water
Article The Development of a 1-D Integrated Hydro-Mechanical Model Based on Flume Tests to Unravel Different Hydrological Triggering Processes of Debris Flows
Theo W. J. van Asch 1,2,*, Bin Yu 2 and Wei Hu 2
1 Faculty of Geosciences, Utrecht UniversityPrinceton 8a, 3584 CB Utrecht, The Netherlands 2 State Key Laboratory of Geohazard Prevention and Geoenvironment Protection, Chengdu University of Technology, Chengdu 610059, Sichuan, China; [email protected] (B.Y.); [email protected] (W.H.) * Correspondence: [email protected]; Tel.:+86-13551168496
Received: 11 June 2018; Accepted: 13 July 2018; Published: 17 July 2018
Abstract: Many studies which try to analyze conditions for debris flow development ignore the type of initiation. Therefore, this paper deals with the following questions: What type of hydro-mechanical triggering mechanisms for debris flows can we distinguish in upstream channels of debris flow prone gullies? Which are the main parameters controlling the type and temporal sequence of these triggering processes, and what is their influence on the meteorological thresholds for debris flow initiation? A series of laboratory experiments were carried out in a flume 8 m long and with a width of 0.3 m to detect the conditions for different types of triggering mechanisms. The flume experiments show a sequence of hydrological processes triggering debris flows, namely erosion and transport by intensive overland flow and by infiltrating water causing failure of channel bed material. On the basis of these experiments, an integrated hydro-mechanical model was developed, which describes Hortonian and saturation overland flow, maximum sediment transport, through flow and failure of bed material. The model was calibrated and validated using process indicator values measured during the experiments in the flume. Virtual model simulations carried out in a schematic hypothetical source area of a catchment show that slope angle and hydraulic conductivity of the bed material determine the type and sequence of these triggering processes. It was also clearly demonstrated that the type of hydrological triggering process and the influencing geometrical and hydro-mechanical parameters may have a great influence on rainfall intensity-duration threshold curves for the start of debris flows.
Keywords: triggering of debris flows; overland flow; infiltration; laboratory experiments; modelling; rain intensity-duration threshold curves
1. Introduction A debris flow is one of the most dangerous types of mass movement because, depending on the rheology and topography, it can reach a very high speed and large run-out distance. Important study aspects of the initiation process of a debris flow are the mechanism and boundary condition, because they determine the meteorological threshold conditions and further evolution, and will provide clues for future mitigation strategies [1]. One can make different classifications of initiation mechanisms based on different viewpoints [1]. It was among others [2,3], who stressed the importance of the infiltration capacity of the soil as a key factor for either the development of shallow landslides or surficial erosion and transport of material by overland flow, that might create different types of flow like mass movements. Effective overland
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flow driven triggering processes are mainly concentrated in channels where high water discharges, and severe erosion and transport lead to high solid concentrations generating debris flows [4–9]. Material is supplied to these debris flows by detachment and transport of the bed material, but also through lateral erosion of the channel bed. The channel can be partly or totally blocked by landslide dams. High runoff discharges eroding these landslide dams can also lead to initiation and rapid grow of debris flows [10–12]. Landslide damming can also be initiated by rapid incision of the channel bed destabilizing the side walls [13]. With infiltrating driven triggering mechanisms, shallow landslides are generated, which may or may not transform into debris flows. This failure mechanism by infiltrating water can occur in channel beds filled with loose material [14] and on planar slopes where shallow landslides can also transform into debris flows [15–18]. The transformation of a failed mass into a debris flow is rather complex and depends on various hydro-mechanical processes related to pore pressure development and supply of abundant overland flow water further mobilizing the failed mass [19–23]. Several authors analyzed partly the role of hydro-mechanical and morphometric factors controlling the type of initiation of debris flows. Berti [24] analyzed the hydrological factors for the generation of debris flows in typical source areas in the Italian Alps by modelling overland flow in the channel bed from a source area as a response to rainfall impulses. Kean [25] proposed an integrated hydro-geotechnical dynamic model to describe sediment transport by overland flow and consequently mass failure transforming into debris flow surges. Hu [26] highlighted the initial soil moisture, and thus infiltration capacity as a controlling factor for the type of initiation; wet soils created mainly surficial runoff, erosion, and incision; bank failure; and damming and debris flow development, while dry soils showed mainly infiltration and landslide failure and debris flow initiation [1]. Zhuang et al. [1] focused more on the slope gradient as a controlling factor for different types of initiation. Their flume studies revealed that at gentler slope gradients around 10◦ ± 2◦, incision and bank failure is dominant, creating channel damming and dam failure, inducing debris flows. At intermediate slopes around 15◦ ± 3◦, erosion of bed material occurs at high discharges. The high sediment transport capacity with high sediment concentrations is sufficient to create debris flows. At steeper slopes around 21◦ ± 4◦, bed failure by infiltrating overland flow water with debris flow formation is the most dominant process. Meteorological thresholds for the initiation of debris flows are closely related to the process of initiation. In many studies about these meteorological thresholds, no clear distinction was made between the types of triggering [27]. The assessment of these thresholds in relation to various morphometric and geological factors was made in most cases using statistical techniques [28–30]. Until now, only isolated aspects of the hydrological triggering system of debris flows have been studied. There is a need for a comprehensive framework which gives insight in the controlling factors for the evolution of different triggering systems in upstream channels of debris flow gullies. Therefore this paper will try to give answers on the following questions:
1. What type of hydro-mechanical triggering mechanisms for debris flows can we distinguish in upstream channels of debris flow prone gullies? 2. What are the main parameters and in what way are they controlling the type and temporal sequence of these triggering processes? 3. What is the influence of hydro-mechanical parameters and related triggering processes on the meteorological thresholds for debris flow initiation?
In order to answer these questions we have carried out a number of flume tests to detect the conditions for different types of hydro-mechanical triggering mechanisms of debris flows (Section2). Based on the process information revealed by these experiments we will develop an integrated hydro-mechanical model describing these triggering processes (Section3). The model will be calibrated and validated using indicator values obtained from the processes measured in the flume (Section4). Virtual model simulations will be carried out in a schematic hypothetical source area of a catchment to make a framework of the type and sequence of these triggering processes as a function of slope Water 2018, 10, 950 3 of 22
Water 2018, 10, x FOR PEER REVIEW 3 of 22 angle and the hydraulic conductivity of the bed material (Section5). The model will also be used for sensitivityused for sensitivity analyses to analyses study the to influencestudy the of influe importantnce of geometricalimportant geometrical and hydro-mechanical and hydro-mechanical parameters andparameters the related and type the ofrelated initiation type process of initiation on rainfall proce intensity-durationss on rainfall intensity-duration threshold curves, threshold for the startcurves, of debrisfor the flows start of (Section debris6 ).flows (Section 6).
2.2. FlumeFlume TestsTests toto RevealReveal TypesTypes of of Debris Debris Flow Flow Triggering Triggering
2.1. Setupp of the Flume Experiments 2.1. Setupp of the Flume Experiments A flume was designed to see whether we could simulate in a 1D framework the initiation of A flume was designed to see whether we could simulate in a 1D framework the initiation of debris flows by different hydro-mechanical triggering mechanisms. (Figure1). The flume had a length debris flows by different hydro-mechanical triggering mechanisms. (Figure 1). The flume had a of 8 m and a width of 0.3 m. The material simulating the channel bed with a thickness of 0.1 m and length of 8 m and a width of 0.3 m. The material simulating the channel bed with a thickness of a width of 0.3 m was positioned at a distance of 4 m from the top of the flume and had a length of 0.1 m and a width of 0.3 m was positioned at a distance of 4 m from the top of the flume and had a 2 m. The material was brought into the flume in layers of about 2 cm and was slightly compacted dry length of 2 m. The material was brought into the flume in layers of about 2 cm and was slightly densitycompacted (see dry Table density1). There (see was Table an outflow 1). There at was a distance an outflow of 2 m at from a distance the lower of 2 end m from of the the channel lower bed end (Figureof the 1channel). The waterbed (Figure entered 1). at The the upperwater endentered of the at flumethe upper with end a controlled of the flume discharge, with a simulating controlled run-ondischarge, water simulating from an upstreamrun-on water area. from an upstream area.
FigureFigure 1.1. DesignDesign ofof thethe flumeflume test.test. ForFor explanationexplanation ofof thethe parametersparameters seesee text.text.
TableTable 1. 1.Hydro-mechanical Hydro-mechanical characteristics characteristics of threeof three types type of beds of material bed material used in used theflume in the tests. flume Friction tests. meansFriction friction means angle friction of theangle material of the inmaterial degrees. in D30/50degrees. means D30/50 that means 30/50% that of30/50% the sample of the hadsample a lower had diametera lower diameter than what than is indicated what is indicated in the column. in the column.
Friction φ Density SD Hydraulic Conductivity D30 D50 D90 Friction ϕ Density SD Hydraulic Conductivity D30 D50 D90 ParticleParticle Size Size Class Class o −3 −3 −1 (o)( ) k Nm−3 k kNm Nm− 3 (m(m s s−)1 ) (mm) (mm)(mm) (mm)(mm) CoarseCoarse 34.634.6 15.4 15.4 1.7 1.7 4.91E-03 4.91E-03 9 9 11 18 18 MediumMedium 33.733.7 16.3 16.3 3.0 3.0 3.28E-03 3.28E-03 4 4 6 16 16 FineFine 29.229.2 19.5 19.5 1.4 1.4 0.54E-03 0.54E-03 0.70.7 1.6 8 8
ThreeThree typestypes ofof materialmaterial werewere usedused inin thethe experimentsexperiments withwith differentdifferent graingrain sizesize distributionsdistributions (Figure(Figure2 ).2). TheThe mean mean density density of of the the bed bed material material was was 15.4, 15.4, 16.3, 16.3, and and 19.4 19.4 k k N N m m−−33 for thethe coarse,coarse, medium,medium, andand finefine material,material, respectivelyrespectively withwith aa SDSD ofof 1.7,1.7, 3.0,3.0, andand 2.4, respectively. WeWe couldcould varyvary thethe slopeslope angleangle ofof thethe flumeflume betweenbetween 1414◦° andand 2020°.◦. TheThe initialinitial moisturemoisture contentcontent ofof thethe flumeflume materialmaterial waswas moremore oror lessless dry.dry. TheThe initialinitial moisturemoisture contentcontent isis importantimportant forfor thethe infiltrationinfiltration capacity,capacity, butbut sincesince wewe usedused inin the laboratory a a large large influx influx of of water water from from above above into into the the coarse coarse bed bed material, material, we weignored ignored the theeffect effect of the of thesorptivity sorptivity (related (related to the to theinitial initial moistu moisturere content) content) on the on theinfiltration infiltration capacity capacity of the of bed the bedmaterial. material.
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100 90 80 70 60 P(%) 50 coarse 40 middle 30 fine 20 10 0 0.001 0.01 0.1 1 10 100 D (mm)
Figure 2. Cumulative grain size distribution of the three bed materials used in the flume tests. Figure 2. Cumulative grain size distribution of the three bed materials used in the flume tests.
TheThe friction of thethe threethree materials materials was was measured measured with with the the conventional conventional direct direct shear shear apparatus apparatus [31]. [31].The hydraulicThe hydraulic conductivity conductivity of saturated of saturated cylindrical cylindrical soil samples soil samples of the three of the grain three sizes grain was sizes measured was measuredwith a constant with a head constant gradient head betweengradient thebetween upper the and upper lower and end lower of the end sample of the [32 sample]. Only [32]. a limited Only aamount limited ofamount hydromechanical of hydromechanical tests were tests carried were out, carried which out, delivered which delivered no information no information about the about mean theand mean SD of and the SD friction of the and friction hydraulic and hydraulic conductivity conductivity values. Table values.1 gives Table further 1 gives information further information about the aboutfriction, the hydraulic friction, hydraulic conductivity, conductivity, and gradient and of grad theient materials of the usedmaterials for the used experiments. for the experiments. PorePore pressure pressure was was measured measured at at three three places (F (Figureigure 11)) atat thethe bottombottom ofof thethe flume.flume. TheThe porepore pressurepressure sensors, type: YP4049, were producedproduced byby YomYom Technology Technology Company. Company. The The measuring measuring range range of ofpore pore pressure pressure was was from from−100 −100 k k Pa Pa to to +100 +100 k k Pa. Pa. LaserLaser sensors (ZLDS100(ZLDS100 ZSYZSY Group; Group; resolution resolution 0.03% 0.03% FS) FS) at threeat three points points with with a spacing a spacing of 0.5 of m 0.5(Figure m (Figure1) were 1) used were to used monitor to monitor topographical topographi heights,cal heights, especially especially with the with aim the to monitoraim to monitor abrupt abruptchanges changes in relief in due relief to beddue failure.to bed failure. InIn addition, addition, video recordingsrecordings werewere performed performed (Figure (Figure1) 1) to to follow follow the the sequence sequence of processesof processes in the in thecourse course of the of the experiments. experiments. During During the processthe process of overland of overland flow flow erosion, erosion, samples samples were were taken taken six times six timesfor more for more or less or steady less steady state conditionsstate conditions at the at outlet the outlet of the of flume the flume (Figure (Figure1). The 1). discharge The discharge of water of waterwith sedimentswith sediments was collected was collected in baskets in baskets every 5 ev s.ery The 5 sediments s. The sediments were sieved, were dried,sieved, and dried, weighed and weighedto determine to determine the solid the discharge solid discharge and the concentration and the concentration of the fluid. of the The fluid. mean The percentage mean percentage deviation deviationbetween thebetween individual the individual measurements measurements during anduring experiment an experiment was 32.5% was and32.5% 19.3% and for19.3% the for water the waterdischarge discharge and solid and discharge,solid discharge, respectively. respectively. AnAn integrated integrated model model (Section (Section 33)) for surfacesurface andand subsurfacesubsurface flow,flow, sedimentsediment transport,transport, andand bedbed slopeslope stability stability was was developed developed to to describe describe the the processes processes in in the the flume, flume, which which was was used used later later to to analyze analyze thethe sequence sequence of of different different initiation initiation processes processes at the field field scale. 2.2. Observations on Different Types of Hydrological Triggering Mechanisms in Flume Tests 2.2. Observations on Different Types of Hydrological Triggering Mechanisms in Flume Tests The flume tests were carried out in order to reveal different types of hydrological triggering The flume tests were carried out in order to reveal different types of hydrological triggering mechanisms which may create debris flows and to establish indicators related to these triggering mechanisms which may create debris flows and to establish indicators related to these triggering processes which were used to calibrate and validate our theoretical model (Section4). During the processes which were used to calibrate and validate our theoretical model (Section 4). During the flume tests with the three bed materials under different slope angles, observation were carried out by flume tests with the three bed materials under different slope angles, observation were carried out means of video images and laser sensors. Some of the observed process indicators are given in Table2. by means of video images and laser sensors. Some of the observed process indicators are given in Table 2.
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Water 2018Water, 10 ,2018 x FOR, 10 PEER, x FOR REVIEW PEER REVIEW 5 of 22 5 of 22 Water 2018, 10, x FOR PEER REVIEW 5 of 22 Table 2. Observed time to overland flow and bed failure, overland flow type and failure mode in flume Table 2.Table Observed 2. Observed time to time overland to overland flow and flow bed and failure, bed failure, overland overland flow type flow and type failure and failuremode inmode in experimentsTable for three2.Table Observed types 2. Observed oftime bed to time materialoverland to overland flow and forand flow differentbed and failure, bed bed failure,overland slope overland angles:flow type flow (a) and saturationtype failure and failuremode overland inmode in flume experimentsflume experiments for three for types three of types bed ofmaterial bed material and for and different for different bed slope bed angles: slope angles:(a) saturation (a) saturation flume experimentsflume experiments for three for types three of types bed materialof bed material and for and different for different bed slope bed angles: slope angles:(a) saturation (a) saturation flow; (b) Hortonianoverlandoverland flow; overland (b) flow; Hortonian flow; (b) Hortonian (c) overland slow overland continuous flow; (c) flow; slow bed(c) continuous slow failure; continuous (d)bed rapidfailure; bed failure;failure; (d) rapid (d) nf: failure; rapid no failure. failure; nf: no nf: no overlandoverland flow; (b) flow; Hortonian (b) Hortonian overland overland flow; (c) flow; slow (c) continuous slow continuous bed failure; bed failure;(d) rapid (d) failure; rapid failure;nf: no nf: no failure. failure. failure. Time to Bed Inflow Time to Run-Off Initiation Time to TimeBed to Bed Grain size Slope −1 −1 Inflow Inflow Time to TimeRun-Off to Run-Off Initiation Initiation FailureTime to Bed Grain sizeGrain L size s Slope m Slope Inflow secTime to Run-Off Initiation Failure Failure Grain sizeGrain size Slope Slope−1 −1 −1 −1 Failuresec Failure Grain size SlopeL s−1 m −1L s−1 m−1 sec sec Failure L s−1 m−1 sec sec sec 20◦ 0.18 402 411 sec 20° 20°0.18 0.18 402 402 411 411 18◦ 0.2220° 0.18 103 402 110 411 18° 18°0.22 0.22 103 103 110 110 ◦ 18° 0.22 103 110 Coarse 0.0049 Coarse16 0.0049 0.2916° 0.29 63 63 72 72 Coarse◦ 0.0049Coarse 0.004916° 16°0.29 0.29 63 63 72 72 15 Coarse 0.00490.40 16° 0.29 73 63 72 ◦ 15° 15°0.40 0.40 73 73 nf 14 0.4115° 0.40 59 73 nf nf 14° 14°0.41 0.41 59 59 nf ◦ 14° 0.41 59 20 0.1120° 20°0.11 0.11 168 168 168 168 168 168 ◦ 20° 0.11 168 168 18 0.1318° 18°0.13 0.13 140 140 140 140 140 140 ◦ 18° 0.13 140 140 Medium 0.0033 Medium16 Medium 0.0033 0.00330.1616° 16°0.16 0.16 54 54 54 106 106 106 Medium◦ Medium 0.0033 0.003316° 16°0.16 0.16 54 54 106 106 15 Medium 0.00330.1815° 16°0.18 0.16 27 27 54 106 15° 15°0.18 0.18 27 27 nf nf 14◦ 0.1915° 0.18 46 27 nf nf 14° 14°0.19 0.19 46 46 nf 14° 0.19 46 ◦ 20° 20°0.03 0.03 30 30 270 270 20 0.0320° 0.03 30 30 270 270 18◦ 0.0618° 18°0.06 0.06 220 220 220 613 613 613 Fine ◦0.00054 16° 18°0.09 0.06 90 220 270 613 Fine 0.00054 Fine16 0.00054Fine 0.000540.0916° 16°0.09 0.09 90 90 90 270 270 270 ◦ Fine 0.0005415° 16°0.10 0.09 110 90 270 15 0.1015° 15°0.10 0.10 110 110 110 nf 14° 15°0.11 0.10 102 110 nf nf ◦ 14° 14°0.11 0.11 102 102 nf 14 0.1114° 0.11 102 102 In slopeIn hydrology,slope hydrology, two types two oftypes overland of overland flow can flow be can distinguished: be distinguished: saturation saturation overland overland flow flow In slopeIn hydrology,slope hydrology, two types two oftypes overland of overland flow can flow be candistinguished: be distinguished: saturation saturation overland overland flow flow In slopeand hydrology, Hortonianand Hortonian overland two overland types flow of [32]. flow overland These [32]. twoThese flow types two can could types be becould distinguished: distinguished be distinguished during saturation during the different the overland different flume flow flume and Hortonianand Hortonian overland overland flow [32]. flow These [32]. twoThese types two could types becould distinguished be distinguished during during the different the different flume flume experimentsexperiments (Table (Table2). Satu 2).ration Satu rationoverland overland flow was flow characterize was characterized, afterd, complete after complete saturation saturation of the of the and Hortonianexperiments overlandexperiments (Table flow (Table2). [ 32Satu]. 2).ration These Satu rationoverland two typesoverland flow could was flow characterize be was distinguished characterized, afterd, complete duringafter complete thesaturation different saturation of the flume of the soil, bysoil, a more by a ormore less or spatially less spatially randomly randomly ponding ponding of water of waterat the atsoil the surface, soil surface, while whileHortonian Hortonian experimentssoil, (Table bysoil, a2 ).more by Saturation a ormore less or spatially overlandless spatially randomly flow randomly was ponding characterized, ponding of water of waterat after the completeatsoil the surface, soil saturationsurface, while whileHortonian of theHortonian soil, overlandoverland flow, whichflow, whichoccurs occurs when thewhen rainfall the rainfall intensity intensity or supply or supply of overland of overland flow water flow wateris larger is larger by a more oroverland lessoverland spatially flow, whichflow, randomly whichoccurs occurs when ponding thewhen rainfall ofthe water rainfall intensity at intensity the or soilsupply or surface, supply of overland whileof overland flow Hortonian water flow iswater larger overland is larger than thethan infiltration the infiltration capacity capacity of the soil,of the showed soil, showed a more a concentrated more concentrated continuous continuous flow over flow the over length the length than thethan infiltration the infiltration capacity capacity of the soil,of the showed soil, showed a more a concentrated more concentrated continuous continuous flow over flow the over length the length flow, whichof occursthe offlume the when flumebed. theAccording bed. rainfall According to intensity these to visualthese or visual supplyindicators, indicators, of we overland could we couldestablish flow establish water a boundary isa largerboundary between than between the of the offlume the flumebed. According bed. According to these to visualthese visualindicators, indicators, we could we couldestablish establish a boundary a boundary between between infiltrationsaturation capacitysaturation overland of the overland soil, flow showed and flow Ho andrtonian a moreHortonian overland concentrated overland flow, whichflow, continuous whichin our influme our flow flumetests over was tests the found was length foundin the of in the the saturationsaturation overland overland flow and flow Ho andrtonian Hortonian overland overland flow, whichflow, whichin our influme our flumetests was tests found was foundin the in the flume bed.medium Accordingmedium grain to size grain these materials size visual materials at a indicators, slope at a gradient slope gradient we of could16° (Tableof 16° establish (Table2). This 2). acould This boundary becould verified be between verified with our with saturation model our model medium grain size materials at a slope gradient of 16° (Table 2). This could be verified with our−1 model simulationsimulation (see below (see belowSection Section 4.2). For 4.2). courser For courser materials materials (Ks values (Ks values of 4.91E-0.3 of 4.91E-0.3 and 3.28E-0.3 and 3.28E-0.3 m s−1) m s−1) overland flowsimulation andsimulation Hortonian (see below (see overland belowSection Section 4.2). flow, For 4.2). whichcourser For courser inmaterials our materials flume (Ks values tests (Ks values wasof 4.91E-0.3 found of 4.91E-0.3 and inthe 3.28E-0.3 and medium 3.28E-0.3 m s grain) m s−1) and higherand higher slope anglesslope angles (>16°) (>16°)the◦ time the to time satu toration satu rationoverland overland flow was flow immediately was immediately followed followed by by size materialsand athigherand a slope higher slope gradient anglesslope angles(>16°) of 16 (>16°)the(Table time the to 2time ).satu This toration satu could rationoverland be overland verified flow was flow with immediately was our immediately model followed simulation followed by by failurefailure or with or a with small a delaysmall untildelay nineuntil seconds. nine seconds. Also, oneAlso, could one couldclearly clearly observe observe that the that time the to time to (see below Sectionfailurefailure or 5.2 with). or For a with small courser a delaysmall materials untildelay nineuntil (Ks seconds. ninevalues seconds. Also, of 4.91E oneAlso, −could 0.3one andcouldclearly 3.28E clearly observe−0.3 observe that m s −the 1that) andtime the higherto time to saturationsaturation overland overland flow (and flow thus (and failure) thus failure) decreased decreased with decreasing with decreasing slope angleslope (Tableangle (Table2). 2). slope angles (>16saturation◦) the time overland to saturation flow (and overland thus failure) flow decreased was immediately with decreasing followed slope angle by failure (Table or 2). with a HortonianHortonian overland overland flow [32]flow was [32] initiated was initiated in most in casesmost oncases the on finer the sediments,finer sediments, which whichis is Hortonian overland flow [32] was initiated in most−1 cases on the finer sediments, which is small delayascribed untilascribed nine to the seconds. tolower the lowerinfiltration Also, infiltration one capacity could capacity (Ks clearly = 0.54E-0.3(Ks observe= 0.54E-0.3 m s− that1). m Bed s the−1 ).failure Bed time failure in to this saturation in case this occurred case overland occurred a a ascribedascribed to the tolower the lowerinfiltration infiltration capacity capacity (Ks = 0.54E-0.3(Ks = 0.54E-0.3 m s ). mBed s−1 ).failure Bed failure in this incase this occurred case occurred a a certaincertain time after time the after start the of start Hortonian of Hortonian overland overland flow with flow a with time alag time ranging lag ranging between between 35 and 35 160 and 160 flow (and thuscertain failure)certain time after time decreased the after start the withof start Hortoniandecreasing of Hortonian overland slope overland flow angle with flow (Table a withtime 2 alag). time ranging lag ranging between between 35 and 35 160 and 160 secondsseconds (Table (Table2), because 2), because in this in case, this due case, to due the tolower the lowerpercolation percolation rate, it rate, took it time took to time bring to thebring the Hortonianseconds overlandseconds (Table (Table2), flow because [2),32 because] wasin this initiated incase, this due case, in to most due the tolower cases the lowerpercolation on the percolation finer rate, sediments, it rate, took it time took which to time bring is to ascribed thebring the groundwatergroundwater in the bedin the material bed material to a critical to a critical failure− failure level. level. to the lowergroundwater infiltrationgroundwater in capacitythe bedin the material (bedKs material= to 0.54E a critical to− 0.3a critical failure m s failure level.1). Bed level. failure in this case occurred a certain Bed failureBed failure initiation initiation is controlled is controlled by the bybed the gradient bed gradient and the and internal the internal friction friction of the ofmaterial the material time after the start ofBed Hortonian failure initiation overland is controlled flow with by a the time bed lag gradient ranging and between the internal 35 andfriction 160 of s the (Table material2), and occurredand occurred in our inexperiments our experiments on slopes on slopesof approximately of approximately 16 degrees 16 degrees and higher. and higher. At lower At lowerslope slope and occurredand occurred in our inexperiments our experiments on slopes on slopesof approximately of approximately 16 degrees 16 degrees and higher. and higher. At lower At slopelower slope because in thisangles, case,angles, no bed due no failure to bed the failure occurred lower occurred percolation (nf in Table(nf in 2)Table rate, and 2)itsediment tookand sediment time delivery to delivery bring occurred the occurred groundwateronly by only overland by overland in flow the bed flow angles,angles, no bed no failure bed failure occurred occurred (nf in Table (nf in 2)Table and 2)sediment and sediment delivery delivery occurred occurred only by only overland by overland flow flow material toerosion a criticalerosion failure level. erosionerosion The mediumThe medium and course and course materials materials show bedshow failure bed failure characterized characterized by slow by movements slow movements over the over the Bed failureThe initiation mediumThe medium is and controlled course and course materials by thematerials show bed gradient bedshow failure bed and failure characterized the characterized internal by frictionslow by movements slow of themovements material over the over and the total depthtotal combineddepth combined with fast with surficial fast surficial entrainmen entrainment of grainst of grainsby saturated by saturated overland overland flow. Movement flow. Movement occurred intotal our depth experimentstotal combineddepth combined on with slopes fast with surficial of fast approximately surficial entrainmen entrainment of 16 grains degreest of grainsby saturated and by higher.saturated overland At overland lowerflow. Movement flow. slope Movement angles, of bed ofmaterial bed material was slow was and slow continuous and continuous or sometimes or sometimes intermittent, intermittent, showing showing a surging a surging pattern pattern (Table (Table no bed failureof bed occurred ofmaterial bed material (nfwas inslow was Table and slow2 continuous) andand continuous sediment or sometimes or delivery sometimes intermittent, occurred intermittent, showing only showing by a surging overland a surging pattern flow pattern (Table erosion (Table 2). Instead2). Instead of the ofslow the andslow more and moreflow-like flow-like movements movements observed observed for the for medium the medium and coarse and coarse 2). Instead2). Instead of the ofslow the andslow more and flow-likemore flow-like movements movements observed observed for the for medium the medium and coarse and coarse The mediumsediments,sediments, and failure course failure of the materials offine the se finediments show sediments occurred bed failure occurred suddenly characterized suddenly with a with very by arapid very slow surgerapid movements ofsurge more of ormore over less or the less sediments,sediments, failure failure of the offine the se finediments sediments occurred occurred suddenly suddenly with a withvery arapid very surgerapid ofsurge more of ormore less or less total depthcoherent combinedcoherent blocks with blocksfollowed fast followed surficial by fluidization by entrainment fluidization (Table of (Table2). grains 2). by saturated overland flow. Movement of coherentcoherent blocks blocksfollowed followed by fluidization by fluidization (Table (Table2). 2). bed material wasSediment slowSediment and transport continuous transport by overland by or overland sometimes flow on flow theseintermittent, on steepthese slopessteepshowing slopesreached reached volumetric a surging volumetric concentrations pattern concentrations (Table 2). SedimentSediment transport transport by overland by overland flow on flow these on steepthese slopessteep slopesreached reached volumetric volumetric concentrations concentrations betweenbetween 0.46 and 0.46 0.64, and which 0.64, whichis characteristic is characteristic for debris for debrisflows. flows. Instead of thebetween slowbetween 0.46 and and 0.46 more 0.64, and flow-likewhich 0.64, whichis characteristic movements is characteristic for observed debris for debrisflows. for flows. the medium and coarse sediments, We canWe conclude can conclude on the onbasis the of basis these of observations these observations that the that flume the testsflume carried tests carried out with out the with three the three failure of the fineWe sediments canWe conclude can conclude occurred on the onbasis suddenly the of basis these of withobservations these a observations very that rapid the that surge flume the of testsflume more carried tests or carried lessout with coherent out the with three blocksthe three materialsmaterials revealed revealed three typesthree oftypes processes, of processes, which whichcreated created debris debrisflows flowsin these in rangesthese ranges of slopes of slopes followed bymaterials fluidizationmaterials revealed (Tablerevealed three2). typesthree oftypes processes, of processes, which whichcreated created debris debrisflows inflows these in rangesthese ranges of slopes of slopes
Sediment transport by overland flow on these steep slopes reached volumetric concentrations between 0.46 and 0.64, which is characteristic for debris flows. We can conclude on the basis of these observations that the flume tests carried out with the three materials revealed three types of processes, which created debris flows in these ranges of slopes gradients, namely debris flow initiation by Hortonian overland flow erosion (RhE-I), saturation WaterWater 20182018,, 1010,, x 950 FOR PEER REVIEW 66 of of 22 22 gradients, namely debris flow initiation by Hortonian overland flow erosion (RhE-I), saturation overlandoverland flowflow erosionerosion (RsE-I), (RsE-I), and and by bedby bed failure failure (BF-I). (BF-I). The occurrence The occurrence and sequence and sequence of these processesof these processesseems to beseems controlled to be controlled by slope gradientby slope andgradient hydraulic and hydraulic conductivity conductivity of the bed of sediment.the bed sediment. Figure3 Figuregives a3 schematicgives a schematic overview overview of these processof these types.process types.
FigureFigure 3. 3. SchematicSchematic diagram diagram showing showing the the different different initia initiationtion processes processes of of debris debris flows flows in in channels. channels.
3. Integrated Model (1D) for Debris Flow Initiation in Upstream Channels 3. Integrated Model (1D) for Debris Flow Initiation in Upstream Channels The flume test observations brought us to the concept of the triggering of debris flows caused The flume test observations brought us to the concept of the triggering of debris flows caused by by Hortonion and saturation overland flow initiating surficial erosion of bed material. Bed failure Hortonion and saturation overland flow initiating surficial erosion of bed material. Bed failure and and entrainment of material was initiated by infiltration and subsurface flow leading to instability. entrainment of material was initiated by infiltration and subsurface flow leading to instability. First, we First, we have to simulate the hydrological component of the triggering mechanisms of debris flows. have to simulate the hydrological component of the triggering mechanisms of debris flows. For that For that we need the mass balance equation for overland (Equation (1a)) and through flow (Equation we need the mass balance equation for overland (Equation (1a)) and through flow (Equation (1b)), (1b)), which is given by: which is given by: ∂q f ℎ∂h f + = = B (1a)(1a) ∂ x ∂t 1
∂qs ∂hs + ℎ = B (1b) ∂x + ∂t = 2 (1b) 3 −1 −1 where qf is overland flow discharge per unit width (m m s ); qs is subsurface discharge per unit where qf is overland flow discharge per unit width (m3 m−1 s−1); qs is subsurface discharge per unit 3 −1 −1 h h x width (m3 m−1 −1s ); f is thickness of overland flow (m); s (m) is thickness of subsurface flow, ∂ width (m m s ); hf is thickness of overland flow (m); hs (m) is thickness− of1 subsurface flow, x (m) (m) is distance along the slope, ∂t is the time (s), and B1–2 are terms (m s ) describing the inflow or is distance along the slope, t is the time (s), and B1–2 are terms (m s−1) describing the inflow or outflow outflow of water from the flow system, which is defined as follows: of water from the flow system, which is defined as follows: h i B 1 = − = r − i f (( a) 00 − i f (( b) (2a)(2a)