hazard Mitigation, San Fran-cisco, Calif., 7–9 August 1997. Edited by C.-I. Chen. AmericanSociety of Civil Engineers (ASCE), New York. pp. 382–394.

Janssen, H.A. 1895. Versuche uber den Getreidedruck in Silozellen.VDI Zeitschrift, 39(35): 1045–1049. [In German.]

King, J. 1996. Tsing Shan debris flow. In Special Project ReportSPR 6/96. Geotechnical Engineering. Office, Hong Kong Gov-ernment, Hong Kong. p. 133.

Kutter, B.L. 1995. Recent advances in centrifuge modeling of seis-mic shaking. In Proceedings of the 3rd International Conferenceon Recent Advances in Geotechnical Earthquake Engineeringand Soil Dynamics, St. Louis, Mo., 2–7 April 1995. Edited byS. Prakash. University of Missouri–Rolla Publications, Rolla,Mo. Vol. 2, pp. 927–941.

Major, J.J. 2000. Gravity-driven consolidation of granular slurries -implications for debris-flow deposition and deposit characteris-tics. Journal of Sedimentary Research, 70(1): 64–83. doi:10.1306/2DC408FF-0E47-11D7-8643000102C1865D.

McArdell, B.W., Bartelt, P., and Kowalski, J. 2007. Field observa-tions of basal forces and fluid pore pressure in a debris flow.Geophysical Research Letters, 34(7): L07406. doi:10.1029/2006GL029183.

Nedderman, R.M. 1992. Statics and kinematics of granular materi-als. Cambridge University Press, Cambridge, UK.

Ponce, V., and Bell, J. 1971. Shear strength of sand at extremelylow pressures. Journal of the Soil Mechanics and FoundationsDivision, ASCE, 97(4): 625–637.

Rickenmann, D., Weber, D., and Stephanov, B. 2003. Erosion by deb-ris flows in field and laboratory experiments. In Proceedings of theThird International Conference on Debris-flow Hazards Mitigation:Mechanics Prediction and Assessment, Davos, Switzerland, 10–12 September 2003. Edited by D. Rickenmann and C.-I. Chen.Millpress, Amsterdam, the Netherlands. Vol. 2, pp. 883–894.

Rombi, J., Pooley, E.J., and Bowman, E.T. 2006. Factors influen-cing granular debris flow behaviour: an experimental investiga-tion. In Proceedings of the 6th International Conference onPhysical Modelling in Geotechnics, Kowloon, Hong Kong, 4–6 August 2006. Edited by C.W.W. Ng, L.M. Zhang, and Y.H.Wang. A.A. Balkema, Rotterdam, the Netherlands. pp. 379–384.

Savage, S.B., and Hutter, K. 1989. The motion of a finite mass ofgranular material down a rough incline. Journal of Fluid Me-chanics, 199: 177–215. doi:10.1017/S0022112089000340.

Schofield, A.N. 1980. Cambridge geotechnical centrifuge operations.Geotechnique, 30(3): 227–268. doi:10.1680/geot.1980.30.3.227.

Schofield, A.N., and Wroth, C.P. 1968. Critical state soil me-chanics. McGraw-Hill, London.

Springman, S.M., Laue, J., Boyle, R., White, J., and Zweidler, A.2001. The ETH Zurich geotechnical drum centrifuge. Interna-tional Journal of Physical Modelling in Geotechnics, 1(1): 59–70.

Sture, S., Costes, N., Batiste, S., Lankton, M., AlShibli, K., Jere-mic, B., Swanson, R., and Frank, M. 1998. Mechanics of granu-lar materials at low effective stresses. Journal of AerospaceEngineering, 11(3): 67–72. doi:10.1061/(ASCE)0893-1321(1998)11:3(67).

Symes, M.J., Gens, A., and Hight, D.W. 1988. Drained principalstress rotation in saturated sand. Geotechnique, 38(1): 59–81.doi:10.1680/geot.1988.38.1.59.

Takahashi, T. 1980. Debris flow on prismatic open channel. Jour-nal of the Hydraulics Division, ASCE, 106(3): 381–396.

Takahashi, T. 1991. Debris flow. A. A. Balkema, Rotterdam, theNetherlands.

Takahashi, T., Satofuka, Y., and Chishiro, K. 1997. Dynamics ofdebris flows in the inertial regime. In Debris-Flow Hazards Mi-tigation: Mechanics, Prediction and Assessment, Proceedings ofthe 1st International Conference on Debris-flow Hazard Mitiga-tion, San Francisco, Calif., 7–9 August 1997. Edited by C.-I.Chen. American Society of Civil Engineers, New York.pp. 239–248.

Tognacca, C., and Bezzola, G.R. 1997. Debris-flow initiation bychannel-bed failure. In Debris-Flow Hazards Mitigation: Me-chanics, Prediction and Assessment, Proceedings of the 1st In-ternational Conference on Debris-flow Hazard Mitigation, SanFrancisco, Calif., 7–9 August 1997. Edited by C.-I. Chen. Amer-ican Society of Civil Engineers, New York. pp. 44–53.

Tognacca, C., and Minor, H.-E. 2000. Role of surface tension, fluiddensity and fluid viscosity on debris-flow dynamics. In Me-chanics, Prediction and Assessment, Proceedings of the 2nd In-ternational Conference on Debris-Flow Hazards Mitigation,Taipei, Taiwan, 16–18 August 2000. Edited by G. Wieczorekand N.D. Naeser. A.A. Balkema, Rotterdam, the Netherlands.pp. 229–235.

Vallance, J.W., and Scott, K.M. 1997. The Osceola Mudflow fromMount Rainier: Sedimentology and hazard implications of ahuge clay-rich debris flow. Geological Society of America Bul-letin, 109(2): 143–163. doi:10.1130/0016-7606(1997)109<0143:TOMFMR>2.3.CO;2.

Vesic, A., and Clough, G. 1968. Behaviour of granular materialsunder high stresses. Journal of the Geotechnical Engineering Di-vision, ASCE, 94(SM3): 661–688.

Wang, G., and Sassa, K. 2006. Physical modeling of landslides inring shear tests and flume tests. In Proceedings of the 6th Inter-national Conference on Physical Modelling in Geotechnics,Kowloon, Hong Kong, 4–6 August 2006. Edited by C.W.W.Ng, L.M. Zhang, and Y.H. Wang. Taylor & Francis, London.Vol. 1, pp. 113–125.

Wang, G., Sassa, K., and Fukuoka, H. 2003. Downslope volumeenlargement of a debris slide — debris flow in the 1999, Hir-oshima, Japan, rainstorm. Engineering Geology, 69(3–4): 309–330. doi:10.1016/S0013-7952(02)00289-2.

Weber, T.M., Laue, J., and Springman, S.M. 2006. Centrifugemodelling of sand compaction piles in soft clay under embank-ment load. In Proceedings of the 6th International Conferenceon Physical Modelling in Geotechnics, Kowloon, Hong Kong,4–6 August 2006. Edited by C.W.W. Ng, L.M. Zhang, and Y.H.Wang. Taylor & Francis, London. Vol. 1, pp. 603–608.

