Landslides

, Volume 2, Issue 3, pp 171–182

Experimental evidences and numerical modelling of debris flow initiated by channel runoff

Authors

    • Dipartimento di Scienze della Terra e Geologico-AmbientaliUniversità di Bologna
  • A. Simoni
    • Dipartimento di Scienze della Terra e Geologico-AmbientaliUniversità di Bologna
Original Articles

DOI: 10.1007/s10346-005-0062-4

Cite this article as:
Berti, M. & Simoni, A. Landslides (2005) 2: 171. doi:10.1007/s10346-005-0062-4

Abstract

Debris flow initiation by channel bed mobilization is a common process in high mountainous areas. Initiation is more likely to occur at the outlet of small, steeply sloping basins where concentrated overland flow feeds an ephemeral channel incised in slope deposits. Such geological conditions are typical of the Dolomite region (Italian Alps), which is characterized by widespread debris flow activity triggered by severe summer thunderstorms. Real-time data and field observations for one of these catchments (Acquabona catchment, Belluno, Italian Alps) were used to characterize the hydrological response of the initiation area to rainfalls of varying intensity and duration. The observed behaviour was then reproduced by means of a simple hydrological model, based on the kinematic wave assumption, to simulate the generation of channel runoff. The model is capable of predicting the observed hydrological response for a wide range of rainfall impulses, thus providing a physical basis for the understanding of the debris flow triggering threshold.

Keywords

Debris flowHydrologic triggeringMonitoringModellingItalian alps

Introduction

Hydrologic conditions leading to debris flow initiation may vary substantially, depending primarily on rainfall pattern and soil types but also on the topography and morphology of the bedrock underlying the soil. Debris flows can be initiated by short, high-intensity rainfall events which occur after a long period of no rainfall (e.g. 30 mm in 60 min and peak intensity of 95 mm/hr; Genevois et al. 2000a), by severe storms at the end of a sustained period of rainfall at low intensity (e.g. rainstorms with peak intensity from 10 to 20 mm/hr after a 20 h rainfall; Cannon and Ellen 1988), or by storms with relatively low intensity (less than 10 mm/hr) preceded by long antecedent rainfall (from days to several months; Wieczorek 1987). An extreme case is that reported by Wieczorek et al. (2000) for Blue Ridge in Central Virginia, where 5 days of moderate rainfall were followed by an exceptionally heavy tropical storm with peak intensities as high as 300 mm/hr.

The mechanism of debris flow initiation (shallow slope failure, progressive erosion operated by surface flow) is mostly dependent on the hydrologic response to rainfall of the unstable slope. Debris flow mobilization from landslides will occur when the triggering rainfall causes an increase of pore-water pressures within the soil associated with critical groundwater levels along a basal slip zone (Sidle and Swanston 1982; Anderson and Sitar 1995). The increase of pore-water pressures is commonly associated with the rise of a water table perched on the bedrock or on top of relatively impermeable soils, with flow parallel (Campbell 1975; Montgomery and Dietrich 1994; Pack et al. 1998) or not-parallel (Iverson 1990) to the slope. Since landslide-induced debris flows require an accumulation of water in the soil, they are more commonly found on slopes consisting of poorly-sorted debris containing a fine fraction of more than 30–40% silt and clay (Ellen 1988). These finer sediment tend to retain water in the unsaturated zone and have limited saturated conductivity that inhibits drainage from the source area (typically less than 10−4 m/s; Fetter 1980).

Debris flows may also initiate by mobilization of a channel bed due to surface water flow (Takahashi 1991; Griffiths et al. 1997; Coe et al. 2003). In this case, the shear force of water mobilizes individual particles and the solid concentration increases until it reaches an equilibrium dependant on slope angle and water supply (e.g. Takahashi 2000). Debris flows thus initiate when a critical surface discharge, rather than a critical groundwater level, is reached. This phenomenon is best described in terms of equilibrium of single particles to the hydrodynamic drag force rather than using the classical, limit-equilibrium analysis of a Mohr-Coulomb material employed for shallow slope stability (Chiew and Parker 1994; Buffington and Montgomery 1997; Armanini and Gregoretti 2000). Surface runoff becomes an important process in recently burned watersheds, where the removal of plant canopy and the duff layer covering forest soils, and the generation of water-repellent soils, can result in significant reduction of infiltration (Martin and Moody 2001; Conedera et al. 2003). Surface runoff is also an important process in high mountainous areas due to concentration of overland flow on steep rocky watersheds upstream the source areas (Berti et al. 1999; D’agostino and Marchi 2003). The latter condition is quite common in the European Alps, where most debris flows are initiated by concentrated surface flow at the bottom of channels filled by coarse loose debris (Tognacca et al. 2000). Although poorly-sorted, such debris contains a low fine fraction (less than 10–20% silt and clay) compared to soils involved in landslide-induced debris flows, and much higher hydraulic conductivity. Because of their ability to drain the rain water infiltrating from the surface, the moisture content of these materials is always far from saturation, therefore failure is very unlikely unless it occurs as a result of surface flow. As pointed out by Tognacca and Bezzola (1997) and Cannon et al. (2003), debris flows initiated by channel bed mobilization are far less studied and poorly understood compared to landslide-induced debris flows. In particular, a framework to adequately characterize runoff generation, erosion processes, and debris flow generation is still missing.

In this paper we aim to obtain a quantitative insight on the hydrologic triggering of a typical Alpine debris flow by developing a simple model based on the kinematic wave theory (Lighthill and Whitham 1955). Direct observations and real-time data collected during three field seasons (’96–’98) on Acquabona catchment (Dolomites, Italy) have been analysed in order to physically explain the empirical rainfall thresholds (Genevois et al. 2000a) and to test predictive capabilities of two threshold criteria recently proposed in the literature (Gregoretti 2000; Tognacca et al. 2000).

Site description

The study site is located in the northeast portion of the Italian Alps (Dolomites, Belluno Province). In the area, dolomite massifs constitute the relief at highest elevations and their steep rocky cliffs are connected to the bottom of alpine valleys by means of milder slopes where bedrock is covered by a thick debris talus, deposited in post-glacial climatic conditions (Panizza et al. 1996). Small headwater basins, located in the upper dolomitic part of the slopes, collect and concentrate rainfalls as overland flow and along trunk streams incised in bedrock. These basins are typically very steep (average slope of 12 debris flow catchments in the area ranges between 45 and 50 deg), and mostly consist of exposed bedrock with no vegetation and almost absent soil cover. Such watersheds respond dramatically to high intensity, short duration rainfalls (more than 15 mm in 30 min), rapidly generating high runoff discharges (more than 1 m3/s) which are delivered downstream to talus cones. Debris flows commonly initiate at the transition between bedrock and talus. The debris flow then travels downslope along channels incised in talus. Channels are deepened by successive events therefore entraining solids to debris flows. The deposition occurs on the gentler parts of the slopes (5–15 deg) or at the valley bottom. In the municipality of Cortina d’Ampezzo (area 254 km2), more than 200 debris flows basins have been surveyed (Lamberti et al. 1999) and most of them display the above described characteristics. However, few are as active as the one we are describing and analysing here.

The Acquabona watershed (Fig. 1) is a typical debris flow catchment of the dolomitic region. Seven debris flows ranging in volume from 500 to 15000 m3 occurred in the last 7 years. The headwater basin has an area of 0.3 km2, an average slope of 44 deg and the dominant geology consists of dolomite. The outlet is located at an elevation of 1600 m., at the transition between bedrock and talus (Fig. 2a, b). The slope of the debris flow channel ranges from 22 to 30 deg in the initiation area, with an average of 27 deg. Channel banks are steeper, with an average 45 deg, locally exceeding 55 deg.
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Fig. 1

(a) Topographic map of the Acquabona catchment (10 m contour interval); (b) panoramic view of the headwater rocky basin that feeds the initiation area of the debris flow

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Fig. 2

Main features of the debris flow initiation area: (a) schematic channel section; (b) topographic map showing the headwater rocky basin (light colour) and the upper part of the debris-incised channel; (c) downstream view of the initiation area (the solid line marks the limit between channel-bed and slope debris); (d) close view of the channel bed debris showing the very open structure and the presence of macropores

The initiation process involves loose granular material filling the bottom of the channel (channel bed material). It mostly represents the deposit of small bank failures which occur in response to channel scouring and deepening caused by debris flows. The channel bed material shows an open structure made of large continuous voids and big pores due to the deposition process (sudden and unsaturated) which follows the bank failures and also to progressive removal of the finer fractions by surface and interstitial flow (Fig. 2c, d). Boulders on the surface exceed 1 m diameter and show darker pigment of lichen which indicate a long permanence in the initiation area. Here, stream flows starts to entrain material (immature debris flows) but does not have the competence to carry boulder-sized clasts.

The debris into which the channel is cut (slope deposit) has a much denser structure if compared to the channel bed material. Macropores are not present and boulder-size clasts are very rare. Slope deposits have lower permeability than the overlying channel bed material; we will see below that this permeability contrast is a key feature to understand the mechanism of runoff generation in the initiation area.

The grain size distribution of channel bed material and slope deposits is significantly different and is also responsible of the above mentioned difference in permeability. Figure 3a reports the two particle-size distribution curves measured on volumetric samples. It can be noted that channel bed material is poorer in terms of fine fraction (<5%) if compared to slope deposits sampled along the channel banks (>15%). Figure 3b compares the results of grain-size measurement by channel bed surface grid sampling (Bagato et al. 2004; Bunte and Abt 2001) and volumetric sampling of channel bed subsurface layer. Boulders can only be included in a widely spaced pebble count while fines require necessarily volumetric sampling. A combination of the two can perhaps give an idea of the overall grain size distribution of the channel bed material.
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Fig. 3

Grain-size distributions in the initiation area: (a) measured on volumetric samples of channel bed and channel bank; (b) overall distribution obtained combining different sampling techniques (see text)

Given its low density and granular nature, the shear strength of the channel bed debris can be described by the critical state friction angle. A mean value of 42 deg was obtained by means of triaxial tests conducted on reconstituted samples (Genevois et al. 1999). This relatively high frictional resistance reflects the angular shape of the particles and their heterogeneous sizes. The typical open structure of the channel bed material should allow a fast contractive response to shearing, suggesting a high potential for static liquefaction. However we have no direct evidence supporting this hypothesis.

Acquabona debris flow channel was equipped in 1997 with a monitoring system aimed to measure rainfall, ground vibrations, pore pressure in the initiation area, pore pressure at the base of the flow, normal stress at the base of the flow, and flow depth (Berti et al. 2000; Genevois et al. 2000b). Among these, rainfalls and pore pressures in the initiation area are the most relevant for this work. Pore pressures were measured at moderate depth (0.4 to 1 m) below the surface within the loose channel-bed material. Four sensors were buried along two verticals positioned 3 to 6 m apart, which were replaced after every event. A fifth pressure sensor was installed at 3.5 m from surface to make sure that no interference from a water table rising from below would affect the initiation process (Fig. 2a). All sensors were located approximately 100 m downstream from the transition between bedrock-incised and debris-incised channel, where loose debris is abundant and the initiation process has been repeatedly observed and videotaped (Fig. 2b) by means of two cameras.

Observations on hydrologic response to rainfall and debris flow initiation

In Acquabona (and the Dolomites generally), debris flows are triggered by heavy summer rainstorms. This conclusion is based on observations and experience gathered by locals. Debris flows generally originate in the upper part of the channel incised into slope deposits, just downstream the outlet of the rocky headwater basin (Figs. 1 and 2). On the basis of pore water pressure measurements within the channel bed and by direct observations and video recordings, we discriminate three different hydrologic responses to rainfall.

A (no response). The pressure sensors buried in the channel bed show no change in pore pressures, and no surface runoff occurs in the channel. We infer that all the rainwater moves downward as unsaturated flow since the rainfall intensity (max recorded value = 3E-2 m/s) is always much smaller than the potential infiltration rates of the channel debris (saturated conductivity is in the order of 1E-1 m/s, see below). Also subsurface lateral flow in the channel bed is either absent or negligible. This may indicate that no water is delivered at the outlet of the rocky basin (which is located 100 m upstream the sensor location) or that the subsurface flow is so small that dissipates before reaching pressure sensors.

B (subsurface stormflow). A transient pore water pressure response is measured within the channel bed by the buried sensors while surface runoff is not present in the channel. The pore pressure response (Fig. 4) generally consists of a rapid pressure increase (5 to 30 cm of water in 5 min or less) followed by a slower falling limb (few hours). However, it is difficult to identify any consistent pattern of subsurface flow. In seven cases out of ten, shallow sensors measured higher pressures than deep sensors, and in four cases out to ten the subsurface flow was detected only by two of the four sensors. Most likely, the subsurface flow within the loose channel bed material is the result of water flowing in a granular porous media and also along conduits and macropores whose geometry can vary during and between successive episodes. Table 1 summarizes the main features of the recorded pressure response. As anticipated, absolute value of pore pressure is not related to either sensor depth or rainfall intensity. Instead, the delay between pore pressure response and rainfall events shows some consistency. In particular, when rainfall intensities exceed 0.1 mm/min, saturated subsurface flow is regularly recorded by pressure sensors 30–55 min after the rainfall onset. Fig. 4 reports an example of subsurface stormflow waves generated by two summer thunderstorms.
Table 1

Data from significant rainfall events occurred in Acquabona from 1996 to 2000

Date

Burst duration (min)

Average intensity (mm/h)

Elapsed timea (min)

Response typeb

Max pressure height in the channel bed (cm)

Sensor depth (cm)

25/07/1998

52

0.19

45

B

19

30

27/07/1998

40

0.31

55

B

13

30

28/08/1997

20

0.40

30

B

7

90

05/09/1997

70

0.27

58

B

27

100

06/11/1997

285

0.07

145

B

16

90

11/06/1998

30

0.16

35

B

27

30

14/07/1998

115

0.11

145

B

19

30

06/10/1998 (1)

235

0.11

65

B

9

50

06/10/1998 (2)

420

0.10

85

B

14

50

06/10/1998 (3)

40

0.32

10

B

5

50

12/06/1996

35

0.73

30

C

  

17/08/1998

65

0.44

35

C

  

20/07/1999

30

0.65

31

C

  

30/09/2000

45

0.36

35

C

  

aMeasured time delay from the start of the rainfall burst to the arrival of the subsurface pressure wave at sensor location

bB=subsurface stormflow; C=channel runoff and debris flow mobilization (see text)

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Fig. 4

Examples of subsurface stormflow waves recorded by pressure sensors buried in the channel-bed debris. The two waves were generated by strong rainfalls that caused subsurface stormflow but no channel runoff (response B)

All the recorded waves were normalized to the peak and combined to create an average response curve (Fig. 5). Each point of the curve is computed by taking the average of all the normalized pressure heights recorded at certain time (t) from the wave arrival time (t=0). This curve indicates a very fast time rise to peak (10 min) followed by a slower exponential decay which lasts about 5 h.
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Fig. 5

Pressure height curve obtained by averaging all the individual sensor response (scaled to peak) recorded for the storms that produced subsurface stormflow in the initiation area (9 time series)

C (surface flow and initiation of debris flow). Rainfall with an intensity higher than about 0.3 mm/min and duration of more than 20 min produces surface flow in the channel. Pressure sensors, buried in the channel bed, start measuring positive pore pressures only when surface water flow appears, indicating that the debris is dry at the beginning of the initiation process. Pore pressures then peaks, corresponding to the mobilization of the bed material; after few seconds the rupture of sensor cables ends the series of data (Genevois et al. 2000a). The delay between the onset of rainfall and the runoff appearance in the channel is similar to what observed in the case of response B (Table 1). Videos of the initiation area (3 events recorded) always show that water flowing along the channel is highly turbulent due to the roughness and steepness of the bed. As soon as the surface flow appears, drag forces are enough to move single debris particles which are either entrained in the flow or move by rolling and bouncing depending on their size. The en-mass movement of portions of channel bed also occur. It generally follows the increase in surface discharge and seems favoured by local conditions (i.e.: mobilization of boulders partially damming the channel bed). It is difficult to decide whether the debris is pushed and dragged by sediment-laden water or it undergoes a discrete failure below the channel-bed surface. The interaction of physical processes simultaneously acting in the channel during the debris flow initiation is too complicated to make a decision about alternative initiation mechanisms. Surface erosion operated by turbulent flow is certainly important but channel bed failures can contribute to mobilize the bed debris.

Comparison of rainfall records with hydrologic responses can be used to define a triggering threshold and to better understand the initiation process. The qualitative analysis indicates that subsurface stormflow (response B) and surface flow (response C) have always shown a close link to a well defined high-intensity rainfall event. Most of such responses occurred after a prolonged period without rain, when the channel bed debris was dry. These data suggest that pre-storm moisture conditions are not relevant in Acquabona, and that no sustained period of prolonged rainfall is needed to trigger debris flows in coarse debris. We therefore concentrate our analysis on single high intensity rainfall events (burst), defined as periods of intense rainfall exceeding an average 0.1 mm/min. Figure 6 reports rainfall parameters occurred in summer seasons from 1997 to 2000. Each rainfall event is represented by a different symbol according to the hydrologic response in the initiation area (A, B, or C). Points classified as A or B derive from monitoring data and are only available for years 1997 and 1998. The figure shows a notable coherence and allows the definition of thresholds based on intensity-duration characteristics. The surface flow threshold line (Fig. 6) also defines the hydrologic condition for debris flow triggering at Acquabona.
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Fig. 6

Rainfall duration-intensity chart showing the available rainfall records from 1996 to 2000. Each storm is classified in terms of hydrologic response in the initiation area (A, B, C see text) and the two threshold lines are drawn separating storms that produced similar response

Hydrologic modelling

The ability to predict the hydrologic response in the initiation area can be important for two purposes: to gain a better understanding of the runoff generation process in a steep channel filled by coarse debris, and to explain on a physical basis the debris flow triggering threshold defined by field data.

Modelling the hydrologic processes leading to the appearance of channel runoff in the initiation area would include all details of flow routing in the dolomitic basin, water infiltration into the channel bed, and variably saturated groundwater flow in both channel bed and surrounding slope deposits. Such analysis requires data that are difficult to obtain: a high-resolution topography of the rocky watershed, a three-dimensional representation of channel stratigraphy, an accurate hydrologic characterization of both the rock mass and the dolomite debris. The analysis presented herein aims to describe the hydrologic response of the initiation area of the debris flow (responses A, B, C; Fig. 6) by using a simple approach. The key components of the runoff generation process were isolated, as shown in Fig. 7, and described using simple hydrological models. The channel bed is modelled as a layer of constant thickness H and slope α (upper layer) that lies above the slope deposits (lower layer). The debris-incised channel is assumed to have a sharp upstream boundary with the rocky headwater basin, which is sketched as a plane of length LW, width BW, and slope αW.
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Fig. 7

Conceptual scheme of the hydrologic response to rainfall in the debris flow initiation area used to model the process of channel runoff generation

Runoff discharge from the headwater basin

The first step to simulate runoff generation in the initiation area is to calculate the water discharge at the outlet of the rocky basin QW (L3/T) produced by a rainfall of known intensity and duration. Given the small size of the headwater basin (A=0.23) km2) and the very steep slopes (αW=44 deg), we decided to compute QW using a finite difference approximation of the kinematic wave equation (explicit solution, backward linear scheme; Chow and Maidment 1988):
$$\frac{{\partial Q_W }}{{\partial x}} + \frac{1}{c}\frac{{\partial Q_W }}{{\partial t}} = q $$
(1)

where x is the distance measured downslope, i is the time, c is the kinematic wave celerity (L/T), and q is the net “lateral inflow” (flow per unit length, L2/T).

The kinematic wave celerity c has been expressed in terms of the average wave velocity on the basis of the Manning’s equation for a wide rectangular channel (energy slope = bed slope; wetted perimeter = flow width; Eagleson 1970):
$$\frac{1}{c} = \left( {\frac{{nB_W^{2/3} }}{{S_0^{1/2} }}} \right)^\beta \beta Q_W^{\beta - 1} $$
(2)

where β=3/5, S0=sin αW is the mean basin slope, and n is the Manning roughness coefficient of the rocky basin. Typical n values for bedrock surfaces are in the range of 0.01–0.025 (Chow 1959).

The net lateral inflow q represents the rainfall water which is neither retained on the surface of the basin nor infiltrated into the rock mass, and it is given by the excess rainfall rate pe (L/T) multiplied by the watershed width BW:
$$q = p_e B_W $$
(3)
A simple model (the Initial Loss and Constant Rate model; USACE 2000) is used to estimate pe from the rainfall hyetograph. The model assumes that no runoff occurs until the cumulative rainfall depth P at the i-th time interval (\(P = \sum {P_i }\)) exceeds an initial loss la (L), which represents interception and depression storage within the basin. Once the initial loss is exceeded, a constant loss rate fc (L/T) is subtracted from the rainfall rate pi at each i-th time interval. This constant loss represents the ultimate infiltration capacity of the rocky headwater basin. The rainfall excess rate pe is then given by:
$$p_e = \left\{ {\begin{array}{*{20}c} 0 & {{\rm if}} & {\sum {P_i < I_a } } & \, & \, \\ {p_i - f_c } & {{\rm if}} & {\sum {P_i < I_a } } & \& & {p_i > f_c } \\ 0 & {{\rm if}} & {\sum {P_i < I_a } } & \& & {p_i < f_c } \\ \end{array}} \right. $$
(4)

The calculation of QW by means of Eqs. (1) to Eqs. (4) only requires an estimate of the loss coefficients la and fc. S0 and BW are in fact geometrical variables that can be easily measured and n (Manning roughness coefficient) can be roughly assumed by standard tables (e.g. Chow 1959). Therefore, the calibration of the model can be easily performed.

Runoff generation in the debris-incised channel

The runoff from the headwater basin flows to the basin outlet and enters the debris channel. Due to the high permeability of the channel bed debris and to the presence of large pore voids, the water infiltrates quickly into the channel bed flowing downstream as subsurface flow; when it exceeds the infiltration capacity of the channel bed, water flow appears on the surface (QR). The explicit interaction between surface flow and transient, unsaturated subsurface flow can be described using quite complex mathematical models to route QW along the debris channel (e.g. Panday and Huyakorn 2004), but such comprehensive models also require more extensive data. Notwithstanding the inherent simplifications, the kinematic wave analogy, by means of the adoption of an appropriate formulation for channel outflows, can simulate fairly well the runoff generation along the debris-incised channel. In the following equation:
$$\frac{{\partial Q_R }}{{\partial x}} + \frac{1}{c}\frac{{\partial Q_R }}{{\partial t}} = q $$
(5)

q (L2/T) represents the flow per unit length of the channel which is lost by infiltration into the bed (flow out of the control volume, q<0) and it is a function of structure, initial soil water content and hydraulic conductivity of the channel bed material In general, the potential outflow discharge Q (L3/T) can be treated as the sum of three components (Fig. 7): the storage variation into the channel debris, QD; the subsurface outflow through the channel bed, QS; and the subsurface leakage into the lower layer, QL. The storage component within the lower layer can be neglected for the reasons discussed later.

The first component QD is estimated by computing, for each time step dt, the unsaturated pore space available into a channel element of length dx, width B, and thickness H:
$$Q_D = (S - 1)\frac{{BHdx\cos \alpha n_e }}{{dt}} $$
(6)

where ne is the effective porosity of the channel debris and S is the degree of saturation of the channel element averaged over the entire depth of the upper layer H. QD can be relevant (0.2–0.4  m3/s) when the channel debris is almost dry (S≈0) and the whole pore space is available to store water, but it decreases to zero as the debris approaches saturation (S=1).

Computation of the two components QS and QL is more difficult because one needs to account for transient, variably-saturated subsurface flow. Stable numerical solutions of unsteady flow in unsaturated soils are difficult to obtain, especially for coarse materials with steep hydraulic functions (Tan et al. 2004), and analytical solutions are only available for very special cases (Serrano 2004). One of these cases is represented by steady, fully-saturated, slope-parallel flow. Under this condition, the potential outflow discharge can be simply computed by summing the component due to slope-parallel flow through the upper layer:
$$Q_S = - BH_n K_U \sin \alpha $$
(7)
and the component due to long-term leakage into the lower layer:
$$Q_L = - BK_L dx $$
(8)
where KU and KL are saturated hydraulic conductivities of the upper and lower debris and Hn=H cos α. A fundamental condition for the occurrence of near-surface, slope-parallel flow is that the flow domain is bounded by a impermeable bed at the bottom, that is KU>>KL. Moreover, the steady-state approximation adopted in (7) and (8) implies that the time required to reach steady-state flow is short enough that the transient component can be neglected. Field observations, real-time data and extensive analyses demonstrated that, in the present case, both conditions are satisfied. Two main arguments support this statement:
  1. (1)

    The occurrence of sustained, subsurface stormflow within the upper layer is demonstrated by the analysis of pressure-sensor response in the initiation area. We considered nine storms which gave well-defined pore-pressure waves at sensors location (approx. 100 m downstream the outlet of the rocky basin) but no surface flow in the channel (Table 1). For each storm, the arrival time of the pressure wave recorded by the monitoring system was compared to the arrival time computed by a finite different solution of the wave equation for kinematic subsurface stormflow (Beven 1981), as shown in Fig. 8. The runoff discharge at the outlet of the rocky watershed QW Eq. (1) was used as upstream boundary condition, and the saturated hydraulic conductivity of the upper layer KU and the bottom leakage within the lower layer QL were changed to obtain the best fit between computed and measured arrival times. Reasonable agreement was obtained for KU≈10-1 m/s and QL≈0 (Fig. 8), which roughly corresponds to a saturated conductivity of the lower debris KL<10−4 m/s <<KU. This result also implies that water losses due to storage into the lower debris can be neglected.

     
  2. (2)

    The validity of the quasi-steady approximation is supported by two-dimensional numerical analyses based on the Richards equation for unsteady, variably saturated flow (Richards 1931). The model considered a longitudinal channel section with zero pressure head at the surface (applied for a length Li downstream the watershed outlet to simulate the infiltration process). The debris is initially dry and it is characterised by a very steep soil-water characteristic curve, a very steep hydraulic conductivity function, and a saturated permeability KU=10−1 m/s>>KL. Model results are shown in Fig. 9. High infiltration rates occur at the beginning of the process, because of the available storage (dry soil, high void ratio), but the steady value predicted by Eq. (7) is reached within few seconds after the wetting front reaches the bottom of the upper layer and the flow develops along the slope. The error introduced by neglecting the transient component is fairly small and corresponds, in terms of volume, to the storage available in the channel-bed material which is accounted for by Eq. (6).

     
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Fig. 8

Comparison between computed and measured time elapsed from the onset of the rainfall to the passage of subsurface stormflow wave at sensors location. Parameter values used in the kinematic wave model: length of the analysis reach, L=100 m; bed slope, α=27 deg; porosity, ne=0.4; saturated hydraulic conductivity of the upper layer, KU=10−1 m/s; saturated hydraulic conductivity of the lower layer, KL<10−4 m/s

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Fig. 9

Results of 2D finite elements modelling of channel-bed infiltration. Curves indicate the decrease of potential infiltration with time for different lengths Li of the infiltration surface, modelled with zero pressure head at the soil surface. The channel bed debris is characterised by a saturated hydraulic conductivity KU=10−1 m/s, very steep hydraulic functions, and it is assumed to be initially dry. The small inset shows the propagation of the wetting front with time

The outflow computed by Eq. (7) provides a conservative estimate of the potential infiltration rate into the channel bed. Moreover, the error related to the steady-state approximation of deep infiltration is negligible since QL is either very small for short-duration rainfalls, or tends to the constant value predicted by (8) for rainfalls of long duration.

Among the three components QD, QL, QS of the model developed so far, the first varies in space and time, the second in space only (because of the steady-state assumption), the third is constant both in time and in space. Since QS is a fixed quantity, it can be omitted from q and simply subtracted from the inflow hydrograph QW at the upstream boundary (x=0). We then used QR(0,t)=QWQS as upstream boundary condition and the following formulation for q (outflow per unit length of the channel):
$$q = \left\{ {\begin{array}{*{20}c} {q_R } \hfill & {S < 1} \hfill & {{\rm and}} \hfill & {q_R \le q_D } \hfill & {(a)} \hfill \\ {\left( {q_D + q_L } \right)} \hfill & {S < 1} \hfill & {{\rm and}} \hfill & {q_R > q_D } \hfill & {(b)} \hfill \\ {q_L } \hfill & {S = 1} \hfill & {{\rm and}} \hfill & \, \hfill & {(c)} \hfill \\ \end{array}} \right. $$
(9)

where qR=QR/dx is the surface inflow from the upstream element, qD=QD/dx is the potential outflow due to storage into the channel debris, qL=QL/dx is the potential outflow due to deep leakage into the lower debris. Equation (9) states that the surface inflow qR will infiltrate completely into the channel-bed debris if enough storage is available (9a), while it will propagate downstream if the storage is insufficient (9b) or the pores are completely saturated (9c). The hydrological behaviour in the initiation area of the debris flow can be thus predicted by using Eq. (9) in conjunction with Eq. (5) to obtain the runoff discharge QR as a function of space and time. Note that in Eq. (5) the kinematic wave celerity c is now the celerity of surface flow along the bed channel, which is a function of channel geometry (slope α and width BB since runoff tends to concentrate in narrow channels) and bed roughness (n).

Model representation of hydrological response in the initiation area

From the above analysis, we can say that the hydrological response is determined by the amount of runoff flowing at the outlet of the headwater basin (QW) and by the possibility that it exceeds the drainage capacity of the debris channel (QD+QS+QL). The model describes three possible cases deriving from rainfall impulses of varying intensity and duration:
  1. 1.

    QW=0, all the rainfall water is retained in the rocky basin: neither subsurface, nor surface flow will occur in the initiation area;

     
  2. 2.

    0<QWQS, runoff is generated at the outlet of the headwater basin but the drainage capacity of the debris channel is not exceeded: subsurface stormflow will occur, but surface runoff will not;

     
  3. 3.

    QW>(QS+QD+QL), the runoff discharge QW exceeds the drainage capacity of the channel debris: both subsurface stormflow and surface runoff will occur in the channel.

     

These cases ideally correspond to the three hydrological responses (A, B, C) experimentally observed in the initiation area at the Acquabona watershed (Fig. 6). Case \(Q_S < Q_W \le \left( {Q_S + Q_D + Q_L } \right)\) corresponds to storms delivering enough water to the channel bed to exceed the slope-parallel outflow component (QW>QS), but not enough to exceed the overall outflow over a long channel reach since \(Q_W \le \left( {Q_S + Q_D + Q_L } \right)\). Channel runoff would not propagate far from the basin outlet and the water would quickly infiltrate into the channel bed. The model cannot predict discharge and volume in such intermediate cases because of the steady-state assumption for channel outflows. Nevertheless, given the high infiltration capacity of the channel bed, it is very likely that runoff would not occur for storms in between cases (2) and (3). Since surface water flow is necessary to trigger debris flows, these intermediate cases were classified as case 2 (response B).

Model application to selected storms

To test the validity of the model we may consider three storms that are below, between, and above the two empirical intensity-duration thresholds (Fig. 6, Fig. 10a). According to the model developed in this paper the hydrologic responses A, B, and C should be predicted respectively. Fig. 10b–d shows the results of the test, computed for the set of values summarised in Table 2.
Table 2

Parameter values used in the computation

Basin losses

Basin runoff

Channel runoff

Ia (mm)

9

LW (m)

900

L (m)

100

Channel routing

fc (mm/min)

0.05

BW (m)

250

BC (m)

2

  

αW (deg)

44

α (deg)

27

  

n

0.01

n

0.08

    

B (m)

6

Channel outflows

    

H (m)

1.5

    

ne

0.4

    

KU (m/s)

10−1

    

KL (m/s)

<10−4

https://static-content.springer.com/image/art%3A10.1007%2Fs10346-005-0062-4/MediaObjects/10346_2005_62_Fig10_HTML.jpg
Fig. 10

Example application of the hydrological model: a) input rainfalls plotted in the rainfall intensity-duration chart; b) total cumulative rainfall (solid lines) and effective cumulative rainfall (dashed lines) available for overland flow in the rocky headwater basin; c) overland flow hydrographs computed at the outlet of the headwater basin; d) channel runoff hydrographs computed 100 m downstream the basin outlet. Parameter values used in computations are listed in Table 2

Values of Ia and fc (the two basin losses parameters) have been obtained from calibration and are consistent with those expected for low-permeability areas (USACE 1994). They also lie in the typical range of soils of group C with a Curve Number CN=85 (low infiltration rate) referring to the SCS loss model (Soil Conservation Service 1986). Representative values of the hydraulic conductivity of the upper (KU) and lower (KL) layer (channel bed material and slope deposits) were also obtained by calibration, as explained in the previous section. All the other parameters were measured using independent methods: length (LW), width (BW), and slope (αW) of the rocky watershed were measured by DEM; Manning roughness coefficients (n) of both the rocky watershed and the debris channel were determined by tables; length (L), width (BC), and slope (α) of the debris channel were measured in the field; length (B) and thickness (H) of the upper layer were determined by seismic refraction surveys conducted in the initiation area; effective porosity of the upper layer (ne) was assumed to be equal to total porosity measured in the field. As expected, storm S1 does not produce runoff at the basin outlet (response A, Fig. 10c), storm S2 produces runoff but all the water infiltrates into the channel bed flowing as subsurface flow (response B, Fig. 10d), storm S3 produces surface flow over the whole channel reach (response C; Fig. 10d).

The model performance can be further evaluated by comparing the results of the simulation obtained by considering the rainfall event which triggered the 1998 debris flow (Fig. 6) with experimental measurements and observations. Fig. 11 shows the runoff discharge computed at three different locations in the initiation area (basin outlet, 50 and 100 m downstream along the channel) as a function of time from the start of the rainfall (19.41). The computed time at which runoff begins (25–37 min) well agrees with the time of bed mobilization, recorded by a pressure sensor buried in the channel-bed which showed a sudden increase of pore pressure just before being destroyed by the surface flow (35 min).The maximum flow depth calculated by the model (approx. 20 cm) is in the range of what observed in the videos, and the expected volume V of the debris flow, that can be estimated on the basis of the overall runoff volume (VR=4000 m3) and the average solid concentration (c=0.6 measured in the deposition area) is \(V = V_R /\left( {1 - c} \right) = 4000/\left( {1 - 0.6} \right) = 10000\,{\rm m}^3\), which is fairly close to the volume of the debris flow measured in the deposition area (8000–9000 m3). Similar results were obtained, in terms of runoff discharge at the basin outlet, by Orlandini and Lamberti (2000) using a diffusion wave model of distributed catchment dynamics.
https://static-content.springer.com/image/art%3A10.1007%2Fs10346-005-0062-4/MediaObjects/10346_2005_62_Fig11_HTML.gif
Fig. 11

Comparison between computed and observed hydrological response in the initiation area to the August 17 1997 storm. The recorded time of bed mobilization well agrees with the computed time of runoff generation in the debris-incised channel. Parameter values used in computations are listed in Table 2

Numerical prediction of the empirical thresholds

The model was validated by analysing over 700 theoretical storms with intensity and duration spanning the full range in Fig. 6. For each storm, the hydrologic response in the initiation area has been simulated by the model, classified (A = no response; B = subsurface stormflow, C = channel runoff at x=100 m), and plotted in the rainfall duration-rainfall intensity chart. All computations were made using the values listed in Table 2 and results are shown in Fig. 12 where different symbols are used depending on the response type. The two solid lines that bound the loci of points with same type of hydrological response (computed thresholds) indicate rainfall beyond which the model predicts an abrupt change of hydrological behaviour. Fig. 12 shows a good agreement between empirical and computed thresholds, indicating that the model adequately explains the observed response in the initiation area, both regarding the occurrence of subsurface stormflow and the appearance of channel runoff.
https://static-content.springer.com/image/art%3A10.1007%2Fs10346-005-0062-4/MediaObjects/10346_2005_62_Fig12_HTML.jpg
Fig. 12

Comparison between the computed hydrological response in the initiation area (a, b, c) and the two empirical thresholds derived from the available observations (Fig. 6). The computed threshold lines are drawn separating storms that give similar response. Parameter values used in computations are listed in Table 2

Threshold criterion for debris flow initiation

Observations indicate that debris flows initiate when rainstorms generate surface runoff downstream the basin outlet. The hydrologic model proved to be capable of predicting the rainstorm parameters (intensity-duration) sufficient to produce surface runoff (Fig. 12) and, according to observations, initiate a debris flow. Still, it might be argued that channel bed surface runoff and debris flow triggering do not necessarily occur simultaneously. A critical surface runoff discharge (Qr) could be required before the process of bed mobilization starts and a debris flow is initiated. Such condition would be ideally represented in Fig. 12 by a further threshold lying above the channel runoff line. More generally, it would be described by a threshold criterion relating runoff discharge (or flow height) with specific material properties and channel slope.

The development of such a criterion would require a complex mathematical model based on the balance of forces acting upon particles, or an empirical equations describing the results of lab experiments. Due to the complexity of the problem and because of the many often unknown parameters, a comprehensive theoretically based debris flow initiation threshold is still lacking. Gregoretti (2000) and Tognacca et al. (2000) recently proposed empirical threshold criteria for debris flow initiation. Both methods follow the approach of Bathurst et al. (1987) and include the representative grain-size as fundamental input parameter beside the channel slope. Such parameter corresponds, as proposed by both authors, to d50 (the diameter through which 50% of the total soil mass is passing), and it is difficult to determine in practice due to the unsorted nature of the granular material usually involved (grain-size distribution often ranging 4 orders of magnitude or more) which introduces uncertainty and subjectivity in the grain-size distribution determination (Fig. 3). The application of the empirical threshold criteria is therefore somehow subjective.

The specific critical discharge (qT) computed by the two methods has been visualized as a function of representative grain-size (Fig. 13a) and can be compared with the specific runoff (qR) discharge predicted by the hydrological model in the initiation area (Fig. 13b). Data used for computation are summarised in the figure caption. Fig. 13a shows the strong dependence of critical discharge on the representative grain diameter. In our case, for a wide range of grain size diameter (from d20=0.2 cm to d80=8 cm referring to the overall distribution in Fig. 3), the critical specific discharge qT (discharge per unit width of the channel, L2/T) is lower than 0.25 m2/s, which corresponds to an average flow depth h<10 cm. Similar values (<0.3 m2/s) of specific runoff discharge (qR) are predicted by our hydrological model for rainfalls lying close to the empirical debris flow triggering threshold in the intensity-duration chart (Fig. 13b). This result confirms that a limited surface water runoff (few centimetres) is enough to start the mobilization of the channel bed (as observed in the video recordings) and corroborates the validity of the empirical threshold. It also indicates that the computed “channel runoff threshold” and the empirical “debris flow triggering threshold” are very close each other. At Acquabona, the range of rainfall impulses that are strong enough to produce channel runoff (qR>0) but not to trigger a debris flow (qR<qT) is so narrow that can be ignored for any practical purposes. The choice of a suitable threshold criterion for debris flow mobilization is far less important than the reliable prediction of runoff discharge in the initiation area.
https://static-content.springer.com/image/art%3A10.1007%2Fs10346-005-0062-4/MediaObjects/10346_2005_62_Fig13_HTML.jpg
Fig. 13

Computation of critical specific discharge for bed mobilization as a function of the diameter of representative grain size (a) and comparison with the specific discharge computed by the hydrological model 100 m downstream the outlet of the headwater basin (b). Within a wide range of grain-size diameters, critical specific discharges predicted by the two empirical models agree with the discharges computed by the hydrological model for rainfalls lying close to the observed threshold for debris flow initiation

Summary and conclusions

The following conclusions can be drawn from the data and the analyses presented in this paper:
  1. (1)

    At the Acquabona watershed, debris flows initiate by progressive bulking of surface water flow with loose debris incorporated from the channel bed. Runoff is generated when the water inflow coming from the headwater rocky basin exceeds the infiltration capacity of the channel bed material. Only very intense, typically short rainstorms lead to this condition.

     
  2. (2)

    The hydrologic response to rainfall in the debris flow initiation area can satisfactorily be described by a kinematic wave model that computes the overland flow hydrograph at the outlet of the headwater basin and routes inflow along the debris-incised channel. Direct observations, experimental data, and analyses demonstrated that the channel runoff along the debris-incised channel can be adequately estimated by subtracting from the inflow hydrograph at the basin outlet a channel outflow component which include soil storage and steady, slope-parallel subsurface flow within the channel bed.

     
  3. (3)

    The proposed model reproduces the observed hydrological response of the initiation area for a wide range of rainfall intensity and duration, thus providing a physical basis for understanding the empirical hydrologic thresholds.

     
  4. (4)

    Empirical threshold criteria for debris flow initiation predict the mobilization of debris for low specific discharges, which can be produced by rainfall events similar to those causing the appearance of channel runoff according to the hydrological model. Therefore, a good description of the runoff generation process is far more important that the prediction of the critical discharge for bed mobilization.

     

These findings are expected to be of quite general validity in similar geological conditions, but more extensive testing is required on different datasets under widely varying conditions. In particular, debris flow catchments characterized by different size of the headwater basin or subjected to different pattern of triggering rainfalls should be tested.

Acknowledgements

The research was funded by grant from the Ministero dell’Istruzione, dell’Università e della Ricerca, Project title “Analisi integrata di casi scelti di colate detritiche nell’arco alpino” (A.Lamberti coord.), years 2003–2005. Thanks to Richard LaHusen (USGS, Cascade Volcanoes Observatory, WA-USA) who installed the monitoring system at Acquabona in late 1997 and to Rinaldo Genevois, who coordinated that monitoring project and introduced us to the fascinating subject of debris flows. Finally, we would like to thank the reviewers for their useful remarks

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© Springer-Verlag 2005