water

Article The Development of a 1-D Integrated Hydro-Mechanical Model Based on Tests to Unravel Different Hydrological Triggering Processes of 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 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 ? 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 and transport by intensive overland flow and by infiltrating water causing failure of bed material. On the basis of these experiments, an integrated hydro-mechanical model was developed, which describes Hortonian and saturation overland flow, maximum 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 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 as a key factor for either the development of shallow or surficial erosion and transport of material by overland flow, that might create different types of flow like mass movements. Effective overland

Water 2018, 10, 950; doi:10.3390/w10070950 www.mdpi.com/journal/water Water 2018, 10, 950 2 of 22

flow driven triggering processes are mainly concentrated in channels where high water discharges, and severe erosion and transport lead to high 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 . 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 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 created mainly surficial runoff, erosion, and incision; 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 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 , 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 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.

Water 2018, 10, 950 4 of 22 Water 2018, 10, x FOR PEER REVIEW 4 of 22

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 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 . 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.

Water 2018, 10, 950 5 of 22

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 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∂hf + == 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 B1 =−= r − i f ((a) 00 − if ((b) (2a)(2a)

B2 == if (2b)(2b)

−1 −1 −1 −1 wherewhere r r(m(m s s) describes) describes the external the external input input of rain of into rain and into if (m and s )i fthe(m outflow s ) the of outflowwater by of infiltration water by outinfiltration of the overland out of the flow overland system flow (Equation system (Equation(2a)) (see also (2a)) Figure (see also 1). FigureWhen1 there). When is no there supply is no of supply rain, likeof rain, in our like flume in our experiments, flume experiments, r = 0. In ther = case 0. Inof thesubsurface case of subsurfaceflow, if in Equation flow, if in(2b) Equation is considered (2b) is nowconsidered as an inflow now as term an inflow of the termsubsurface of the subsurfaceflow system. flow If h system.f/Δt is larger If hf/∆ thant is larger the infiltration than the infiltration capacity, −1 − Kscapacity, (m s ) Ksof the(m sbed1) ofmaterial the bed the material latter one the is latter the limiting one is the factor. limiting Therefore factor. Thereforethe infiltration the infiltration term if of −1 −1 Equationterm if of (2) Equation is the minimum (2) is the (min) minimum value (min)of the valueinfiltration of the capacity infiltration Ks (m capacity s ) andKs the(m s ) and water the depthcurrent (hf water), which depth can (infiltratehf), which in can one infiltrate time step in Δ onet into time the step bed∆ material:t into the bed material:

= (,ℎ /∆) (3) i f = min Ks, h f /∆t (3) We introduce here a general momentum equation for the water flow processes [33]:

Water 2018, 10, 950 7 of 22

We introduce here a general momentum equation for the water flow processes [33]:

β f h f = α f q f (4a)

βs hs = αsqs (4b)

For turbulent overland flow, the parameters α f and β f in Equation (4a) can be defined as follows:

 n 0.6 = = α f 0.5 and β f 0.6 (5) S0 where n is Manning’s n and S0 the slope gradient of the bed material. For subsurface flow we can write according to Darcy’s law:

1 q = Ks sin θ h → h = q (6) s s s Ks sin θ s

3 −1 −1 where qs is the amount of subsurface flow water per unit width (m m s ), θ is slope angle (degrees), and hs is the height of the flowing water component in the soil matrix (m). By comparing Equation (6) with the general momentum Equation (4b) we can define the parameters αs and βs for subsurface flow:

1 α = and β = 1 (7) s Ks sin θ s A combination of the mass balance Equation (1) with Equation (4) delivers an expression for overland flow or subsurface flow discharge (qf, qs) [33]:

∂q f ∂q f + α β q (β f ,s−1) = B (8a) ∂x f f f ∂t 1 ∂q ∂q s + α β q (βs−1) s = B (8b) ∂x s s s ∂t 2 The 1D model is implemented in a fixed Eulerian frame where the variation in water flow variables is described at fixed coordinate points at a distance ∆x along the slope as a function of time step ∆t. A numerical solution for Equation (8) is given by [33]:

β−1  t + t+1   t+1 + t  ∆t t+1 t qx+1 qx Bx+1 Bx+1 ∆x qx + αβqx+1 2 + ∆t 2 qt+1 = x+1 β−1 (9)  t + t+1  ∆t qx+1 qx ∆x + αβ 2 where qx, α and β should be read as qf,s αf,s and βf,s, respectively. To simulate the initiation of debris flows by mass failure we used the equation for the infinite slope equilibrium model [31], which is the trigger for failure:

(γ z cos θ − p) tan ϕ F = s (10a) γsz sin θ

p = γwhs cos θ (10b)

−3 where F is the safety factor; failure occurs when F = 1; γs and γw (k N m ) are the saturated of the material and water, respectively; ϕ is friction angle of the material; z and hs are the thickness of the soil and the height of the groundwater layer, respectively; hs can be solved with Equation (6) and (9), respectively. Water 2018, 10, 950 8 of 22

The overall stability of the bed material expressed with the safety factor (F) for the infinite slope model was calculated as an average of the safety factor of the different nodes. The inflow of water into the flume is coming from upstream, and therefore the pore pressure gradient is decreasing downstream. This means that the safety factor is always increasing downstream, and therefore the average approach of the safety factor over the length of the sample in the flume seems a reasonable approximation of the overall safety factor. For estimating the transport capacity on steep slopes Rickenmann [34,35] proposed a bedload transport equation based on a shear approach, where discharge, bed slope gradient, and material grading are used as parameters to characterize flow hydraulics. For steeper slopes, in the range of 0.03 < S < 0.2 (1.7◦–11.3◦), Rickenmann [34] performed a regression analysis with the steep flume data on transport obtained at ETH Zurich that resulted in the equation: 12.6  D 0.2  = 90 − 2 qsolid 1.6 q f qc S (11) (ds − 1) D30 where D90 and D30 are grain sizes at which 90% and 30%, respectively, by weight of the material are finer; ds is the mass density of the , S is the slope gradient, and qc is the critical flow discharge for bedload entrainment. The experimental slopes were in the range of 0.03 > S > 0.20 (1.7◦–11.3◦), and the D90 of the material ranged between 0.9 and 2 cm and D30 between 0.06 and 1 cm with inflow rates of 10–30 L s−1. In the section below, we will calibrate Equation (11) for the steeper slopes in our flumes. The integrated model developed in this section is able to describe the different types of hydro-mechanical triggering mechanisms for debris flows. It delivers us the physical parameters, which controls these processes, which will be applied in our virtual simulations in Sections5 and6. In the next section, we will calibrate our model on some process indicator values obtained from our flume tests.

4. Calibration and Validation of the Theoretical Model on the Basis of Flume Test Results We will use here a number of process indicator values measured during the flume experiments to calibrate and validate the outcomes of our theoretical model. These are saturation or Hortonian overland flow, time to overland flow, maximum pore pressure, time to bed failure, and solid concentration by overland flow erosion. Hortonian overland flow and the time to Hortonian overland flow in the model is declared when hf reaches the lower end of the bed material, while the bed material is still not saturated (hs < Zs). Saturation overland flow and the time towards it is declared when hs = Zs over the entire bed. Pore pressure is calculated each time step according to Equation (10b). The discharge of hf + hs is reported each time step at the end of the flume. Bed failure is declared as mentioned earlier when the average safety factor F over the bed length reaches the value of 1. For the flume simulations, the distance between the nodes (∆x) was 0.1 m and the time interval (∆t) was 0.2 s. Figure4 shows the relation between observed and calculated time to overland flow for the different flume tests. There is a moderate 1:1 correlation between observed and predicted time to overland flow for the medium and coarse sediments and for the fine sediments, showing Hortonian overland flow there is no correlation at all. The deviations in observed and predicted time to overland flow can be ascribed to the variation in density of the bed material in combination with a poor estimate of the Ks value based on a limited amount of measurements, which was used as input for the modelling (see Section 2.1). However the model was able to predict the type of overland flow according to what was observed during the flume tests (see Table2). WaterWater 2018 2018,, 10, 10, x 950, xFOR FOR PEER PEER REVIEW REVIEW 99 9of of of 22 22 22

180180 160160 140140 1:11:1 line line 120120 coarsecoarse 100100 mediummedium 8080 6060 finefine 4040 2020 Time to overland flow bserved (sec) flow bserved Time to overland Time to overland flow bserved (sec) flow bserved Time to overland 00 00 50 50 100 100 150 150 200 200 TimeTime to to overland overland flow flow Calculated Calculated (sec) (sec)

FigureFigureFigure 4. 4. Observed Observed and and calculated calculated time time to to saturation saturation overland overland flow flow flow (black (black symbols) symbols) and and Hortonian Hortonian overlandoverlandoverland flow flow flow (open (open symbols). symbols).

DespiteDespiteDespite thethe the malfunctioningmalfunctioning malfunctioning of someofof some some pore pore pressurepore pressure pressure sensors sensors sensors we were we we able were were to make able able ato 1:1to make comparisonmake a a1:1 1:1 comparisonbetweencomparison the between average between maximumthe the average average measured maximum maximum pore measured measured pressure pore for pore the pressure pressure three sensors for for the the (Figure three three 1sensors )sensors and the (Figure (Figure average 1) 1) andcalculatedand the the average average maximum calculated calculated pore pressuremaximum maximum (Figure pore pore 5pressure ).pressure (Figure (Figure 5). 5).

1.41.4 1.21.2 11 0.80.8 1:11:1 line line 0.60.6 calculated (kPa) calculated (kPa) 0.40.4 p p 0.20.2 00 0.60.6 0.7 0.7 0.8 0.8 0.9 0.9 1 1 ppmeasuredmeasured (kPa) (kPa)

Figure 5. Maximum pore pressure measured during flume tests in relation to calculated pore pressures. FigureFigure 5. 5. Maximum Maximum pore pore pressure pressure measured measured during during fl umeflume tests tests in in relation relation to to calculated calculated pore pore pressures.pressures. The Figure shows that in many cases there is a slight overestimation of the calculated pore pressure. Time series of measured pore pressure of the three sensors compared to modelled temporal TheThe Figure Figure shows shows that that in in many many cases cases there there is is a aslight slight overestimation overestimation of of the the calculated calculated pore pore pore pressure development showed that in most cases the onset towards maximum pore pressure for pressure.pressure. Time Time series series of of measured measured pore pore pressure pressure of of the the three three sensors sensors compared compared to to modelled modelled temporal temporal the three sensors was more irregular compared to the calculated development of the pore pressures porepore pressure pressure development development showed showed that that in in most most cases cases the the onset onset towards towards maximum maximum pore pore pressure pressure for for (Figure6). This can be ascribed to the variation in density, which occurred during the compaction of thethe three three sensors sensors was was more more irregular irregular compared compared to to the the calculated calculated development development of of the the pore pore pressures pressures the sediment layers or (and) the imperfect response of the sensors. (Figure(Figure 6). 6). This This can can be be ascribed ascribed to to the the variation variation in in density, density, which which occurred occurred during during the the compaction compaction of of thethe sediment sediment layers layers or or (and) (and) the the imperfect imperfect response response of of the the sensors. sensors.

Water 2018,, 1010,, 950x FOR PEER REVIEW 10 of 22 Water 2018, 10, x FOR PEER REVIEW 10 of 22

0.8 0.8 0.7 0.7 0.6 0.6 0.5 0.5 0.4 0.4 Calculated 0.3 Calculated 0.3 Observed

Pore pressure kPa Pore pressure 0.2 Observed Pore pressure kPa Pore pressure 0.2 0.1 0.1 0 0 0 50 100 150 200 250 300 350 400 450 0 50 100 150 200 250 300 350 400 450 Time seconds Time seconds

Figure 6. Example of the rise inin porepore pressurepressure (measured/calculated)(measured/calculated) due to infiltration infiltration of run-on Figure 6. Example of the rise in pore pressure (measu◦ red/calculated) due to infiltration of run-on water in the bed material (test: medium grain size/20size/20°).). water in the bed material (test: medium grain size/20°). In relation to pore pressure development we compared the time to failure for the different test InIn relationrelation toto porepore pressurepressure developmentdevelopment wewe comparedcompared thethe timetime toto failurefailure forfor thethe differentdifferent testtest runs on the different materials. Since the time towards average maximum calculated and measured runsruns onon thethe differentdifferent materials.materials. SinceSince thethe timetime towardstowardsaverage average maximummaximum calculatedcalculated andand measuredmeasured pore pressure coincided more or less, one would expect also corresponding calculated and measured porepore pressurepressure coincided coincided more more or or less,less, oneone wouldwould expectexpect alsoalso correspondingcorresponding calculatedcalculated andand measuredmeasured failure times. Table 2 and Figure 7 show that the match between observed and calculated failure time failurefailure times. times. Table Table2 and2 and Figure Figure7 show 7 show that that the the match match between between observed observed and and calculated calculated failure failure time time is is reasonable except for two outliers (coarse-20°;◦ fine-18°).◦ Figure 7 shows further that the calculated reasonableis reasonable except except for twofor two outliers outlie (coarse-20rs (coarse-20°;; fine-18 fine-18°).). Figure Figure7 shows 7 shows further further that the that calculated the calculated time time to failure seems to be underestimated for the coarse material and, although not so clear, totime failure to failure seems toseems be underestimated to be underestimated for the coarse for materialthe coarse and, material although and, not although so clear, overestimated not so clear, overestimated for practically all the tests on the medium and fine materials. This suggests that the foroverestimated practically all for the practically tests on the all medium the tests and on finethe me materials.dium and This fine suggests materials. that This the percolation suggests that rate the is percolation rate is lower, and hence the observed time to failure is higher for the coarser bed materials lower,percolation and hence rate is the lower, observed and hence time to the failure observed is higher time for to thefailure coarser is higher bed materials for the coarser and higher bed materials for finer and higher for finer bed materials. The average volumetric concentrations of the runoff water are bedand materials.higher for The finer average bed materials. volumetric The concentrations average volumetric of the runoffconcentrations water are of 0.62, the 0.65,runoff and water 0.70 forare 0.62, 0.65, and 0.70 for the coarse, medium, and fine bed materials, respectively. However, we would the0.62, coarse, 0.65, and medium, 0.70 for and the fine coarse, bed materials, medium, respectively.and fine bed However, materials, we respectively. would expect However, lower percolation we would expect lower percolation rates (and therefore higher times to failure) in finer bed materials with ratesexpect (and lower therefore percolation higher timesrates (and to failure) therefore in finer higher bed materialstimes to withfailure) higher in finer concentrations bed materials of runoff with higher concentrations of runoff water and more fine material and vise versa: higher percolation rates waterhigher and concentrations more fine material of runoff and water vise and versa: more higher fine material percolation and ratesvise versa: on the higher courser percolation bed materials rates on the courser bed materials with lower runoff concentrations. We must conclude that the effect of withon the lower courser runoff bed concentrations. materials with Welower must runoff conclude concentrations. that the effect We must of concentration conclude that and the gradient effect of concentration and gradient of the sediment in the water is not visible in our observed time to failure. ofconcentration the sediment and in thegradient water of is the not sediment visible in in our the observed water is not time visible to failure. in our Therefore, observed thetime deviations to failure. Therefore, the deviations between calculated and observed values must be ascribed to the betweenTherefore, calculated the deviations and observed between values calculated must be ascribed and observed to the heterogeneity values must of the be material, ascribed incorrect to the heterogeneity of the material, incorrect estimate of the friction values, and Ks values and bulk density estimateheterogeneity of the of friction the material, values, incorrect and Ks values estimate and of bulk the densityfriction ofvalues, the percolating and Ks values water, and and bulk incorrect density of the percolating water, and incorrect assessment of the overall safety factor. assessmentof the percolating of the overall water, safetyand incorrect factor. assessment of the overall safety factor.

700 700 600 600 500 500 400 coarse 400 coarse 300 medium 300 medium 200 fine 200 fine 100 100 Time to failure calculated (s) Time to failure calculated

Time to failure calculated (s) Time to failure calculated 0 0 0 100 200 300 400 500 600 700 0 100 200 300 400 500 600 700 Time to failure observed (s) Time to failure observed (s)

Figure 7. Observed and calculated time of failure of bed material during the flume tests. Figure 7. Observed and calculated time of failure of bed material during the flume tests. Figure 7. Observed and calculated time of failure of bed material during the flume tests.

WaterWater2018 2018, 10, 10, 950, x FOR PEER REVIEW 1111 of of 22 22

We calibrated also the parameters of the Rickenmann [35] equation, (Equation (11)) on our flume tests,We which calibrated were alsocarried the out parameters on slopes of ranging the Rickenmann between [0.2535] equation,> S > 0.36 (Equation(14°–20°), (11))with ongrain our sizes flume for ◦ ◦ tests,0.9 > which d90 > 2 were and carried0.05 > d out30 > on1 cm, slopes and ranging with flow between rates 0.5 0.25 > >qfS >> 15 0.36 L s (14−1 m–20−1. Figure), with 8 grainshows sizes the forbest −1 −1 0.9linear > d90 fit> between 2 and 0.05 qsolid >/qdf30 and> 1(d cm,90/d30 and)0.2S with2, which flow delivered rates 0.5 the > q followingf > 15 L s modifiedm . Figure equation8 shows for slopes the 0.2 2 bestbetween linear 14° fit between and 20°:q solid/qf and (d90/d30) S , which delivered the following modified equation for slopes between 14◦ and 20◦: .  0.2 =7.28D90 2 (12a) qsolid = 7.28 q f S (12a) D30 which gives for ds = 2.6: which gives for ds = 2.6: 15.4415.44  D .0.2 = 90 2 qsolid = 1.6. qfS (12b)(12b) (d(s − −1)1) D30

2.6 2.4 2.2 2 1.8 1.6

qs/qf 1.4 1.2 1 0.8 0.6 0.4 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.2 2 (D90/D30) S FigureFigure 8. 8.Calibration Calibration of of Rickenmann’s Rickenmann’s bedload bedload equation equation for for steeper steeper slopes slopes in in our our flume flume tests tests between between 1414 and and 20 20 degrees. degrees.

The calibration revealed that qc in Equation (11) becomes zero or practically zero in Equation The calibration revealed that qc in Equation (11) becomes zero or practically zero in Equation (12). (12). At slopes larger than 15° the down slope component of the grain weight may reduce the critical At slopes larger than 15◦ the down slope component of the grain weight may reduce the critical shear τc which in our case obviously reduced to nearly zero. stress τc which in our case obviously reduced to nearly zero. We may conclude that the model is able to predict in a reasonable way essential process We may conclude that the model is able to predict in a reasonable way essential process indicators indicators for different hydrological triggering processes of debris flows in upstream channels. In the for different hydrological triggering processes of debris flows in upstream channels. In the next section, next section, we will apply the model on the field scale to predict hydro-mechanical triggering we will apply the model on the field scale to predict hydro-mechanical triggering patterns for debris patterns for debris flows as a function of the hydrological conductivity of the bed material and the flows as a function of the hydrological conductivity of the bed material and the channel slope gradient. channel slope gradient. 5. Hydro-Mechanical Triggering Patterns for Debris Flows in Relation to Hydrologic Conductivity5. Hydro-Mechanical of Bed Materials Triggering and Patterns Channel fo Gradientr Debris Flows in Relation to Hydrologic Conductivity of Bed Materials and Channel Gradient 5.1. The Design of a Schematic Source Area at the Field Scale 5.1.First, The Design we will of designa Schematic a virtual Source landscape Area at the of Field a potential Scale debris flow source area where our model can beFirst, applied we towill analyze design thea virtual influence landscape of terrain of a parameters potential debris on the flow type source of triggering area where mechanisms our model (Sectioncan be 5.2applied) and to the analyze meteorological the influence thresholds of terrain of debris parameters flows (Section on the 6type). of triggering mechanisms (SectionFigure 5.2)9 shows and the this meteorological virtual source thresholds area, which of debris is linked flows to (Section an upstream 6). channel filled with bed materialFigure receiving9 shows this surface virtual water source from area, the which surrounding is linked slopes to an to upstream initiate a channel potential filled debris with flow. bed Thismaterial geomorphological receiving surface setting water resembles from the more surrounding or less the slopes source to initiate areas described a potential among debris others flow. This by Coegeomorphological [7] and Berti [24 ].setting The upstream resembles area more of ouror less hypothetical the source catchment areas described has a radiusamongR others. The channel by Coe is[7] furtherand Berti surrounded [24]. The byupstream lateral slopesarea of with our hypothetical a length L. The catchment length of has the a channel radius R bed. The is Lxchannel, the width is furtherW, andsurrounded the slope by angle lateral is θ .slopes The hydraulic with a length conductivity L. The length of the of bed the material channel isbedKs ,is the Lx, porosity the widthPor Wand,, and thethe friction slope angle angle isϕ (Figureθ. The 9hydraulic). conductivity of the bed material is Ks, the porosity Por and, the friction angle φ (Figure 9).

Water 2018, 10, 950 12 of 22 Water 2018, 10, x FOR PEER REVIEW 12 of 22

Figure 9. Morphometric and hydro-mechanical parameters, which were used for model simulations Figure 9. Morphometric and hydro-mechanical parameters, which were used for model simulations of of debris flow initiation. For an explanation see Table 3 and text. D90/D30: 90% and 30% lower than debris flow initiation. For an explanation see Table3 and text. D90/D30: 90% and 30% lower than grain grainsize D90 size and D90 D30, and respectively. D30, respectively.ϕ: Friction φ: Friction angle; angle;Ks: Hydraulic Ks: Hydraulic conductivity; conductivity;Por: Porosity; Por: Porosity;Zs: Depth Zs: Depth of material; θ: Slope angle; qup: Water that flows into the upper end of the channel bed; R: of material; θ: Slope angle; qup: Water that flows into the upper end of the channel bed; R: Radius of Radiussource areaof source above area the above channel; theLx channel;and W :Lx Length and W and: Length width and of thewidth channel of the bed; channelL: Length bed; L of: Length lateral ofcontributing lateral contributing slope; latin slope;: Lateral latin inflow: Lateral of inflow water of to water the channel; to the channel;CN: Curve CN number: Curve number value for value the soilfor thehydrological soil hydrological and land and use land characteristics use characteristics of the contributing of the contributing slopes. slopes.

The sink term B in (1) and (8) is now adapted to the field scene and given by: The sink term B in (1) and (8) is now adapted to the field scene and given by:

=2+− (13) B = 2latin + r − i f (13) where latin (m s−1) is the lateral inflow of overland flow water from the slopes along the channel − where(Figurelatin 9), r(m direct s 1 )rain is the intensity lateral inflowinput to of the overland channel flow bed, water and i fromf infiltration the slopes rate along into the the bed channel (see (FigureEquation9), (3)).r directThe lateral rain inflow intensity is calculated input to thefor these channel sensitivity bed, and analysesif infiltration in a simple rate way, into assuming the bed (seesteady Equation state conditions (3)). The in lateral the mass inflow balance is calculated equation for overland these sensitivity flow: analyses in a simple way, assuming steady state conditions in the mass balance equation for overland flow: = (14) r L latin = cn (14) rcn (m s−1) is calculated using the curve number methodW [36], L is the length of the lateral slope, and W the width of the channel (see Figure 9). In our simulations we selected overland flow −1 supplyingrcn (m slopes s ) iswith calculated soils with using moderate the curve to slow number infiltration method rates [36 and], L a ispoor the condition length of grass the lateralcover, whichslope, andcorresponds W the width to a curve of the number channel (CN) (see Figureof abou9t). 80. In The our simulationsCN number, wereflecting selected the overland hydrological flow soilsupplying characteristics, slopes with land soils use, with and moderate antecedent to slow soil infiltrationmoisture conditions rates and athat poor we condition can expect grass in cover,high whichmountainous corresponds areas, towas a curve chosen number arbitrarily (CN) and of about was kept 80. The constant CN number, in our si reflectingmulations. the The hydrological overland flowsoil characteristics,water that flows land into use, the upper and antecedent end of the soilchannel moisture bed is conditions given by qup that (m2 we s−1) can (Figure expect 9). in high mountainous areas, was chosen arbitrarily and was kept constant in our simulations. The overland 0.5 cos 2 −1 flow water that flows into the upper end of the= channel bed is given by qup (m s ) (Figure9). (15) r 0.5πR2 cos θ q = cn (15) 5.2. The Influence of the Hydraulic Conductivityup (Ks) andW Slope (θ) of the Channel Bed on the Type and Sequence of Hydrologic Triggering Processes for Debris Flows 5.2. The Influence of the Hydraulic Conductivity (Ks) and Slope (θ) of the Channel Bed on the Type and SequenceIn the of Hydrologicflume we could Triggering observe Processes the effect for Debris of slope Flows angle and hydraulic conductivity on the type and sequence of triggering processes, which may lead to the initiation of debris flows. In this section In the flume we could observe the effect of slope angle and hydraulic conductivity on the type we will investigate with our theoretical model the effect of these two factors at the catchment scale. and sequence of triggering processes, which may lead to the initiation of debris flows. In this section The values of the other factors used in our model simulations are shown in bold as default parametric we will investigate with our theoretical model the effect of these two factors at the catchment scale. values (Zs, φ, W, Lx,P or, R, L, n, bed) in Table 3 (see also Figure 9).

Water 2018, 10, 950 13 of 22

The values of the other factors used in our model simulations are shown in bold as default parametric values (Zs, ϕ, W, Lx,P or, R, L, n, bed) in Table3 (see also Figure9).

Table 3. Default values (bold italic) and maximum and minimum values of input parameters for overland flow erosion (RE-I) and bed failure (BF-I) triggering debris flows. Ks: Saturated hydraulic conductivity; Zs: Thickness of bed material; ϕ friction angle of material; θ: Slope angle of channel bed; W and Lx: width and length of channel bed respectively; Por: Available volumetric pore space; R: Radius of source area; L: Length of lateral slopes; n: Manning’s n of bed material.

Ks for RE-I 0.001–0.0025–0.005 m s−1 Lx 50–100–200 m Ks for BF-I 0.001–0.01–0.1 m s−1 Por 0.4–0.3–0.2 Zs 2–4–6m R 250–350–450 m ϕ 28–32–36 L 250–350–450 m θ 16◦–20–28◦ n bed 0.08 W 2–4–6-m

Table4 gives the range in Ks values (first row) and bed slope angles (first column), which were used in our simulations to study the effect of these parameters on the hydro-mechanical process development at the catchment scale. For these simulations, two rain scenarios were used with an intensity of 80 mm (Table4a) and 40 mm per hour (Table4b), respectively. The tables show domains with different shades of gray with various combinations of hydro-mechanical triggering processes. In the white sections, no debris flow initiation is expected to develop in the source area because of a too low sediment concentration of the overland flow. Table4a shows that in the domain θ = 28◦–20◦ and Ks = 0.001–0.005 m s−1, the debris flow is initiated in the first stage by Hortonian overland flow erosion (RhE-I). The overland flow discharge reaches a steady state after a certain relatively short time. During the steady state, groundwater will rise by infiltration of run-on water until failure of the bed material, which happens between 1.7 and 11.2 minutes depending on the slope θ and Ks. In Table4a, we see a dramatic drop in discharge between slopes with Ks = 0.001 and 0.005. The last Ks value reaches a significant boundary which determines whether or not a debris flow can be initiated by Hortonian overland flow transport. It is confirmed by Table4b, with a lower rain input (40 mm) where at Ks ≥ 0.005, no initiation by Hortonian overland flow is possible anymore. Going back to Table4a, in the domain θ = 16◦–12◦ and Ks = 0.001–0.005 m s−1 slope failure does not occur. The debris flow is initiated by overland flow; first by Hortonian overland flow and later when the groundwater has reached the surface by saturation overland flow. Discharge is relatively low when there is Hortonian overland flow, while obviously discharge dramatically increases at saturation overland flow. However, due to the lower slope angles, the volumetric sediment concentration is low (0.21 at 16◦ and 0.13 at 12◦) (Table4a, last column), which means the flow changes from a hyperconcentrated flow into a water flood with conventional and bed load. At higher conductivities in the domain Ks = 0.01–0.1 m s −1 and θ = 28◦–20◦, bed failure seems the most dominant process (Table4a). Due to the larger Ks values, infiltration into the bed is more important than overland flow discharge. The bed material turns out to be partly saturated in the upper part due to the larger upstream inflow, creating partly saturation overland flow and Hortonian overland flow. However, within one minute after the runoff discharge reached the lower end of the bed, failure of the bed material occurred already. Therefore, the contribution of overland flow to the transport of debris by overland flow can be ignored. In the domain Ks = 0.01–0.1 m s−1 and lower slope gradients (θ = 16◦–12◦), there is no slope failure but only saturation overland flow, (Table4a) with low sediment concentrations in most cases not enough to call it a debris flow. Table4b shows the simulation results with an intensity of 40 mm per hour. The domains with a specific combination of hydro-mechanical triggers still exist. There is only a shift of the boundary for the Ks-values with no Hortonian overland flow (>0.005 m/s) to the left. The Table4a,b show a Water 2018, 10, 950 14 of 22 decrease in overland flow discharge and increase in time to bed failure with a decreasing slope angle. Around 16 degrees the channel bed is stable but still steep enough to have transport capacities with concentrations in the domain of a hyper concentrated flow. These are induced by Hortonian and Saturation overland flow at lower Ks values and only Saturation overland flow at higher Ks values. At lower slope angles (see slopes around 12 degrees) sediment concentrations are too low to call it a debris flow. Table5 gives a summary of the type and sequence of initiation processes related to different Ks and slope angle values.

Table 4. Time sequence of different initiation processes RhE-I and RsE-I, (erosion by Hortonian and saturation overland flow respectively) and BF-I (bed failure) in relation with hydraulic conductivity (Ks) and slope angle of bed material. Further are given the discharge (discharg) and solid concentration

(concent) during RhE-I and RsE-I. Tables4a and4b: simulated rain intensities of 80 mm and 40 mm, respectively.

a 80 mm Ks 0.001 m s−1 0.005 m s−1 0.01 m s−1 0.1 m s−1 Slope Initiat Time Dischar Time Dischar Time Dischar Time Dischar Vol Concent Degrees Proc. min. L s m−1 min. L s m−1 min. L s m−1 min. L s m−1 LL−1 R E-I 1.0 912 1.3 139 28 h 0.47 BF-I 5.4 1.7 2.4 3.0 R E-I 1.0 783 1.3 119 24 h 0.39 BF-I 8.4 2.3 2.8 3.1 R E-I 1.1 683 1.4 104 20 h 0.30 BF-I 11.2 2.9 3.1 3.1 R E-I 1.1 606 1.5 92 16 h 0.21 RsE-I 14.2 732 3.7 733 3.7 732 3.6 705 R E-I 1.2 550 1.5 83 12 h 0.13 RsE-I 14.8 666 3.9 665 3.8 664 3.6 646 b 40 mm Ks 0.001 m s−1 0.005 m s−1 0.01 m s−1 0.1 m s−1 Slope Initiat Time Dischar Time Dischar Time Dischar Time Dischar Vol Concent Degrees Proc. min. L s m−1 min. L s m−1 min. L s m−1 min. L s m−1 LL−1 R E-I 1.5 162 28 h 0.47 BF-I 5.8 7.2 7.9 8.0 R E-I 1.6 139 24 h 0.39 BF-I 8.8 7.8 8.2 8.3 R E-I 1.7 121 20 h 0.30 BF-I 11.7 8.5 8.5 8.4 R E-I 1.8 108 16 h 0.21 RsE-I 14.8 234 9.5 235 9.4 233 9.3 208 R E-I 1.9 98 12 h 0.13 RsE-I 15.0 214 9.6 213 9.5 212 9.2 170

Table 5. Sequence of different initiation processes for debris (hyperconcentrated) flows in relation to the hydraulic conductivity and slope of the channel bed material. Simulated rain intensity is 40 mm.

40 mm Ks Values 0.001 m s−1 0.005 m s−1 0.01 m s−1 0.05 m s−1 0.1 m s−1 Gradient Flow type Initiation process Initiation process 28o t1: Hortonian overland flow 24o Debris flow t1: Bed failure t2: Bed failure 20o t1: Hortonian overland flow 16o Hyper -concentratedflow t1: Saturation overland flow t2: Saturation overland flow t1: Hortonian overland flow 12o No debris flow t1: Saturation overland flow t2: Saturation overland flow

We designed a framework, which gives insight in what kind of debris flow initiation can be expected for a given slope gradient and hydraulic conductivity of the material. In the next section, we will give an impression how different hydro-mechanical parameters of triggering processes can influence meteorological thresholds for debris flows. Water 2018, 10, 950 15 of 22

6. Sensitivity Analyses for Parameters Influencing the Rain Intensity-Duration (I-D) Threshold Curves for Different Initiation Processes of Debris Flows In the foregoing, we revealed the influence of Ks and bed slope gradient on the sequence of processes mechanisms involved in the initiation of debris flows. We want to investigate here the effect of the other parameters (including Ks and slope gradient) on rainfall thresholds in terms of intensity duration (I-D) curves for the triggering of debris flows by two main process mechanism: initiation by Hortonian overland flow (RhE-I) and bed failure (BF-I). As we have seen in Tables4 and5, debris flow initiation by saturation overland flow (RsE-I) can only take place around 16 degrees. At lower slope angles, sediment concentrations are too low to call it a debris flow (Table4). At higher slope angles, we have bed failure before saturation overland flow can take place. Figure 10 shows the effect of different parameters on the I-D curves for debris flows initiated by Hortonian overland flow. The intensity and duration value of a rain event which creates overland flow that just reaches the end of the channel bed with a sediment concentration of >0.2, is defined by us as a threshold rain event for debris flow initiation. The intensity and duration values for a variety of different critical rain events were plotted in a graph with on the Y-axis the intensity and on X-axis the duration. In this way, an intensity duration (ID) curve can be constructed. Table3 gives an overview of the range of the different parameters and the default values (in bold italic), which were used in the simulation and which give a realistic representation of geometric and geotechnical parameters for source area conditions The threshold curves for debris flow initiation by Hortonian overland flow are shown in Figure 10. In this figure, the threshold curves, which are constructed using the default values given in Table3, are depicted with open rectangular markers. They are equal in all the sub-figures. This enables one to compare for the different parameters the difference between the ultimate curves and the default curve. For each selected parametric value there is an ultimate minimum rain intensity below which not enough overland flow, and thus a debris flow can be initiated, irrespective the duration (D) of the rain event (see horizontal dotted lines).

Figure 10. Cont. Water 2018, 10, 950 16 of 22

Figure 10. I-D curves for debris flow initiation by Hortonian overland flow in relation to different geometrical and hydrological parameters. The regression formula belong to the curves from top to bottom. For the definition of parameters see Table3.

The simulations show that at intensities below this critical dotted line the overland flow water never reach the lower end of the bed due to a too high infiltration rate on its pathway compared to the supplied amount of water (direct rain input and surrounding overland flow), and finally bed failure may be the primary triggering process. The most obvious selected parameter for overland flow initiation is the hydraulic conductivity Ks. Other parameters are related to geometry of the source area (see Figure6) like length of the lateral slopes along the channel (L), radius of the upstream area of the channel (R), Length (Lx) and width (W) of the channel bed, channel bed gradient (θ), and further Manning’s n of the bed material. We saw in the forgoing that Hortonian overland flow plays a dominant role for Ks values <0.005 m s−1. Figure 10a shows the influence of the Ks value on the I-D threshold curves for runoff erosion initiation (RhE-I). The range of Ks values was chosen between 0.0005 and 0.005 m s−1. The figure shows that for Ks values lower than 0.001 m s−1 there is nearly no effect of Ks on the position of the I-D curve, but there is a difference in the minimum intensity values (dotted lines) below which no debris flow can occur. A slight difference can be observed for lower intensities (<60 mm h−1). Higher Ks values (>0.001 m s−1) have a larger influence on the I-D curves. (Figure 10a). The simulations show that the scale of the source area and lateral slopes (R&L), the length of the bed (Lx), and the width of the bed (W) have the largest effect on the position of the threshold curve for the initiation of debris flow by Hortonian overland flow (Figure 10b,d,f, respectively). The threshold curves are less sensible for the effect of the slope gradient θ and Manning’s n of the bed material (Figure 10c,e respectively). Figure 11 shows the influence of the different geotechnical and geometrical factors on the threshold values for the triggering of debris flows by bed failure. The range in Ks values for which bed failure (BF-I) is the dominant process were chosen between 0.001 and 0.1 m s−1 with a default value of 0.01 m s−1. The effect of the selected range in geometric values R&L, Lx, W, θ, and Zs (Figure 11b,d,f–h, respectively) seems to be more or less the same. Less effect has the porosity (Por) of the bed material and the ϕ values (Figure 11c,e, respectively). No effect had the hydraulic conductivity Ks (Figure 11a), which is related to the simplicity of the model describing instantaneous downward percolation for these high permeable bed materials. Interesting was to see that at lower Ks values (around 0.001 m s−1) and higher rain intensities, the rate of groundwater storage, and therefore the critical duration for failure, was nearly the same (Figure 11a). Water 2018, 10, 950 17 of 22 Water 2018, 10, x FOR PEER REVIEW 17 of 22

100 100 Ks R&L 80 80

60 60 y = 236.1x-0.6 y = 171.0x-0.6 40 40 y = 127.8x-0.6 20 y = 171.0x-0.6 Intensity (mm/hr) 20 Intensity (mm/hr) Intensity

0 0 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 Duration ( min) Duration ( min) Ks=0,001m/s Ks=0,01 ms-1 Ks=0,1 m/s R&L=250m R&L=350m R&L=450m

(a) (b)

100 100 Por Lx -0.7 80 y = 209.1x 80 y = 171.0x-0.6 y = 245.3x-0.6 60 y = 165.0x-0.7 60 y = 171.0x-0.6 40 40 y = 118.4x-0.6

20 20 Intensity (mm/hr) Intensity Intensity (mm/hr) Intensity

0 0 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 Duration ( min) Duration ( min) Por=0.2 Por=0.3 Por=0.4 Lx=50m Lx=100m Lx=200m

(c) (d)

100 100 φ W 80 80 y = 204.1x-0.6 60 y = 194.5x-0.6 60 y = 171.0x-0.6 40 y = 171.0x-0.6 40 y = 121.8x-0.6 y = 139.8x-0.6 20 Intensity (mm/hr) Intensity 20 Intensity (mm/hr) Intensity

0 0 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 Duration ( min) Duration ( min)

φ=28 φ=32 φ=36 W=2m W=4m W=6m

(e) (f)

100 100 θ Zs 80 80

60 60 y = 210.8x-0.6 40 y = 171.0x-0.6 y = 212.2x-0.6 40 y = 124.6x-0.6 20 y = 171.0x-0.6 20 Intensity (mm/hr) Intensity Intensity (mm/hr) y = 92.1x-0.6 0 0 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 Duration ( min) Duration ( min) θ=16 θ=20 θ=28 Zs= 2m Zs=4m Zs=6m

(g) (h)

Figure 11. I-D curves for debris flow initiation by bed failure in relation to different geometrical and Figure 11. I-D curves for debris flow initiation by bed failure in relation to different geometrical and hydro-mechanical parameters. The regression formula belong to the curves from top to bottom. For hydro-mechanical parameters. The regression formula belong to the curves from top to bottom. For the the definition of parameters see Table 3. definition of parameters see Table3.

The I-D curves obtained by our simulations suggest that the duration range was strongly influencedThe I-Dby the curves type obtained of initiation. by ourDebris simulations flows initiated suggest by thatHortonian the duration overland range flow wasseems strongly to be initiatedinfluenced within by theseveral type minutes of initiation. while debris Debris flow flows initiated initiated by bybed Hortonian failure within overland one to flowtwo hours. seems I- to Dbe curves initiated find within in the several literature minutes give whilethreshold debris curv flowes with initiated a larger by bed duration failure range within of one one to to two several hours. hours. The relative quick response to debris flow initiation can be explained by the large effect we give in our simulations to the contributing slopes with sparse vegetation and low infiltration rates,

Water 2018, 10, 950 18 of 22

I-DWater curves 2018, 10 find, x FOR in PEER the literature REVIEW give threshold curves with a larger duration range of one to several18 of 22 hours. The relative quick response to debris flow initiation can be explained by the large effect we give inwhich our simulationsin other areas to themay contributing be minor due slopes to higher with sparse infiltration vegetation rates andof denser low infiltration vegetation rates, and whichlower inoverland other areas flow may rates. be minorThe use due of to the higher curve infiltration number ratesmethod of denser also explains vegetation the and quick lower response overland to flowinitiation, rates. because The use it of does the curve not take number into account method the also effect explains of the the initial quick moisture response content to initiation, which because for dry itsoils does gives not takelarger into infiltration account therates effect and oftime the to initial pondin moistureg in the content first period which of fora rain dry event. soils gives It also larger does infiltrationnot simulate rates the andtravel time time to towards ponding the in thechannel. first period The relative of a rain quick event. response It also for does channel not simulate bed failure the travelinitiation time was towards also thefound channel. by Berti The [24] relative dealing quick wi responseth nearly for impermeable channel bed failure slopes initiation in the was source also foundarea. by Berti [24] dealing with nearly impermeable rock slopes in the source area. FigureFigure 1212 comparescompares twotwo extremeextreme I-DI-D curvescurves [[37,3837,38],], andand oneone inin betweenbetween thethe twotwo [[39]39] obtainedobtained worldwideworldwide withwith thethe twotwo extremeextreme curvescurves producedproduced inin ourour simulation.simulation. TheThe minimumminimum curvecurve inin ourour simulationsimulation was related related to to the the maximum maximum channel channel slope slope (28°), (28 ◦and), and the themaximum maximum threshold threshold curve curve was wasrelated related to the to thelargest largest length length (Lx ()Lx of) ofthe the channel channel bed. bed. Figure Figure 12 12 shows shows that that a a simple variationvariation ofof parametersparameters forfor thethe initiationinitiation ofof debrisdebris flowsflows inin channelchannel bedsbeds ofof sourcesource areas,areas, whichwhich givesgives alreadyalready aa significantsignificant rangerange inin variationvariation comparedcompared toto thethe rangerange in threshold values for debris flowsflows worldwide. TheThe figurefigure showsshows that,that, forfor reasonsreasons givengiven above,above, ourour simulatedsimulated curvescurves areare positionedpositioned inin thethe lowerlower partpart ofof thethe domaindomain coveredcovered byby allall thethe curvescurves obtainedobtained fromfrom differentdifferent parts parts of of the the world. world.

120

100 This paper (theta) 80

60 This paper (Lx)

40 Innes (1983) Intensity ( mm/hr) 20 Chien-Yuan et al 0 (2005) 0 50 100 150 200 250 300 350 400 Caine (1980) Duration minutes

Figure 12. Ultimate variation in I-D curves as a result of our sensitivity analyses compared to the Figure 12. Ultimate variation in I-D curves as a result of our sensitivity analyses compared to the maximum difference in I-D curves found worldwide. maximum difference in I-D curves found worldwide.

WeWe havehave shown shown in in this this section section that that the the I-D I-D curves curves for for debris debris flows flows triggered triggered by overland by overland flow flow and bedand failurebed failure are especially are especially sensitive sensitive to the morphometricto the morphometric parameters parameters of the source of the area source and area less sensitiveand less tosensitive the hydro-mechanical to the hydro-mechanical parameters. parameters. The I-D curves The forI-D debris curves flows, for debris triggered flows, by the triggered overland by flow the processoverland are flow more process sensitive are to more these sensitive parameters to these than parameters the I-D curves than related the I-D to thecurves bed related failure triggeringto the bed processfailure (comparetriggering Figures process 10 (compare and 11). The Figures sensitivity 10 an ofd these11). The curves sensitivity for these of process these parameterscurves for coverthese aprocess range, parameters which is quite cover significant a range, comparedwhich is quite with si thegnificant ultimate compared range of with I-D curves the ultimate found range worldwide. of I-D curves found worldwide. 7. Discussion 7. DiscussionThis paper unraveled the effect of different hydro-mechanical processes on the initiation of debris flows.This It ispaper focused unraveled on the initiationthe effect inof channels different and hydro-mechanical it gives a detailed processes insight on in thethe influenceinitiation ofof differentdebris flows. hydro-mechanical It is focused on process the initiation mechanisms in channels in the source and it areagives on a thedetailed type ofinsight debris in flow the initiation.influence Itof shows different how hydro-mechanical the hydrologic conductivity process mechanisms (Ks) and slope in gradient the source (θ) determine area on the the type sequence of debris of various flow processinitiation. mechanisms. It shows how the hydrologic conductivity (Ks) and slope gradient (θ) determine the sequence of various process mechanisms. Our simulations suggest that the type of initiation and related factors have also a clear influence on the values of the I-D curve as shown in Figures 10 and 11. These I-D curves, determined by our two simulated process mechanisms, Hortonian overland flow and bed failure show a relative quick

Water 2018, 10, 950 19 of 22

Our simulations suggest that the type of initiation and related factors have also a clear influence on the values of the I-D curve as shown in Figures 10 and 11. These I-D curves, determined by our two simulated process mechanisms, Hortonian overland flow and bed failure show a relative quick response of debris flow initiation compared to what is generally provided by the literature. Our calculations were focused on the initiation of debris flows in the source area in channel beds surrounded by slopes with scarce vegetation and rather impermeable soils. A quick response (within one hour) was also observed by Berti [24] where, as in our simulations, debris flows were initiated in the source area by the dominant effect of run-on water to the channel delivered by a bare, impermeable catchment upstream. The assessment of rainfall threshold values for debris flow initiation are based in most cases on statistical empirical approaches using large data sets without detailed knowledge of the different triggering processes and its influencing factors [2,29]. Our quantitative approach to analyze the threshold conditions for debris flow initiation gives a more detailed insight in the effect of different parameters than the indicative parameters used in statistical techniques. Apart from the fact that no distinction is made in the mechanism of initiation, important morphometric characteristics, like channel width, slope, length, and thickness of bed material are ignored in most cases. As a consequence, the prediction of the probability debris flow initiation on the basis of rainfall for individual catchments can be very inaccurate. Further investigations must reveal the accuracy of both approaches to predict the initiation of debris flows. The CN value, which we used in the simulation of overland flow on the contributing slopes, reflects in a lumped way the dynamic soil and land use characteristics. Especially the amount of storage of water before the time to ponding, and thus the estimate of the total overland flow production of a rain event can be rather inaccurate, especially for rain events with shorter durations. The use of a more detailed infiltration model incorporating the effect of the initial moisture content will give better predictions. However, in this paper we did not unravel in detail the effect of these soil and land use characteristics on threshold conditions for debris flow initiation, but used a constant CN value as input for the run-on simulation to the channel bed. Initial moisture conditions in the channel bed, which will affect the permeability and hence the boundary conditions for the initiation of overland flow were not considered either in this paper. The effect of the initial moisture content of the bed material is minor due to the large amounts of influx of water and the relative coarse material in the channel bed. In this paper we mentioned the transport capacity of overland flow as a limiting factor for the initiation of debris flows. On slopes (<±16◦) sediment concentrations are too low (<0.2) to call it a debris or hyper-concentrated flow. For these lower channel gradients we did not consider the effect of the delivery of extra material by side wall collapses and failure of landslide dams [1,13,40], which may lead downstream to a rapid loading of the fluid and an instantaneous transformation into a debris flow The initiation of debris flows by bed failure is also more complex since it depends on certain boundary conditions related to pore pressure development at failure and a large amount of runoff water, which must be supplied during failure to keep the material moving [20,22,23,41,42]. It is interesting to analyze the potential in development further downstream of debris flows triggered by bed failure (BF-I) with high solid concentrations. On steeper slopes failure of the bed material occurs under lower groundwater heights (hs), and therefore after failure much additional overland flow water is needed to maintain the movement further down slope. Important is also the mechanism of erosion and erosive power of both types of debris flows further downstream in order to grow to a mature debris flow [6,43–47].

8. Conclusions We could distinguish in our flume tests three types of hydro-mechanical processes which may trigger debris flows in channel beds of first order source areas. These are erosion and transport by intensive Horton overland flow (ROh-I), saturation overland flow (ROs-I), and by infiltrating water causing failure of channel bed material (BF-I). On the basis of these flume tests, an integrated Water 2018, 10, 950 20 of 22 hydro-mechanical model was developed, which was calibrated and validated with a number of process indicators measured during the flume tests. We were able to assess by means of this model the influence of important parameters on the mode of debris flow initiation. The hydraulic conductivity of the bed sediments is an important factor controlling the type and sequence of processes triggering debris flows. At lower Ks values, Hortonian overland will be the first process to start debris flows followed by bed failure or saturation overland flow. At higher Ks values, triggering by Hortonian overland flow is not possible anymore in this relatively coarse bed material, and triggering by bed failure will be the dominant process if the slope gradient is steep enough (>16◦). Therefore, the slope gradient of the channel bed is a second important factor controlling the type of hydro-mechanical triggering. On gentler slopes which remain stable under saturated conditions, saturation overland flow might create debris flows if slope gradient is not too gentle, and therefore sediment concentration too low to call it a debris flow. We further analyzed also the effect of different important morphometric and hydro-mechanical parameters on meteorological thresholds for triggering debris flows by overland flow or bed failure, respectively. With respect to overland flow triggering, the morphometric factors related to the size of the source area and width and length of the channel bed have the largest influence on the position of the I-D curves. Meteorological thresholds for bed failure triggering are also sensitive to morphometric parameters while the hydro-mechanical parameters have relative less influence on these threshold values.

Author Contributions: T.W.J.v.A., B.Y. and W.H. conceived and designed the experiments; B.Y. performed the hydro-mechanical measurements on the materials and performed the experiments; T.W.J.v.A. and B.Y. analyzed the data; T.W.J.v.A. did the modelling and wrote the paper. Funding: This research was funded by the National Natural Science Foundation of China (NSFC) grant number [41672341]. Acknowledgments: We thank the two anonymous reviewers and Niek Rengers for their valuable comments and suggestions which improved our paper. Conflicts of Interest: The authors declare no conflict of interest.

References

1. Zhuang, J.; Cui, P.; Peng, J.; Hu, K.; Iqbal, J. Initiation process of debris flows on different slopes due to surface flow and trigger-specific strategies for mitigating post- in old Beichuan County, China. Environ. Earth Sci. 2013, 68, 1391–1403. [CrossRef] 2. Cuomo, S.; Della Sala, M. Rainfall-induced infiltration, runoff and failure in steep unsaturated shallow soil deposits. Eng. Geol. 2013, 162, 118–127. [CrossRef] 3. Cuomo, S.; Della Sala, M.; Novita, A. Physically based modelling of soil erosion induced by rainfall in small mountain basins. Geomorphology 2015, 243, 106–115. [CrossRef] 4. Berti, M.; Genevois, R.; Simoni, S.; Tecca, P.R. Field observations of a debris flow event in the Dolomites. Geomorphology 1999, 29, 265–274. [CrossRef] 5. Armanini, A.; Gregoretti, C. Triggering of debris flow by overland flow: A comparison between theoretical and experimental results. In Proceedings of the 2nd International Conference on Debris flow Hazards Mitigation, Taipei, Taiwan, 16–18 August 2000; pp. 117–124. 6. Takahashi, T. Initiation and flow of various types of debris flow. In Proceedings of the 2nd International Conference on Debris Flow Hazards Mitigation: Mechanics, Prediction and Assessment, Taipei, Taiwan, 16–18 August 2000; pp. 15–25. 7. Coe, J.A.; Kinner, D.A.; Godt, J.W. Initiation conditions for debris flows generated by runoff at Chalk Cliffs, central Colorado. Geomorphology 2008, 96, 270–297. [CrossRef] 8. Yu, B. Research on the prediction of debris flows triggered in channels. Nat. Hazards 2011, 58, 391–406. [CrossRef] 9. Van Asch, T.W.J.; Tang, C.; Zhu, J.; Alkema, D. An integrated model to assess critical rainfall thresholds for the critical run-out distances of debris flows. Nat. Hazards 2014, 70, 299–311. [CrossRef] Water 2018, 10, 950 21 of 22

10. Tang, C.; Rengers, N.; Van Asch, T.W.J.; Yang, Y.H.; Wang, G.F. Triggering conditions and depositional characteristics of a disastrous debris-flow event in Zhouqu city, Gansu Province, northwestern China. Nat. Hazards Earth Syst. Sci. 2011, 11, 2903–2912. [CrossRef] 11. Cui, P.; Zhou, G.G.D.; Zhu, X.H.; Zhang, J.Q. Scale amplification of natural debris flows caused by cascading failures. Geomorphology 2013, 182, 173–189. [CrossRef] 12. Zhou, G.G.D.; Cui, P.; Chen, H.Y.; Zhu, X.H.; Tang, J.B.; Sun, Q.C. Experimental study on cascading landslide dam failures by upstream flows. Landslides 2013, 10, 633–643. [CrossRef] 13. Hu, W.; Xu, Q.; van Asch, T.W.J.; Zhu, X.; Xu, Q.Q. Flume tests to study the initiation of huge debris flows after the Wenchuan earthquake in S-WChina. Eng. Geol. 2015, 182, 121–129. [CrossRef] 14. Cannon, S.H.; Kirkham, R.M.; Parise, M. Wildfire-related debris flow initiation processes, King Mountain, Colorado. Geomorphology 2001, 39, 171–188. [CrossRef] 15. Hungr, O.; Evans, S.G.; Bovis, M.J.; Hutchinson, J.N. A review of the classification of landslides of the flow type. Environ. Eng. Geosci. 2001, 7, 221–238. [CrossRef] 16. Malet, J.-P.; Laigle, D.; Remaître, A.; Maquaire, O. Triggering conditions and mobility of debris flows associated to complex earthflows. Geomorphology 2005, 66, 215–235. [CrossRef] 17. Cascini, L.; Cuomo, S.; Della Sala, M. Spatial and temporal occurrence of rainfall induced shallow landslides of flow type: A case of Sarno-Quindici, Italy. Geomorphology 2011, 126, 148–158. [CrossRef] 18. Zhang, S.; Zhang, L.M.; Peng, M.; Zhang, L.L.; Zhao, H.F.; Chen, H.X. Assessment of risks of loose landslide deposits formed by the 2008 Wenchuan earthquake. Nat. Hazards Earth Syst. Sci. 2012, 12, 1381–1392. [CrossRef] 19. Iverson, R.M.; Reid, M.E.; LaHusen, R.G. Debris flow mobilization from landslides. Ann. Rev. Earth Plan. Sci. 1997, 25, 85–138. [CrossRef] 20. Fuchu, D.; Lee, C.F.; Sijing, W. Analysis of rainstorm-induced slide-debris flows on natural terrain of Lantau Island, Hong Kong. Eng. Geol. 1999, 51, 279–290. [CrossRef] 21. Gabet, E.J.; Mudd, S.M. The mobilization of debris flows from shallow landslides. Geomorphology 2006, 74, 207–218. [CrossRef] 22. Van Asch, T.W.J.; Malet, J.-P. Flow-type failures in fine-grained soils: An important aspect in landslide hazard analysis. Nat. Hazards Earth Syst. Sci. 2009, 9, 1703–1711. [CrossRef] 23. Hu, W.; Donga, X.J.; Xua, Q.; Wang, G.H.; Van Asch, T.W.J.; Hicher, P.Y. Initiation processes for overland flow generated debris flows in the Wenchuan earthquake area of China. Geomorphology 2016, 253, 468–477. [CrossRef] 24. Berti, M.; Simoni, A. Experimental evidences and numerical modelling of debris flow initiated by channel runoff. Landslides 2005, 2, 171–182. [CrossRef] 25. Kean, J.W.; McCoy, S.W.; Tucker, G.E.; Staley, D.M.; Coe, J.A. Runoff-generated debris flows: Observations and modeling of surge initiation, magnitude, and frequency. J. Geophys. Res. Earth Surf. 2013, 118, 2190–2207. [CrossRef] 26. Hu, W.; Xu, Q.; Wang, G.H.; van Asch, T.W.J.; Hicher, P.Y. Sensitivity of the initiation of debris flow to initial soil moisture. Landslides 2015, 12, 1139–1145. [CrossRef] 27. Liu, C.; Dong, J.; Peng, Y.; Huang, H. Effects of strong ground on the susceptibility of type debris flows. Eng. Geol. 2009, 104, 241–253. [CrossRef] 28. Chang, T.C.; Chien, Y.H. The application of genetic algorithm in debris flow prediction. Environ. Geol. 2007, 53, 339–347. [CrossRef] 29. Tiranti, D.; Bonetto, S.; Mandrone, G. Quantitative basin characterization to refine debris-flow triggering criteria and processes: An example from the Italian Western Alps. Landslides 2008, 5, 45–57. [CrossRef] 30. Yu, B.; Li, L.; Wu, Y.; Chu, S. A formation model for debris flows in the Chenyulan River Watershed, Taiwan. Nat. Hazards 2013, 68, 745–762. [CrossRef] 31. Smith, G.N.; Smith, I.G.N. Elements of Soil Mechanics, 7th ed.; Blackwell Science Ltd.: Oxford, UK, 1988; p. 494, ISBN 0-632-04126-9. 32. Hendriks, M.R. Introduction to Physical Hydrology, 1st ed.; Oxford University Press: Oxford, UK, 2010; p. 331, ISBN 978-0-19-929684-2. 33. Chow, V.T.; Maidment, D.R.; Mays, L.W. Applied Hydrology; McGraw-Hill Book Company: New York, NY, USA, 1988; p. 572, ISBN 0-07-010810-2. Water 2018, 10, 950 22 of 22

34. Rickenmann, D. Hyperconcentrated flow and sediment transport at steep slopes. J. Hydraul. Eng. 1991, 117, 1419–1439. [CrossRef] 35. Rickenmann, D. Comparison of bed load transport in torrents and gravel bed . Water Resour. Res. 2001, 37, 3295–3305. [CrossRef] 36. United States Department of Agriculture (USDA-SCS). National Engineering Handbook; Section 4: Hydrology 1985; USDA-SCS: Washington, DC, USA, 1985. 37. Innes, J.L. Debris flows. Prog. Phys. Geogr. 1983, 7, 469–501. [CrossRef] 38. Chen, C.-Y.; Chen, T.-C.; Yu, F.-C.; Yu, W.-H.; Tseng, C.-C. Rainfall duration and debris-flow initiated studies for real-time monitoring. Environ. Geol. 2005, 47, 715–724. [CrossRef] 39. Caine, N. The rainfall intensity duration control of shallow landslides and debris flows. Geogr. Ann. A Phys. Geogr. 1980, 62, 23–27. 40. Stancanelli, L.; Lanzoni, M.S.; Foti, E. Propagation and of stony debris flows at channel confluences. Water Resour. Res. 2015, 51, 5100–5116. [CrossRef] 41. George, D.L.; Iverson, R.M. A depth-averaged debris-flow model that includes the effects of evolving dilatancy I. Physical basis. Proc. R. Soc. 2014, A470.[CrossRef] 42. Lehmann, P.; Or, D. Hydromechanical triggering of landslides: From progressive local failures to mass release. Water Resour. Res. 2012, 48, W03535. [CrossRef] 43. McDougall, S.; Hungr, O. Dynamic modelling of entrainment in rapid landslides. Can. Geotech. J. 2005, 42, 1437–1448. [CrossRef] 44. Medina, V.; Hürlimann, M.; Bateman, A. Application of FLATModel, a 2D finite volume code, to debris flows in the northeastern part of the Iberian Peninsula. Landslides 2008, 5, 127–142. [CrossRef] 45. Iverson, R.M.; Reid, M.E.; Logan, M.; LaHausen, R.G.; Godt, J.W.; Griswold, J.P. Positive feedback and momentum growth during debris-flow entrainment of wet bed sediment. Nat. Geosci. 2011, 4, 116–121. [CrossRef] 46. Quan Luna, B.; Remaître, A.; Van Asch, T.W.J.; Malet, J.-P.; Van Westen, C.J. Analysis of debris flow behavior with a one dimensional run-out model incorporating entrainment. Eng. Geol. 2012, 128, 63–75. [CrossRef] 47. Lanzoni, S.; Gregoretti, C.; Stancanelli, L.M. Coarse-grained debris flow dynamics on erodible beds. J. Geophys. Res. Earth Surf. 2017, 122.[CrossRef]

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).