Sediment entrainment by debris flows: In situ measurements from the headwaters of a steep catchment

Authors


Abstract

[1] Debris flows can dramatically increase their volume, and hence their destructive potential, by entraining sediment. Yet quantitative constraints on rates and mechanics of sediment entrainment by debris flows are limited. Using an in situ sensor network in the headwaters of a natural catchment we measured flow and bed properties during six erosive debris-flow events. Despite similar flow properties and thicknesses of bed sediment entrained across all events, time-averaged entrainment rates were significantly faster for bed sediment that was saturated prior to flow arrival compared with rates for sediment that was dry. Bed sediment was entrained from the sediment-surface downward in a progressive fashion and occurred during passage of dense granular fronts as well as water-rich, inter-surge flow.En massefailure of bed sediment along the sediment-bedrock interface was never observed. Large-magnitude, high-frequency fluctuations in total normal basal stress were dissipated within the upper 5 cm of bed sediment. Within this near surface layer, concomitant fluctuations in Coulomb frictional resistance are expected, irrespective of the influence of pore fluid pressure or fluctuations in shear stress. If the near-surface sediment was wet as it was overridden by a flow, additional large-magnitude, high-frequency pore pressure fluctuations were measured in the near-surface bed sediment. These pore pressure fluctuations propagated to depth at subsonic rates and in a diffusive manner. The depth to which large excess pore pressures propagated was typically less than 10 cm, but scaled as (D/fi)0.5, in which D is the hydraulic diffusivity and fiis the frequency of a particular pore pressure fluctuation. Shallow penetration depths of granular-normal-stress fluctuations and excess pore pressures demonstrate that only near-surface bed sediment experiences the full dynamic range of effective-stress fluctuations, and as a result, can be more easily entrained than deeper sediment. These data provide robust tests for mechanical models of entrainment and demonstrate that a debris flow over wet bed sediment will be larger than the same flow over dry bed sediment.

1. Introduction

[2] Debris flows are gravity driven mixtures of soil, rock, and water that have properties intermediate between water floods and dry rock avalanches [Iverson, 1997]. They can initiate from discrete landslides that liquefy upon failure [e.g., Iverson et al., 1997, 2000] or from processes ranging from brief, high-intensity rainstorms to crater lake outburst floods that cause rapid entrainment of sediment [e.g.,Meyer and Wells, 1997; Cannon et al., 2001; Coe et al., 2008; Breien et al., 2008; Procter et al., 2010]. Regardless of initiation mechanism, debris flows can dramatically increase their volume by entraining sediment as they travel through a drainage network. Despite the ubiquity of sediment entrainment by debris flows, the mechanics of the entrainment process remain poorly constrained.

[3] Empirical evidence and scaling considerations demonstrate that increases in flow volume can increase flow inundation area, inundation height, travel distance, and velocity, all of which escalate debris-flow hazards and impact to downstream environments [Iverson et al., 1998; Rickenmann, 1999, 2005]. As either sediment or water is entrained by a debris flow, the mixture composition can evolve to dramatically change the magnitude and spatial distribution of frictional and viscous flow resistance as well as significantly alter flow boundary conditions [e.g., Pierson, 1980; Iverson, 1997; Hungr, 2000; Pierson, 2005; Iverson et al., 2011]. Hence, to accurately simulate debris-flow motion and to predict related hazards and sediment flux it is critical to isolate which bed and flow properties control the occurrence and rates of sediment entrainment.

[4] Field observations following debris-flow events in diverse settings indicate that large volumes of sediment are entrained by debris flows from channel bed and banks [e.g.,Dietrich and Dunne, 1978; Gallino and Pierson, 1984;Hungr et al., 1984; Benda, 1990; Fannin and Wise, 2001; Wang et al., 2003; Revellino et al., 2004; May, 2002; Guthrie et al., 2010; Suwa and Okuda, 1980; Meyer and Wells, 1997; Berti et al., 1999; Cannon and Reneau, 2000; Godt and Coe, 2007; Breien et al., 2008; Gartner et al., 2008; Pierson et al., 1990; Vallance and Scott, 1997; Scott et al., 2005; Procter et al., 2010]. Volumetric increases of fifty times the initial slide volume have been reported [Hungr et al., 2005], as have volumetric growth rates greater than 20 m3 m−1 [Santi et al., 2008]. Although these studies illustrate the erosive nature of many debris flows, it is extremely difficult to determine the mechanics of sediment entrainment from post-flow observations.

[5] Many experimental and theoretical studies have investigated sediment entrainment by debris flows and related granular flows, yet little consensus has emerged as to which bed or flow properties dictate entrainment rates or style [e.g., Takahashi et al., 1992; Brufau et al., 2000; Papa et al., 2004; Takahashi, 2007; Rickenmann et al., 2003; Bouchut et al., 2008; Mangeney et al., 2010; Iverson, 2012]. Some studies predict that sediment entrainment will occur progressively from the sediment surface down (as shown schematically in Figure 1b), but commonly disagree on how entrainment rate depends on the ratio of bed grain size to flow depth [e.g., Egashira et al., 2001], the density difference between the flow and bed, sediment concentration in the flow, flow depth, and flow velocity [e.g., Takahashi et al., 1992; Fagents and Baloga, 2006; Iverson, 2012]. Other theories predict behavior ranging from slab-by-slab entrainment toen massefailure along the sediment-bedrock interface (Figures 1c and 1d) as a function of a static balance of forces [e.g., Takahashi, 1978; Hungr et al., 2005].

Figure 1.

Schematic illustrating the range of potential mechanisms by which debris flows might entrain sediment. Overriding debris flow and flowing bed material is depicted using a higher concentration of dark-colored clasts. Discrete failure planes are shown using a heavy dashed line. Orange tracer elements highlight displacements. (a) Initial condition. (b) Progressive entrainment during which the entrainment front moves down from the sediment-bed surface grain by grain. (c) Progressive failure during which the entrainment front moves from the sediment-bed surface down via multiple failures with thicknesses of many grain diameters, but with depths less than the total sediment thickness. (d)En massefailure of the sediment bed along the bedrock-sediment interface.

[6] Three recent studies have made direct measurements of sediment entrainment by debris flows. Berger et al. [2011]made in situ measurements of bed-sediment entrainment on a low-gradient fan during three different debris-flow events and demonstrated that entrainment generally occurred during passage of the dense granular front and coincident with the largest mean and fluctuating stress components. In large-scale debris-flow experiments over an erodible bed,Iverson et al. [2011] and Reid et al. [2011]showed that entrainment began ∼1 s after arrival of the granular front and corresponded closely with increases in bed-sediment pore pressure. The entrainment front moved progressively down into bed sediment at rates of 5–10 cm s−1. Iverson et al. [2011] and Reid et al. [2011]also demonstrated that the bed-sediment moisture content exhibited primary control on whether entrainment occurred or not.

[7] Here we build on this recent work by presenting and analyzing a data set from the headwaters of a natural debris-flow basin at Chalk Cliffs, Colorado, USA. This data set combines in situ measurements of bed-sediment entrainment with measurements of flow dynamics and bed properties for six different debris-flow events, two of which occurred on the same day. During the six distinct periods of entrainment, approximately 0.55 m, 0.4 m, 1.1 m, 0.5 m, 0.25 and 0.5 m of unconsolidated bed sediment were entrained, respectively. The debris flows during each period of entrainment had similar characteristics, but the pre-flow moisture content of the bed sediment varied from dry (<5% volumetric water content) in four events to saturated (∼40% volumetric water content) in two. The entrainment rate was strongly controlled by the bed-sediment moisture content, due to its role in controlling pore fluid pressures. In addition, our measurements demonstrate that entrainment occurred progressively, from the sediment surface downward, rather than byen massefailure along the bedrock-sediment interface.

2. Chalk Cliffs Study Basin

2.1. Catchment Description and Geologic Setting

[8] The Chalk Cliffs study basin is located on the southern flank of Mount Princeton in the Sawatch Range of central Colorado, USA. The steep, 0.3 km2semi-arid basin is incised into pervasively fractured and hydrothermally altered quartz monzonite [Coe et al., 2008], adjacent to the range-bounding Sawatch normal fault [Miller, 1999]. Steep bedrock cliffs and chutes dominate the headwaters of the basin and make up ∼60% of the total basin area (Figure 2). Unconsolidated colluvium forms slopes at or near the angle of repose below the bedrock cliffs. In places, these colluvial slopes grade directly to the channels, but more commonly, they have steep toes due to recent channel incision. Bedrock slopes in the basin are devoid of vegetation, and colluvial slopes are sparsely vegetated (Figure 2a). Dry ravel (the down-slope movement of individual particles [e.g.,Gabet, 2003]) from steep colluvium and frequent rockfall from bedrock cliffs rapidly fill the channels with loose debris. Upstream of the east-west channel junction (Figure 2b) the bedrock channels become thinly mantled (<1 m) with this debris between debris-flow events. During a debris-flow event the majority of the loose debris is entrained, exposing the bedrock channels. Downstream of the east-west channel junction the channels are filled more deeply with varying thicknesses of debris-flow, rockfall and dry-ravel deposits, and scouring down to bedrock during a debris-flow event occurs less frequently. Basin topographic characteristics are summarized inTable 1.

Figure 2.

Monitoring basin overview. (a) Photograph of the monitoring basin. Note predominance of bedrock and sparse vegetation in the basin. (b) Shaded relief image of the Chalk Cliffs study area with colored slope map overlain (both from 1 m airborne laser swath mapping data provided by NCALM). Lower right corner of map is at 38.7277°, −106.1734°. High slope values (>45°) colored red correspond to bedrock surfaces or very steep colluvium. Intermediate slope values (15°–45°) colored brown correspond to colluvial surfaces and steep channels. Low slope values (<15°) colored blue correspond to fan surfaces and low to intermediate gradient channels. Inset top right: Longitudinal profile of east and west channel. Note east channel profile is nearly identical to west channel.

Table 1. Topographic Characteristics of the Chalk Cliffs Study Basina
 Upper StationMiddle StationLower StationChalk Creek
  • a

    Locations, slope, and length parameters correspond to the west channel profile (Figure 2b inset). Table from McCoy et al. [2011].

  • b

    Mean channel slope is the mean channel from the drainage divide to the location.

  • c

    Local slope is calculated over 10 m centered on the location.

Contributing area (km2)0.060.160.240.43
Maximum elevation (m)3100310031003100
Station elevation (m)2780275026902520
Mean channel slope (deg)b35322616
Station local channel slope (deg)c131587
Channel length to drainage divide (m)5866789972194

[9] The general lack of vegetation and the predominance of bedrock in the upper basin provide ideal conditions to rapidly concentrate rainfall into water-rich flows. Steep channels filled with ample loose material allow these water-rich flows to rapidly entrain and concentrate large quantities of sediment to form a debris flow. A typical debris-flow event at Chalk Cliffs consists of multiple fluid-poor, coarse-grained granular surges separated by water-rich, inter-surge flow [McCoy et al., 2010, 2011]. These flow features are similar to those observed during many debris-flow events worldwide [e.g.,Pierson, 1980; Costa, 1984; Pierson, 1986; Hungr et al., 2001]. Where water-rich flows thin over bedrock steps in the channel it is possible to observe transport of large quantities of coarse-grained bedload. It should be noted that flows with similar properties to the inter-surge flow are sometimes referred to as hyperconcentrated flows [e.g.,Pierson, 2005] as well as debris floods [Hungr et al., 2001].

[10] Short-duration (1–2 hr) rainstorms of moderate to high intensity typically initiate debris-flow events in the study basin, although longer-duration storms (>12 hr) of low intensity occasionally initiate debris flows [Coe et al., 2008; McCoy et al., 2010, 2011]. Response times are generally very short, with measured lags between the onset of rain and the arrival of the first granular surge as little as ten minutes at the upper station [McCoy et al., 2011]. A more complete description of the geologic setting, surface water-runoff related debris-flow initiation mechanisms, and site selection can be found inCoe et al. [2008, 2010].

3. Methods

3.1. Monitoring System

[11] Through collaboration between the U.S. Geological Survey (USGS) and the University of Colorado we developed a sensor network that consists of three instrumented cross sections (upper, middle, and lower stations) and two video cameras filming at two frames per second (one filming the middle station, the other filming the upper station) [Coe et al., 2010; McCoy et al., 2011]. In principle, this monitoring system is a field adaptation of that developed at the USGS debris-flow flume [Iverson et al., 2010]. With this automated sensor network we measured the hydrological conditions that initiated debris-flow events, flow and bed properties during the event, and the rates of bed-sediment entrainment. All instrumentation to study flow properties, bed-sediment entrainment and bed-impact stress is co-located at the upper station, which allows us to directly relate flow and bed properties to measured entrainment. The upper station is located in the west channel, 38 m above the junction with the east channel and ∼590 m downstream from the drainage divide (Figure 2b).

[12] The instrumentation at the upper station evolved over the years of investigation. Instrument specifications and year of installation are summarized in Table 2. The most recent instrumentation is pictured in Figure 3and consists of sensors to measure total normal stress, pore fluid pressure, and temperature at the bedrock-sediment interface, flow stage, bed-sediment height above the bedrock channel floor, bed-sediment pore fluid pressure, bed-sediment volumetric water content, and rainfall. To install sensors in the loose bed sediment we excavated a trench, installed the sensors and then shoveled the sediment back in place. Given the loose and unstructured nature of the bed sediment these installations did not significantly alter the character of the bed. Video and still imagery of the reach surrounding the upper station were shot from across the valley at the location shown inFigure 2. On the hillslope above the instrumented cross section, instrumentation consists of volumetric water content probes at depths of 1 cm and 30 cm.

Table 2. Upper Station Instrumentation Specifications and Year of Installation
MeasurementMake and ModelInstallation YearSampling RateAccuracyResolution
  • a

    Any use of trade or product names does not constitute endorsement by the U.S. Government.

  • b

    Sampling rate for basal force decreased to 33 Hz in 2011.

  • c

    Sampling rate for erosion increased to 33 Hz in 2011.

  • d

    Sampling rate for bed-sediment water content increased to 33 Hz in 2011.

Soil moistureDecagon ECH2Oa200410 min±5 %0.001 m3 m−3
Stage (ultrasonic)Campbell Scientific SR50A20082 sec±0.01 m0.001 m
Basal pore pressureSolinst Levelogger 300120082 sec±0.003 m0.001 m
RainHydrological Services TB420082 sec±2 %0.00025 m
Basal force and stressTovey Engineering SWS102009100 Hzb±25 N,1100 Pa0.05 N, 2 Pa
Stage (laser)SICK DT50-HI201010 Hz±0.007 m0.001 m
Erosion (i.e., bed height)Custom made-JWK201010 Hzc+0.05 m0.05 m
Bed-sediment water contentDecagon EC-520101 mind±3 %0.001 m3 m−3
Bed-sediment pore pressureHoneywell 26PC201133 Hz±0.005 m0.001 m
Figure 3.

Schematic and photographs depicting the upper-station reach and instrumentation. (a) Schematic cross section of upper station as of 2011. (b) Photograph looking upstream at upper-station reach with instrumentation bridge. Local slope is 13°. Large rain gauge is 0.33 m tall. Note loose channel sediment produced by dry ravel and rockfall that is filling the bedrock channel. (c) Photograph of instrumentation that was placed in the loose channel sediment or cemented flush with bedrock-channel surface. Out of view are bed-sediment pore pressure sensors and a hand providing support for the erosion sensor. We buried the bed-sediment pore pressure and water content sensors after the picture was taken. Force plate is 15.24 cm by 15.24 cm.

[13] We used Campbell Scientific data loggers to sample the sensors and store the signals in digital form. All sensors at the upper station exit a slow (once a minute) continuous-sampling mode and enter a high-frequency (0.5–100 Hz) storm mode after 0.25 mm of rain has been measured by the station's rain gauges (Figure 3a), regardless of the duration over which the rainfall accumulated. The one-minute continuous data were sent via a cellular-phone modem to a server at the USGS where they were used to remotely monitor the site.

3.1.1. Stress Measurements

[14] We made basal stress measurements using a force plate. The force plate consisted of a 2.54 cm thick metal plate, with surface dimensions of 15.24 cm by 15.24 cm (232 cm2), attached to a single axis load cell and placed in a sealed enclosure (Figure 3c). To install the force plate we excavated a 20 cm by 20 cm by 20 cm hole in the bedrock channel floor, placed the enclosure in the hole and secured it with anchoring cement. During hammer-strike impulse tests the force plate had in situ natural frequencies that ranged from 200–250 Hz. We sampled the force plate at 100 Hz up to June 2011 when we decreased the rate to 33 Hz. Each individual measurement was the result of a 250μs analog integration of the signal.

3.1.2. Stage Measurements

[15] We measured flow stage every 2 s with an ultrasonic distance meter that was suspended ∼2 m above the bedrock channel from an aluminum bridge (Figure 3a). From this height the measurement footprint was ∼ 1 m in diameter. In 2010 we added a more accurate, small footprint (<1 cm diameter) laser-stage sensor, sampled at 10 Hz. The datum for the stage measurements was the surface of the force plate, which was cemented flush with the surface of the bedrock channel.

3.1.3. Bed-Sediment Entrainment Measurements

[16] In 2010, we installed an erosion sensor, directly adjacent to the force plate, to measure bed-sediment entrainment (Figure 3c). We designed this sensor after that described by Berger et al. [2010, 2011]to measure changes in the height of the bed sediment above the bedrock channel floor. It consisted of a stack of 5 cm tall, 4.3 cm diameter PVC elements. Within each element was a resistor. The resistors in each element were connected in parallel to form a resistance chain using small plugs that required only a small amount of tensile force to unplug. Voltage was measured at the bottom of the chain. We used low-resistance resistors (620 to 2000 Ohms) to ensure a negligible voltage change when exposed leads contacted water. We sampled the erosion sensor at 10 Hz in 2010 and 33 Hz in 2011. In 2010, the bottom-most element was partially cemented to the bed to protect the cable, thus its time of entrainment is not plotted. In 2011, we did not use cement so the bottom-most element was entrained naturally.

[17] Lab experiments showed that the shear force required to rotate an element off of the subjacent element was small (less than 1.5 N) and did not increase significantly as a greater portion of the element was buried by sediment, until more than half of the element was buried (auxiliary material, Figure S1). Once more than half of the element was buried in sediment, the shear force required to remove the element increased linearly with the amount of element buried up to a maximum of ∼9 N, when the entire element was buried. The low shear strength of the exposed elements, relative to the shear stress expected in a flow, indicated that each element would likely be rotated off the subjacent element and entrained once a small portion of the element is exposed to the flow. These experiments also showed that it is extremely unlikely that an element would stay in place once half of the sediment supporting it is removed.

3.1.4. Pore Fluid Pressure Measurements

[18] We measured pore fluid pressure pat the sediment-bedrock interface using two unvented Solinst pressure transducers. We cemented the two pressure transducers alongside the force plate (Figure 3c). The sensing ends of the two pressure transducers were separated by only a few centimeters. We sampled these pressure transducers every 2 s. In July 2011, we placed Honeywell 26PC unvented pressure transducers at 12.5, 22.5, 32.5, 42.5, 47.5 cm below the bed-sediment surface (42.5, 32.5, 22.5, 12.5,and 7.5 cm above the force plate). These burial depths aligned with the midpoint of an erosion-sensor element. We sampled these pressure transducers at 33 Hz.

3.1.5. Bed-Sediment Volumetric Water Content Measurements

[19] In 2010, we installed three sensors to measure the volumetric water content θ in the bed sediment (i.e., the fraction of the total sediment volume occupied by water), adjacent to the erosion sensor (Figure 3c). These sensors use a capacitance technique and a measurement frequency of 70 MHz to quantify the dielectric permittivity of the sediment, which in turn is related to θ through empirical calibration [Kizito et al., 2008]. We used the calibration curves provided by the manufacturer for mineral soil. Kizito et al. [2008] showed that a single mineral soil calibration curve gave accurate results across a range of mineral soils. We buried the θsensors at 2 cm, 10 cm, and 25 cm below the bed-sediment surface and sampled them every minute. In July 2011, we installed two additionalθsensors and changed the configuration of the sensors to be paired with the bed-sediment pressure transducers at the five depths described in the previous section. We sampled these sensors at 33 Hz.

3.2. Data Processing and Analysis

3.2.1. Stage Data

[20] We passed the 10 Hz laser stage data through two filters to smooth high-frequency noise associated with small splashes and waves and to highlight more persistent changes in flow depth. First, we used a 3-point moving-window-median filter centered on the current point. This filter preserved the complex structure of the time series, but removed anomalously high and low readings due to missed returns or returns from very large splashes. We then used a moving-window-mean filter centered on the current point with a window width of 1 s, which acted as a low-pass filter with a cutoff frequency (the frequency at which amplitude gain equals inline image) of ∼0.5 Hz [Smith, 1997]. We filtered the 2 s ultrasonic stage data based on echo return strength to remove low-strength inaccurate returns. These ultrasonic-stage data were only used in 2009 and for the debris-flow event that occurred on 30 June 2011.

3.2.2. Stress Data

[21] We also filtered the stress data to smooth the signal in the time domain and highlight low-frequency components. Before filtering, we converted the raw force data (100 Hz or 33 Hz) to stress by dividing the time series by the force plate area (232 cm2). We then filtered the raw stress data with a moving-window-mean filter with a window width of 1 s, centered on the current data point. This procedure acted as a low-pass filter with a cutoff frequency of ∼0.5 Hz.

[22] The mean state of stress on the force plate was non-stationary due to entrainment of the static bed sediment and to large changes in flow depth as deep surges passed the station. To determine how stress measurements were distributed relative to this non-stationary mean stress, we calculated probability density functions (pdfs) of scaled stress in which each stress measurement was normalized by the median of a 1 s centered moving window. The window width was chosen to be a fraction of the average surge duration (∼5 s).

3.2.3. Pore Fluid Pressure Data

[23] We measured pusing unvented, temperature-compensated pressure transducers. To remove atmospheric pressure from the measured gauge pressure we subtracted the pre-storm, dry-bed pressure (assumed to be purely atmospheric) from all subsequent pressure measurements. Similar results were obtained by subtracting independent and concurrent measurements of atmospheric pressure from the gauge pressure. Hence, we discontinued use of a separate atmospheric pressure sensor. To quantify the degree to which pore pressure signals generated in the near-surface bed sediment experienced frequency-dependent attenuation during propagation to deeper depths, we calculated power spectra of the signals from each bed-sediment pressure transducer. The power spectra were calculated from short segments (7 s) of the time series that directly preceded removal of an erosion-sensor element. Amplitude attenuation was reported as the ratio of signal amplitude at depth to the amplitude at the near-surface transducer.

3.2.4. Average Entrainment Rates

[24] Initiation of entrainment and average entrainment rates were determined from direct measurements of changes in bed sediment height when available. To determine average entrainment rates for events in which direct measurements were not made, we used two separate indirect methods. For both methods we assumed that entrainment began when a granular surge deeper than 0.15 m arrived. This assumption is supported by events for which initiation of entrainment was directly measured with the erosion sensor. In the first method, we used the temperature sensor onboard the basal pressure transducer to determine the timing of complete removal of bed sediment, which was indicated by an abrupt drop in temperature when the sensor contacted a cold flow. We determined the uncertainty in response time of the temperature sensor to be ±3.5 s during laboratory and field tests. In the second method, we used the timing of the first occurrence of a large-magnitude (>1.5 times the current mean stress) high-frequency stress signal to determine the timing of complete removal of bed sediment. This approach was developed after a combined analysis of the erosion sensor and stress data demonstrated that thin layers of bed sediment rapidly damped impulsive loading.

3.2.5. Video

[25] We used spatially referenced video imagery at the upper station, taken at 2 frames per second, to calculate flow-front velocityūfor each granular surge as it passed the upper station and to separate events into granular surges and inter-surge flow (auxiliary materialVideos S1, S2, S3, S4 and S5 ). Water-rich inter-surge flows lacked visible coarse particles, and were characterized by turbulence, waves, and splashes. Despite their watery appearance, inter-surge flows generally had bulk densities >1300 kg m−3. Shallow flows that transported thin sheets of granular material, approximately a grain diameter thick, were also designated as inter-surge flow. Granular surges were defined as those having a visibly high concentration of coarse-grained particles (cobbles and boulders) on the surface of the flow, and flow depths many grain diameters deep.

3.2.6. Discharge and Total Event Volume Estimate

[26] To create a continuous time series of flow velocity at the upper station, needed for discharge and volume estimates, we developed a rating curve. The rating curve relates surge-front velocityū to flow depth h as inline image(root-mean squared error equals 0.7 m s−1), in which g is the gravitational acceleration. We calculated the time series of flow depth as the difference between the stage time series and a bed sediment height time series. We calculated the bed height time series by linearly interpolating between known sediment heights at initiation and cessation of entrainment determined from the temperature perturbation method described above. We used this interpolated time series here because it was available for all events, but as demonstrated below, the interpolated sediment heights closely match the continuous measurements made during events in which the erosion sensor was present.

[27] For each debris-flow event, we estimate the total event volume passing the upper station,V (sediment plus water), using

display math

in which the summation was taken from the beginning of a flow event tb to the end te, ū(h(t)) is the mean cross-sectional velocity from the rating curve, Δt is the length of time between two stage measurements, and A(t) is the active cross-sectional area at a given time, calculated using the surveyed bedrock cross section, the corresponding bed height and flow depth.

3.2.7. Bulk Density and Factor of Safety

[28] We calculated the wet bulk density of a flow ρf(t) by assuming a one-dimensional static stress state and by using

display math

in which h(t) is the time series of measured flow depth and σf(t) is the time series of total normal stress due to the flow only, g is gravitational acceleration, and α is the bed and force plate inclination. We calculated σf(t) as the difference between the total normal stress measured at the sediment bedrock interface σ(t) and the total normal stress due to the weight of the bed sediment covering the force plate σs (σf(t) = σ(t) − σs(t)). Accurate bulk densities can only be determined from this method when the assumption of a static stress state is valid. This assumption was most closely approximated when meter-scale bedrock bedforms near the force plate were covered by a graded layer of bed sediment. Such a state was present at the beginning of each event, before entrainment of the bed sediment. The reported uncertainty forρf(t) (±350 kg m−3) is a maximum and accounts for the uncertainty in flow depth and stress.

[29] To assess the stability of the total thickness of bed sediment, we calculated a factor of safety FOSat the bedrock-sediment interface by assuming cohesionless sediment and by using the measured time series of total normal stressσ(t) and pore fluid pressure p(t) in

display math

3.2.8. Bed Sediment Characterization

[30] At the beginning of this study, we collected 3 kg samples of channel-bed sediment at the upper station to analyze the fine fraction (<5 cm) using standard sieve and hydrometer methods [Coe et al., 2008]. We used a random-walk point count to select 100 rocks from the channel-bed surface and levee deposits and measured the length of the three axes to characterize the coarse (>5 cm) fraction. To measure the internal angle of frictionϕ we excavated 30 kg of bed sediment, oven dried the sample at 105°C for 24 hours, and used a tilt table with dimensions of 60 cm by 37 cm by 6 cm deep following methods described in Iverson et al. [2010].

[31] Sieve and hydrometer results from two samples collected in 2008 show that the fine fraction of channel sediment was ∼60% gravel, ∼35% sand ∼3% silt and ∼2% clay. These results are very similar to results obtained by Coe et al. [2008]. The median grain sizes of these two samples were 10 mm and 8 mm. The median values of the A, B, and C axes of the coarse fraction present on the bed and on levee-deposit surfaces were 100 mm, 70 mm, and 40 mm, respectively. The liquid and plastic limits for both samples were nearly equal and <20%, which places them in the cohesionless soils category according to the Unified Soil Classification System plasticity chart.Coe et al. [2008]determined that field-saturated hydraulic conductivity of recently deposited channel sediment, as well as older, consolidated channel and levee deposits, ranged from 0.014 to 0.024 cm s−1. Tilt table tests showed ϕ = 44° ± 1°.

4. Results

4.1. Debris Flows Over Initially Dry Bed Sediment

4.1.1. Overview of Events

[32] The dry-bed debris-flow events on 26 July 2011, 28 June 2010, 15 September 2009 and 30 June 2011 were initiated by rainstorms with similar characteristics (shown in order of quantity of instrumentation,Figure 4). Storm characteristics and bed and flow properties for each event are summarized in Table 3. Storm durations were short (10–115 min) and peak 5-minute rain intensities were high (34–64 mm hr−1). The first measurable flow was generally a granular surge that arrived at the upper station less than 7 min after the onset of rain at that station (except the 15 September 2009 event, which arrived 32 min after the onset of rain). The combination of rapid onset of intense rain and rapid initiation of flow in the channel ensured that the pre-flow water contentθ of the bed sediment at depths greater than a few cm was low (0%–3.5%) and no positive basal pore pressure was measured before the first surge arrived (Table 3 and Figure 4). Each of these four flow events entrained all of the bed sediment at the upper station.

Figure 4.

Measurements of stage, basal pore pressure, bed-sediment height, and rainfall at the upper station for debris flows moving over initially dry bed sediment. Light-grey shaded area encompasses the time during which bed sediment was entrained. MWM is moving-window-mean filter. Hbed is the bed-sediment height. Each flow entrained all of the bed sediment present at the upper station. Upper x-axis plots rain intensity calculated over a five-minute interval. (a) Overview of sensor data 26 July 2011. Basal pore pressure sensor was clogged during this event. (b) Overview of sensor data 28 June 2010. (c) Overview of sensor data 15 September 2009. (d) Overview of sensor data 30 June 2011. Note that erosion sensor was not sampled during 15 September 2009 or 30 June 2011 events.

Table 3. Storm Characteristics, Bed Properties, and Flow Properties Measured at the Upper Station
 26 July 2011 16:28:38 (Dry Bed)28 June 2010 19:22:00 (Dry Bed)15 Sept. 2009 17:38:18 (Dry Bed)30 June 2011 13:10:00 (Dry Bed)12 June 2010 17:08:02 (Wet Bed 1)12 June 2010 17:20:07 (Wet Bed 2)
  • a

    For 15 September 2009 and 30 June 2011 events, θ was measured at shallow depth on the hillslope above the upper station.

  • b

    Maximum error was ±350 kg m−3.

  • c

    For 15 September 2009 event and 30 June 2011 event, reported flow depths are peak surge depths while entrainment was taking place.

Time entrainment began16:28:4019:22:0917:43:5513:10:0017:09:1117:20:07
Time entrainment ended16:30:3119:23:5517:49:0813:14:4017:09:12.417:20:54
Time peak flow depth16:30:1719:29:2217:46:4813:14:4017:09:3517:21:22
Total entrainment at US (m)0.550.361.10.550.20.55
Mean entrainment rate at US (m s−1)0.0050.0030.0030.0020.140.01
θ at 0.25 m depth when bed entrainment began (%)026a6a39∼40
Flow density when bed entrainment began (kg m−3)b170019002100Not available20002150
Flow depths when erosion-sensor elements were removed (m)c0.1, 0.22, 0.22, 0.28, 0.26, 0.2, 0.58, 0.21, 0.740.3, 0.35, 0.28, 0.28, 0.60.4, 0.7, 0.6, 0.7, 1.1, 0.4, 0.4, 0.50.4, 0.41, 0.37, 0.36, 0.29, 0.36, 0.29, 0.430.28, 0.40.34
Peak flow depth during event (m)0.861.21.10.510.660.88
Max front velocity (m s−1)3.94.64.33.03.43.9
Max discharge (m3 s−1)6.511142.64.26
Event volume at US (m3)30028001100900100400
inline image at US (m3 s−1)2.03.03.02.06.08.0
Cumulative rain (mm)31925112525
Rain storm duration (minutes)104511520720720
Peak 5-minute rain intensity (mm hr−1)345240641818
Time of peak rain intensity16:29:0019:23:0017:50:0013:12:3017:18:0017:18:00

[33] These four events were composed of multiple granular surges separated by fluid-rich, inter-surge flow, which is characteristic of debris-flow events at Chalk Cliffs. Flow properties were comparable for each event (Table 3), although events with more debris in the channel had more granular surges (e.g., compare video from 30 June 2011, which had 7 months of accumulated debris with that from 26 July 2011 event, which had less than a month of accumulated debris). The granular surges were steep-fronted, composed predominantly of coarse-grained material, and had little interstitial fluid visible. The granular surges carried boulders >0.5 m in diameter, had maximum flow depths of 0.5–1.2 m, densities of 1700–2100 kg m−3, and maximum flow velocities of 3.0–4.6 m s−1. Following passage of a granular surge, depth decreased and the flow transitioned into a visually distinct inter-surge flow or debris flood. The surface of the inter-surge flow was turbulent, but these flows still had bulk densities generally greater than 1300 kg m−3, indicating a solids concentration greater than 20%. Flow properties like this are commonly observed during debris floods and hyperconcentrated flows [e.g., Pierson, 1986; Hungr et al., 2001; Pierson, 2005].

4.1.2. Entrainment Rates

[34] Average entrainment rates for all four dry-bed events were between 0.2–0.5 cm s−1 (Table 3). The entrainment front moved from the bed-sediment surface downward in a progressive or continuous manner as demonstrated by the element-by-element removal of the erosion sensor (Figures 5a and 10a). During both the 26 July 2011 and 28 June 2010 events, only once were multiple elements removed within a single sampling interval. In those events, the rate of propagation of the entrainment front measured by the erosion sensor was nearly constant; the two indirect measures of entrainment rate yielded comparable rates (Figures 5a and 10a). En massefailure of the bed sediment along the sediment-bedrock interface was not observed.

Figure 5.

Four-minute time-slice of stage, bed-sediment height, basal stress, pore pressure, and soil moisture measurements made on 26 July 2011 at the upper station for a debris flow moving over initially dry bed sediment. Light-grey bar encompasses the time during which bed sediment was entrained. Thick magenta lines along upper x-axes indicate times when granular surges were present. Vertical dashed lines indicate times when erosion-sensor elements were entrained. (a) Unfiltered 10 Hz stage (light line) and stage smoothed using a 1-second-wide moving-window-mean filter, 1 s MWM (dark line). Hbedes, Hbedf, and Hbedtare the bed-sediment heights determined by the erosion sensor, force, and temperature methods, respectively. The corresponding average entrainment rates areĖes = Ėf = Ėt = 0.5 cm s−1. Colored dots indicate height of sensors used to measure signals plotted in Figures 5c and 5d. (b) Unfiltered 33 Hz total normal basal stress σ (light line) and σsmoothed using a moving-window-mean filter (dark line). Large-magnitude, high-frequency components are damped by sediment depths >5 cm. Note that large excursions in the unfiltered stress data are truncated. (c) Pore fluid pressurepmeasured at different heights in the bed sediment. (d) Volumetric water content measured at different heights in the bed sediment. Pore pressure and water content time series are truncated five seconds after the corresponding erosion-sensor element was entrained.

4.1.3. Bed Properties During Entrainment

[35] During the 26 July 2011 and 28 June 2010 events, θ at all depths in the bed sediment was initially near zero and generally did not increase until shortly before the entrainment front reached the depth of the θ sensor (Figures 5, 6, 7, 8, 10). This indicates that a wetting front generally preceded the entrainment front. During the 26 July 2011 event, erosion-sensor-element entrainment coincided with or preceded increases inθ at the lowest two sensor clusters (Figures 5 and 6). As discussed in the methods section and Figure S1, it is likely that these erosion-sensor elements were rotated off the subjacent element before the supporting sediment was eroded. Thus, even during these two cases it is likely that the wetting front slightly preceded entrainment.

Figure 6.

Compilation of 13-second time-slices of sensor data measured on 26 July 2011. Dry bed before flow arrival. Time slices, separated by gaps, surround times of erosion-sensor element removal (marked by dotted line). (a) Unfiltered 10 Hz flow depth (light line) and flow depth smoothed using a 1-second-wide moving-window-mean filter, 1 s MWM (dark line). (b) Unfiltered 33 Hz total normal basal stressσ (light line) and σsmoothed using a moving-window-mean filter (dark line). (c) Pore fluid pressurep measured at different heights in the bed sediment. Colors same as Figure 5. Note that only the sensor closest to the surface during each time slice has values appreciably above zero. Thick grey line is the pore fluid pressure required to locally liquefy the near-surface bed-sediment (p = σf + ρgzscos(α)). (d) Volumetric water content θ measured at different heights in the bed sediment. Colors same as Figure 5.

Figure 7.

Fifteen-second time-slice of sensor data measured on 26 July 2011 during entrainment of the top four erosion-sensor elements. Thick magenta lines along upper x-axes indicate times when granular surges were present. (a–d) Same as inFigure 5.

Figure 8.

Fifteen-second time-slice of sensor data measured on 26 July 2011 during entrainment of the fifth highest erosion-sensor element. Thick magenta lines along upper x-axes indicate times when granular surges were present. (a–d) Same as inFigure 5.

[36] While flow overrode the bed sediment, pore pressure signals having diverse frequencies were measured in the bed (Figure 7 and 8). Low-magnitude (0.5–1.5 kPa), long-period (∼5–10 s) pressure fluctuations, which were correlated with changes in flow depth and basal normal stress, were measured throughout the entire depth of the sediment pile, even though peak pressures were only a fraction of the hydrostatic load of the flow. These far-traveled, low-frequency pressure fluctuations propagated primarily through interstitial pore air becauseθ remained near zero in the sediment below the wetting front, and wet sediment was limited to a narrow layer below the entrainment front and above the wetting front. These pressure fluctuations propagated into the bed sediment at rates that ranged from 0.6–1.6 m s−1, which is over two orders of magnitude slower than the speed of sound in air.

[37] As the entrainment front and wetting front approached each sensor cluster, increases in θabove zero either preceded or were coincident with the first appearance of large-magnitude (pto 12 kPa), high-frequency (>10 Hz) pressure fluctuations in the near-surface sediment (Figures 5, 6, 7, 8, S2, S3, and S4). In contrast to the low-magnitude, low-frequency pressure fluctuations, these large-magnitude, high-frequency fluctuations were not correlated with changes in flow depth or basal normal stress, and were almost completely attenuated during propagation from the near-surfacep sensor to the sensor 10 cm below (Figure 7, 8, 9). In the majority of element-entrainment events, the highest erosion-sensor element was entrained shortly after near-surfacep exceeded σf + ρgzscos(α) and locally liquefied the bed sediment (Figure 6c).

Figure 9.

Attenuation of pore pressure amplitude as a function of frequency. Pressure signals were generated in the near-surface bed sediment by the overriding flow and experienced frequency-dependent attenuation during propagation to deeper depths. Data from 26 July 2011 plotted as solid lines. Theoretical predictions usingequation (9) plotted as dashed lines. D that resulted in the best fit between data and theory is reported in the legend in units of m2 s−1. Gain is the ratio of signal amplitude at a specified height (colors same as in Figure 5c) to the amplitude measured at the sensor nearest the sediment surface. (a–f) Gain measured at different heights over 7 s time intervals directly preceding erosion-sensor-element-removal events.

[38] Although we did not measure θat the upper station during the 15 September 2009 and 30 June 2011 events, we infer that the bed sediment was dry. Our inference is based on observations that these events were triggered by similarly short, intense storms, had similarly rapid flow responses to intense rains, and had no pre-flow positive basal pore pressures. In addition, pre-flowθmeasured at shallow depth on a hillslope above the upper station were similarly low (∼6%) across all dry-bed events, which strongly contrasted with measurements near saturation at this location during wet-bed events.

[39] The 2 s measurement rate of basal p(i.e., the only pressure transducer installed for events other than 26 July 2011) precluded comparison of high-frequency pressure components across events, but the resolvable low-frequency pressure fluctuations had similar characteristics across events. The magnitudes of the low-frequency pressure signals that propagated through the sediment were generally less than 1 kPa and were generally correlated with changes in flow depth (Figures 7, 8, 10c and 11c). An increase in basal p beyond ∼1 kPa was not measured until less than 5 cm of bed sediment covered the sensor.

Figure 10.

Five-minute time-slice of stage, bed-sediment height, basal stress, basal pore pressure, and soil moisture measurements made on 28 June 2010 at the upper station for a debris flow moving over initially dry bed sediment. Thick magenta lines along upper x-axes indicate times when granular surges were present. (a) Unfiltered 10 Hz stage (light line) and stage smoothed using a 1-second-wide moving-window-mean filter, 1 s MWM (dark line). Average entrainment rates areĖes = 0.5 cm s−1, Ėf = 0.4 cm s−1, and Ėt = 0.3 cm s−1. (b) Unfiltered 100 Hz total normal basal stress σ (light line) and σsmoothed using a moving-window-mean filter (dark line). Note that large excursions in the unfiltered stress data are truncated. (c) Basal pore fluid pressurep measured adjacent to the force plate at two locations separated by ∼5 cm. (d) Volumetric water content θof bed sediment at different heights. Soil-moisture time series is truncated when erosion depth equals that of the probe. The last soil moisture measurements precede the time of entrainment due to the 1-minute sampling rate on these probes.

Figure 11.

Fifteen-minute time-slice of stage, bed-sediment height, basal stress, and basal pore pressure measurements made on 15 September 2009 at the upper station for a debris flow moving over initially dry bed sediment. Thick magenta lines along upper x-axes indicate times when granular surges were present. Note erosion sensor and soil moisture probes were not installed at the upper station during this event. (a) Unfiltered 0.5 Hz sonic stage. Some returns when the stage was high (i.e, approaching the level of the sensor at 2.0 m) were discarded due to poor quality returns. Average entrainment rates areĖf = 0.4 cm s−1 and Ėt = 0.3 cm s−1. (b) Unfiltered 100 Hz total normal basal stress σ (light line) and σsmoothed using a moving-window-mean filter (dark line). (c) Basal pore fluid pressurep measured adjacent to the force plate.

[40] For all dry-bed events, theFOScalculated at the sediment-bedrock interface using the measured time series ofσ and basal p remained high (4 to 5) as bed sediment was progressively entrained. It was not until the entrainment front was less than 5 cm above the sensors that the factor of safety dropped to its lowest value near 1.5. During the 26 July 2011 event, pin only the near-surface sediment reached values sufficient to liquefy sediment, while approximately 10 cm below the surfacepremained close to zero due to attenuation of the large-magnitude, high-frequency components.

4.1.4. Flow Properties During Entrainment

[41] Sediment entrainment occurred over a range of flow properties. Flow density at the onset of sediment entrainment ranged from 1700–2100 kg m−3 (Table 3). Although sediment entrainment generally began with the arrival of a granular surge >0.2 m deep, entrainment of erosion-sensor elements did not always correspond to the presence of deep granular surges or peaks in the smoothed total normal basal stress (Figures 5b and 10b). Instead, entrainment occurred over a range of flow depths (Table 3). The separation of a debris-flow event into granular surges and water-rich, inter-surge flow, based on the video footage, revealed no preferential process responsible for sediment entrainment (Figure 5a or 10a).

4.2. Debris Flows Over Initially Saturated Bed Sediment

4.2.1. Overview of Events

[42] Unlike the short-duration, high-intensity storms that triggered flows that moved over initially dry bed sediment, a long-duration (∼12 hr), low-intensity (18 mm hr−1) storm triggered two debris-flow events on 12 June 2010, which passed over saturated beds. Although these two events occurred on the same day, they were separated by a period of small, water-rich flows that deposited saturated sediment and recharged the bed (Figure 12a). Because the bed was recharged with fresh sediment between debris-flow events, we treat each as an independent experiment.

Figure 12.

Measurements of stage, basal pore pressure, bed-sediment height, rainfall, and soil moisture at the upper station for debris flows moving over initially saturated bed sediment on 12 June 2010. Light-grey bars encompass the times during which bed sediment was entrained. (a) Complete storm duration (12 hr) measured at the upper station. Around 11:00 a shallow water flow eroded some bed sediment, but was not vigorous enough to transport the 5 cm tall erosion-sensor elements, hence the discrepancy between Hbedes and stage that lasts until ≈16:00. Discrepancy between Hbedes and stage after 16:00 is due to deposition. (b) Volumetric water content θof bed sediment at different heights. Soil-moisture time series is truncated when erosion depth equals that of the probe. At ∼11:00 the sediment reached saturation (θ≈ 40%) at all depths. (c) 2-hour time slice from Figure 12a encompassing the two debris-flow events over wet bed sediment.

[43] The first flow recorded at ∼11:00 was water-rich, had a maximum depth <0.1 m, and arrived at the upper station ∼3 hours after the onset of rain at the upper station (Figure 12a). This shallow, water-rich flow eroded the bed by 10 cm over the course of 18 min (erosion rate of 0.009 cm s−1), but was not vigorous enough to transport the 5 cm tall erosion-sensor elements (note the persistent discrepancy inFigure 12abetween stage and bed height measured by the erosion sensor when no flow was present, which indicates that the exposed elements were presumably lying on the bed surface, but remained connected to the buried elements via their electrical wires). Coincident with this shallow, water-rich flow the water content of the bed 25–48 cm above the force plate increased to near saturation (Figure 12b). Simultaneously, basal pore fluid pressure rose to a value indicative of a water table 10 cm below the bed surface (assuming slope-parallel groundwater flow) (Figure 12a). Light rain continued for the next five hours and the bed sediment remained at or near saturation.

[44] At 16:04, a small, 0.15 m deep granular surge entrained and transported erosion-sensor elements that the earlier shallow, water-rich flows exposed, but did not transport. This lowered the erosion-sensor height to 35 cm (Figure 12c). Over the next hour, shallow, water-rich flows reworked the bed so that just prior to the beginning of the first debris-flow event, the bed-sediment height was 40 cm, 5 cm above of the top of the uppermost erosion-sensor element (Figure 12c). At 17:08, the first debris-flow event began when a granular surge 0.3 m deep arrived. In the sequence of surges that followed, 25 cm of sediment were entrained, which lowered the erosion-sensor height to 15 cm (Figure 13). Following this debris-flow event, the channel was locally recharged when 40 cm of sediment was deposited. This deposition increased the bed-sediment height to 55 cm and introduced a 40 cm discrepancy between the bed-sediment height measured with the laser stage sensor and the top of the buried erosion sensor (Figure 13). We assume the sediment deposited by small granular surges and inter-surge flow was near saturation. Measurements ofpat the sediment-bedrock interface show that the water table was approximately 20 cm below the new sediment surface. At 17:20, a second debris-flow event began, during which all bed sediment was entrained (Figure 13 and auxiliary material videos).

Figure 13.

Four-minute time-slices of stage, bed-sediment height, basal stress, and basal pore pressure made on 12 June 2010 at the upper station for two different debris flows moving over initially saturated bed sediment (note break in time axis).Thick magenta lines along upper x-axes indicate times when granular surges were present. (a) Unfiltered 10 Hz stage (light line) and stage smoothed using a 1-second-wide moving-window-mean filter, 1 s MWM (dark line). Inset: Enlarged view of bed sediment height during first debris-flow event that shows progressive entrainment of two distinct 10 cm thick packages of sediment. (b) Unfiltered 100 Hz total normal basal stressσ (light line) and σsmoothed using a moving-window-mean filter (dark line). (c) Basal pore fluid pressurep measured adjacent to the force plate at two locations separated by ∼5 cm.

4.2.2. Entrainment Rates

[45] When flows overrode saturated bed sediment, the entrainment front propagated downward from the bed-sediment surface in a progressive manner (Figure 13a), but at rates of two to more than ten times greater than that observed when flows overrode dry bed sediment (Table 3). In the first debris-flow event, measured entrainment began when two erosion-sensor elements (10 cm of bed sediment) were removed within the 0.1 second sampling interval. Just 1.4 s later, two more erosion-sensor elements were entrained within the 0.1 second sampling interval (Figure 13a and inset). The average entrainment rate over this time was 14.3 cm s−1. Following deposition of 40 cm of bed sediment, the second debris-flow event began (after 17:20) and had an average entrainment rate of 1.1 cm s−1.

[46] Unlike the dry-bed events, multiple, rather than individual, elements were entrained over a single sampling interval when flows overrode saturated bed sediment. Such a shift to multiple element entrainment could indicate a change from grain-by-grain entrainment (Figure 1b) to slab-by-slab entrainment along discrete failure planes (Figure 1c). But many other interpretations are possible. For example, a cobble larger than the 5 cm height of an erosion-sensor element could have been entrained. Although the median grain size of the sieved bed-sediment samples was ∼1 cm, cobbles larger than 5 cm were present in all beds and were entrained. It is possible that when these larger cobbles were entrained they simultaneously sheared multiple elements. However, because the grain-size distributions were similar between the wet- and dry-bed events, the presence of large cobbles cannot account for the higher proportion of multiple-element removals during wet-bed events. Entrainment of cobbles could account for the rare multiple-element removals of dry sediment. Another interpretation is that wet-bed entrainment occurs grain by grain, but that entrainment rates exceed 1 m s−1for short periods of time. Alternatively, multiple-element removal could be an artifact due to mechanical or electrical issues with the sensors that cause multiple elements to be tripped, even though entrainment occurred continuously grain by grain.

4.2.3. Bed Properties During Entrainment

[47] The bed sediment remained at or near saturation during both the first and second debris-flow events. When flows overrode the saturated bed sediment, long-period pressure fluctuations were measured at the bottom of the bed sediment. These fluctuations propagated at subsonic speeds and had magnitudes that ranged from 1.0–1.5 kPa, a fraction of the hydrostatic load of the flow (Figure 13). When the first 0.3 m deep surge front arrived at 17:08, pmeasured at the sediment-bedrock interface (i.e., through 0.4 m of mostly saturated bed sediment) increased, but the 1.5 kPa (0.15 m H2O) response was only half the expected hydrostatic load. Similarly small increases of ∼1 kPa were measured through the bed sediment in response to overriding surges during the second debris-flow event (Figure 13c). Despite the fact that these pressure fluctuations propagated through interstitial pore water, they were of similar magnitude to the low-frequency pressure fluctuations measured in the dry-bed events, which propagated primarily through interstitial pore air. Once the majority of the bed sediment was entrained, the basal pore fluid pressure approximately equaled and occasionally exceeded the hydrostatic load expected from the stage time series. During the last granular surge of the 17:20 sequence, the two basal pore fluid pressure sensors registered very different values (Figure 13c). The cause of this discrepancy could not be determined, but most likely was the result of temporary clogging of a sensor.

[48] The FOSfor saturated bed sediment measured at the sediment-bedrock interface was approximately 3. When entrainment occurred at 17:09, the measured factor of safety at the sediment-bedrock interface dropped, but remained above 1. Another drop in the measured factor of safety occurred during entrainment of the bottom most erosion-sensor elements, but it remained above 1.

4.2.4. Flow Properties During Entrainment

[49] Entrainment of wet-bed sediment occurred over a narrower range flow properties compared with those observed during entrainment of dry-bed sediment. The flow density when entrainment began was ∼2000 kg m−3 (Table 3) for both wet-bed debris-flow events. Flow depths recorded at the time when each element of the erosion sensor was removed ranged from 0.28–0.4 m. Unlike the dry-bed events, entrainment of erosion-sensor elements was nearly coincident with the local peak flow depth and the local peak of the smoothed basal stress of granular surges (Figure 13).

[50] We infer that the first flows that arrived around 17:08 were composed of a series of granular surges with little intervening inter-surge flow. Although the video camera had turned off, the high densities and a lack of high-frequency variations from the mean stage measurements, common when surface waves and splashes are present, support our inference (Figure 13a). Thus, in the first debris-flow event all erosion-sensor elements were removed during granular surges. The video camera turned on during the second debris-flow event and imagery (auxiliary materialVideo S5) indicated that granular surges were present approximately 70% of the time during which bed-sediment entrainment took place.

4.3. Basal Stress Data From All Events

[51] For all dry- and wet-bed events, the unfiltered basal stress measurements had a very different character when the force plate was deeply buried under sediment compared to when it was thinly covered with sediment (Figures 5b, 10b, 11b, and 13b). When the force plate was buried under more than 5 cm of bed sediment, unfiltered measurements were similar to those filtered with the 1-second-wide moving-window-mean filter. The difference between filtered and unfiltered data (the magnitude of the fluctuating stress component) was not much larger than measurement uncertainty, indicating that there were no significant fluctuations around the mean stress at the depth of the force plate. In contrast, as the bed sediment was eroded to less than 5 cm, large-magnitude, high-frequency fluctuations of stress appeared. The magnitudes of these high-frequency fluctuations were as large as 260 kPa and commonly exceeded 50 kPa.

[52] Stress measured through bed sediment <5 cm deep had a broad distribution around the mean stress, and stress fluctuations an order-of-magnitude greater than or less than the concurrent mean were measured (Figure 14). In contrast, stress measured when the force plate was more deeply buried lacked a significant fluctuating component, which resulted in a tight distribution around the mean stress expected from the static weight of overlying material (Figure 14). The appearance of large-magnitude stress fluctuations can be attributed solely to changes in bed-sediment thickness covering the force plate, because the character of the flows was similar before and after the force plate was uncovered. Erosion-sensor data revealed that the first appearance of stress fluctuations with a magnitude more than 1.5 times the concurrent mean stress reliably indicated when the force plate was buried by less than 5 cm of sediment. Thus, as a debris flow overrode bed sediment, the state of stress in the near-surface sediment was characterized by large normal-stress fluctuations, whereas farther below the sediment surface, the fluctuating component was dissipated to such a degree that variability about the concurrent mean stress was low.

Figure 14.

Probability density functions of total normal basal stress σ.Each debris-flow event was divided into two populations, one composed of stress measurements made while the force plate was covered by bed sediment of depths >5 cm (filled circles) and another population composed of stress measurements made when the force plate was uncovered or thinly covered by bed sediment with depths <5 cm (open circles). Each stress value was scaled by the median of a 101-point centered moving window inline image. (a) Scaled pdfs from the 28 June 2010 event. (b) Scaled pdfs from the 15 September 2009 event. (c) Scaled pdfs from the 12 June 2010 events. Data from the 26 July 2011 event are not shown due to different sampling rate. Data were not available for the 30 June 2011 event.

5. Discussion

5.1. Timing, Rates, and Style of Bed Sediment Entrainment

[53] Entrainment of bed sediment during the monitored debris-flow events began with the arrival of significant flow in the channel (i.e., generally >0.2–0.3 m deep). The first substantial flow was commonly a granular surge with a density of ∼2000 kg m−3 (Table 3). Berger et al. [2011]also observed that entrainment of bed sediment occurred during dense granular surges. For debris-flows traveling ∼10 m s−1, Iverson et al. [2011]observed that entrainment began ∼1 s after the granular surge front arrived. We observed that as flow transitioned from dense granular slurries to water-rich, inter-surge flow with densities generally greater than 1300 kg m−3, entrainment of bed sediment continued and the measured entrainment rate did not change. This is in contrast to the observations made by Berger et al. [2011], who observed that entrainment stopped, in two events, as flow bulk densities began to decrease. In one event, Berger et al. [2011]observed entrainment during water-rich, inter-surge flow, but at an average rate of only 0.02 cm s−1. This rate is comparable to one episode of measured water erosion at Chalk Cliffs (0.01 cm s−1) that preceded debris-flow arrival on 12 June 2010.

[54] During events when our erosion sensor was installed, the number of elements entrained by either granular surges or inter-surge flow was directly proportional to the amount of time each flow type was present. Such proportionality was demonstrated during both the 26 July 2011 and 28 June 2010 dry-bed debris-flow events, and indicates that both granular surges or inter-surge flow were equally erosive. No distinction between entrainment by granular surges and inter-surge flow could be made during the wet bed debris-flow events because granular surges dominated those flow events (Figure 13). For the 15 September 2009 and 30 June 2011 dry-bed debris-flow events, no erosion sensor was present, but the time during which bed sediment entrainment took place was almost equally divided between granular surges and inter-surge flow (e.g.,Figure 11).

[55] The average rates of bed sediment entrainment were strongly correlated with volumetric water content θ of the bed sediment before entrainment began (Table 3). For the four debris-flow events over dry-bed sediment, the average entrainment rates ranged from 0.2–0.5 cm s−1. In contrast, average entrainment rates for the two debris-flow events over saturated bed sediment ranged from 1.1–14 cm s−1. Iverson et al. [2011] and Reid et al. [2011] observed a similarly strong correlation between θand entrainment rate. During experimental debris-flow events over wet bed sediment (θ > 22%) Iverson et al. [2011] reported entrainment rates of 5–10 cm s−1, whereas for those events over dry bed sediment (θ < 22%) average entrainment rates were <0.4 cm s−1. Berger et al. [2011] did not measure θ of the bed sediment that was eroded, but for the one event during which significant erosion occurred they measured average rates of 5 cm s−1.

[56] Bed sediment was entrained in a progressive manner from the top down. En massefailure of the bed sediment along the sediment-bedrock interface (e.g., the style pictured inFigure 1d) was not observed, irrespective of initial bed-sediment water content.Iverson et al. [2011] and Berger et al. [2011] also ruled out en masse failure of bed sediment as a means of entrainment.

5.2. Bed and Flow Properties During Entrainment

[57] The volumetric water content of sediment at the active bed surface was either increasing or already high (∼40%) when each erosion-sensor element was entrained. During the 26 July 2011 and 28 June 2010 dry-bed events, arrival of the wetting front at different depths generally preceded that of entrainment front, but only by a short amount of time (<10 s). This indicates that wetting-front propagation rates were on the order of dry-bed entrainment rates and suggests that the rate limiting process in the dry-bed events was the rate at which water could infiltrate into the bed sediment.

[58] Values of saturated hydraulic conductivity of recently deposited channel sediment were on the order of 10−2 cm s −1 [Coe et al., 2008], which is an order of magnitude slower than the observed dry-bed entrainment rates. The bed sediment for the 15 September 2009 event was composed of a hard, consolidated debris-flow deposit, while the bed sediment for the remaining events was composed of loosely packed dry-ravel deposits. The dry-ravel deposits may have had higher hydraulic conductivities than the debris-flow deposit, but that does not explain why the 15 September 2009 entrainment rate was similar to that of other dry-bed events. Dynamic increases of near-surface bed-sediment porosity during interaction with the agitated flow might explain wetting-front propagation rates much greater than the measured saturated hydraulic conductivity, which should be a maximum rate. Many studies show that permeability and hydraulic conductivity vary as exponential or power law functions of porosity. As a result, small changes in porosity, as small as 2%, can increase permeability by as much as an order of magnitude [e.g.,Freeze and Cherry, 1979; Torquato, 1991; Major et al., 1997].

[59] Rates and occurrence of bed-sediment entrainment were not well correlated with bulk-flow properties such as density, flow depth, or velocity (Table 3). For events in which pre-flowθwas low, the lack of correlation between entrainment rate and bulk-flow properties demonstrates the dominant controlθhas on entrainment rate. For the two events in which pre-flowθ was high, it is unclear why the thinner, slower flow entrained sediment ∼14 times faster than the thicker, faster flow; this needs further investigation.

5.3. Event Volumes and Volumetric Water Content

[60] In large-scale flume experiments in which debris flows of constant initial volume overrode entrainable beds of nearly constant volume,Iverson et al. [2011] observed that final flow volume increased in a linear fashion with increasing θ. As θapproached 30%, post-entrainment flow volumes were as much as a factor of three larger than the same flow over a fixed bed. We observed a strong correlation between sediment entrainment rate andθ, which should also yield a strong correlation between event volume and θ. However, faster entrainment rates do not necessarily translate to larger total event volumes V (e.g., compare V and θ measured at the upper station in Table 3) because of the effects of other variables, such as rainfall intensity, sediment supply, and flow duration. For example, McCoy et al. [2011] showed that V was related to the total time flow depth was greater than a threshold depth. To compare Vfrom long- and short-duration flow events, we normalizeVmeasured at the upper station by the amount of time flow depth exceeded 0.3 m (which was a typical flow depth during entrainment) to get an event-averaged volumetric yield per unit time inline image for the catchment upstream from the upper station (Table 3). inline image shows a positive correlation with θ in which a factor of two to four increase in inline imageis observed as pre-flowθ increased from ∼0% to ∼40%. Although high antecedent θ of channel sediment is not required for initiation of debris flows by runoff [Coe et al., 2008; Kean et al., 2011], our results suggest that, all else being equal, debris flows over wet bed sediment will increase their volume more rapidly, and have larger total volumes, than if the bed sediment is dry.

5.4. Stress Transmission Through Bed Sediment

[61] As bed sediment above the force plate eroded, increasingly larger normal-stress fluctuations were measured beneath the bed (e.g.,Figures 5 and 14). These fluctuations had a broad range of magnitudes, which at times increased or decreased the normal stress by over an order of magnitude from the concurrent mean stress (Figure 14). A sediment thickness exceeding 5 cm dissipated all but the very largest high-frequency normal-stress fluctuations. This short length scale over which fluctuations propagated into the bed sediment highlights that two distinct layers exist. An upper sediment layer, on the order of centimeters thick, senses the full dynamic range of stress present at the base of the flow and deforms to attenuate stress fluctuations through inelastic contacts and frictional dissipation, and a lower layer that is effectively shielded from high-frequency stress fluctuations and senses only low-frequency changes in stress due to changes in bulk flow properties. In the upper layer, the fluctuating normal stress may cause concomitant fluctuations in Coulomb frictional resistance, irrespective of the influence of pore fluid pressure or fluctuations in shear stress. As a result, large stress fluctuations might facilitate entrainment directly by momentarily reducing local normal stress.

[62] Unfortunately, we cannot test the hypothesis that entrainment is correlated with large fluctuations in basal stress because the force plate was covered by sediment during these times. However, there is some anecdotal evidence that there might be a correlation. Using a 0.3 m by 0.3 m force plate mounted on a vertical wall parallel to the flow direction, Berger et al. [2011]measured the wall-normal stress (assumed to scale with bed-normal stresses in the orthogonal direction) at a height of 0.3 to 0.6 m above the channel bed. Data from this vertically oriented force plate had large fluctuations about the mean state of stress, as was measured by our force plate mounted on and parallel to the bed surface once it was no longer shielded by static bed sediment.Berger et al. [2011]found that periods of bed-sediment entrainment were correlated with times when the fluctuating wall-normal stresses were near peak values.

5.5. Pore Pressure Generation in Bed Sediment

[63] High-frequency pore pressure fluctuations having magnitudes large enough to locally liquefy the bed were measured only when the near-surface bed sediment was wet when it was overridden by debris flows (e.g.,Figures 5, 6, 8, 13, and S4). Iverson et al. [2011] observed a similarly strong control of θ on the generation of pin sediment during debris-flow-passage. When bed sediment hadθ < 22%, no significant pressure response was measured, in contrast to p large enough to nearly liquefy the bed when θ > 22%. Such measurements support the hypothesis that rapid loading and deformation of wet bed sediment by overriding debris flows can cause significant increases in sediment pore pressures and aid entrainment [e.g., Hutchinson and Bhandari, 1971; Bovis and Dagg, 1992; Sassa, 1984; Hungr et al., 2005; Sassa and Wang, 2005].

[64] The strong control of θ on pore pressure development in overridden bed sediment can be better understood by looking at how differences in the compressibility and viscosity of water versus air affect various mechanisms of pore pressure generation. In a recent theoretical analysis, Iverson [2012]demonstrated that for loosely packed, water-saturated beds, the observed growth of bed-sediment pore pressure likely resulted from bed-sediment consolidation due to compressional loading and shear deformation by overriding debris flows. Starting with a constitutive equation for changes in bed-sediment porosity,Iverson [2012]derived a pore pressure diffusion equation that includes two types of pore pressure forcing, both of which are modulated by pore pressure diffusion. The first type of forcing is pore contraction due to increases in mean normal effective stress that arise from changes in flow depth or bed-sediment height. The second type of forcing is pore contraction resulting from shear-driven consolidation.

[65] Our measurements of bed-sediment pore pressures provide evidence for pore pressure generation by both types of forcing proposed byIverson [2012] and highlight that each type of forcing generates pressure fluctuations with unique frequencies due to the contrasting timescales over which they operate. Long period fluctuations in p, on the order of 10 s, generally had small peak amplitudes for both wet and dry beds (∼1 kPa), and were correlated with similar long-period fluctuations in both flow stage and basal normal stressσ associated with the arrival of deep surges (e.g., Figures 7, 8, and 13). Such a correlation suggests that long-period pore pressure fluctuations were generated by gravitational compression of bed-sediment pores in response to the increasing weight of the overriding flow, or for completely saturated beds, direct loading of the static water column. In contrast, high-frequency pore pressure fluctuations with periods <0.1 s and amplitudes exceeding 10 kPa, were measured only in wet sediment, were commonly uncorrelated with fluctuations inσ, and were much too short to be correlated to changes in flow depth. This lack of correlation suggests that high-frequency fluctuations were generated during shear deformation of bed sediment [Iverson et al., 2011; Iverson, 2012]. Because the magnitude of pore pressure fluctuations due to changes in flow depth were small relative to those due to shear deformation, we focus on the latter.

[66] To dynamically generate high fluid pressure in bed sediment at the scale of a pore, the rate of pore pressure generation via pore contraction Λg must be faster than the rate at which pore pressure will decrease Λd due to diffusion [Iverson and LaHusen, 1989]. Λg is likely controlled by pore fluid compressibility Cf and the timescale of pore contraction inline imagec, Λg = (1/Cf)/ inline imagec. In turn, the velocity of sediment grains in the sheared layer ug and the grain diameter δ will set inline imagec = δ/ug [Iverson and LaHusen, 1989]. Λd can be expressed as P/ inline imaged, in which P = ρgδcosα is a characteristic pressure scale, inline imaged = δ2/D is the diffusion timescale, and D is the hydraulic diffusivity. The ratio of Λgd is a dimensionless number Ithat describes the propensity for shear deformation to generate non-equilibrium pore pressure

display math

Iverson [2012]used a similar nondimensional number to scale a normalized shear-driven pressure-forcing term. IfI is large, the rate of pore pressure generation exceeds that of pore pressure diffusion and development of large pore pressures during shear deformation is expected.

[67] Because water and air differ markedly in their compressibility and viscosity, equation (4)suggests a strong contrast in the potential for shear deformation of water-saturated and air-saturated sediment to generate high-frequency pore pressure fluctuations.Dis a function of pore fluid material properties, in addition to granular-matrix properties, and can be written as

display math

where K is the hydraulic conductivity, Ss is the specific storage, k is the intrinsic permeability, ρpf is the pore fluid density, g is the gravitational acceleration, μ is the dynamic viscosity of the pore fluid, Cm is the matrix compressibility, which is the inverse of the bulk modulus of elasticity, n is the matrix porosity, and Cf is the compressibility of the pore fluid [Freeze and Cherry, 1979]. Using reasonable values for variables in equation (5) (listed in Table S1), it is clear that Dfor water-saturated sediment can be orders of magnitude larger or smaller thanDfor the same air-saturated sediment. For the bed sediment in this study, which was characterized as sandy gravel (Cm ∼ 10−8 Pa−1 [Freeze and Cherry, 1979]), Dfor air-saturated and water-saturated sediment can be similar.Equation (5) also emphasizes that potentially large decreases in D could be possible if k was reduced at depth due to compaction. The compressibility of air is approximately four orders of magnitude larger than the compressibility of water (Table S1). As a result, Ifor certain air-saturated sediment could be orders of magnitude smaller thanIfor the same water-saturated sediment. Such a large difference inIfor air- versus water-saturated sediment might explain why dramatic increases in near-surface pore pressures were only measured onceθin the near-surface bed sediment rose above zero, even ifDwas similar for both water-saturated and air-saturated portions of the bed (e.g.,Figures 6, 7, and 8).

5.6. Pore Pressure Transmission Through Bed Sediment

[68] Pore pressure fluctuations having magnitudes exceeding those required to liquefy the bottommost layers of bed sediment were measured in the wet near-surface sediment (Figure 6), but en massefailure did not occur because these pressure fluctuations were attenuated before they could reduce the frictional strength of deeper layers. To quantify how near-surface pore pressure fluctuations attenuated with depth, we calculated the ratio of pressure measured at depth to the pressure measured in the near-surface sediment for measurements made during the 26 July 2011 event (Figure 9). Figure 9reveals that not only were pressure fluctuations attenuated during transmission, but that this attenuation also had a characteristic frequency dependence in which low-frequency fluctuations experienced little attenuation and high-frequency fluctuations were strongly attenuated. Such attenuation of high-frequency fluctuations is characteristic of pore pressure diffusion, as are the measured subsonic wave speeds [e.g.,Biot, 1956; Iverson and LaHusen, 1989]. In the 26 July 2011 event, deeply penetrating pressure fluctuations propagated in air due to the dry-bed conditions, but similar subsonic, diffusive pressure propagation was observed during both wet-bed entrainment events.

[69] Under dynamic loading conditions pore pressure propagation is complicated [Biot, 1956], but Iverson [1993] showed that dynamic effects can be small in magnitude, and the diffusive mode of propagation dominant, for bed sediment similar to that in this study if ug is less than 10 m s−1. If dynamic effects can be ignored, and if it can be assumed that the bed has constant diffusivity, constant fluid compressibility, and bulk matrix compressibility exceeding the compressibility of fluid or solid constituents, Biot's dynamic theory can be reduced to a quasistatic pore pressure diffusion theory [Iverson, 1993]. The validity of these last three assumptions is uncertain, though the strong diffusive behavior revealed by the measurements suggests they are at least partially met within water-saturated layers and in air-saturated layers. As such, we use the simple, quasistatic-diffusion theory [Iverson, 1993] to explore the first-order effects of diffusive pressure propagation, but acknowledge it is an imperfect representation of the full physics.

[70] An important consequence of diffusive propagation of pore pressure fluctuations is the presence of a frequency-dependent length scale over which Coulomb frictional resistance can be reduced by nonequilibrium pressure fluctuations. To highlight this length scale, we simply specify that a sinusoidal pressure fluctuation at the bed-sediment surfacep′(z = 0, t) is generated via pore contraction, which allows us to drop pressure-forcing terms [Rice and Cleary, 1976; Iverson, 2012], and write the diffusion equation as

display math

where p′ is the non-equilibrium fluctuating component of pore pressure,D is the hydraulic diffusivity, t is time, and z is the depth below the surface. Equation (6) has the same form as that used to model a broad range of diffusion processes [e.g., Carslaw and Jaeger, 1959; Freeze and Cherry, 1979; Lambe and Whitman, 1979; Major, 2000].

[71] For an infinitely thick layer of porous media and p′(z = 0, t) that has been decomposed into discrete frequency components as

display math

in which Ai is the amplitude and fi is the frequency of the ith frequency component, the solution to the diffusion equation is given by [Carslaw and Jaeger, 1959]

display math

Given the shallow nature of the bed sediment filling the bedrock channel at the upper station, a more accurate solution to the diffusion equation can be found by acknowledging the finite depth to the lower boundary to obtain [Carslaw and Jaeger, 1959]

display math

Solutions to equations (8) and (9) are plotted in Figure 15. Because both equations (8) and (9)have similar behavior at the high frequencies that carried large-magnitude fluctuations, we focus here on the simplerequation (8). The exponential expression in equation (8) controls the attenuation that a particular frequency component of p′(z = 0, t) experiences as it travels through the bed sediment. The second term within the cosine expression in equation (8) dictates the phase shift of a particular frequency component. From the exponential term the thickness of bed sediment required to reduce the amplitude of a particular frequency component of p′(z = 0, t) by 1/e(i.e., the e-folding scale) can be written as

display math

Equation (10) and Figure 15 indicate that for an order of magnitude increase in D or an order of magnitude decrease in fi, the length scale required for significant damping to occur increases by over a factor of three. In other words, damping at a particular depth increases as the period of p′(z = 0, t) and diffusivity decrease. Thus, the diffusive nature by which pore pressure fluctuations propagate and the resulting frequency-dependent amplitude attenuation severely limit the depth to which large-magnitude, high-frequency pressure fluctuations can reduce Coulomb frictional resistance and aid entrainment.

Figure 15.

Depth profiles of excess pore pressure resulting from various frequencies of sinusoidal pressure fluctuations applied at the bed-sediment surface. Solutions for bothequations (8) (dashed line) and (9) (solid line) are plotted given the diffusivity estimated for the bed sediment at the upper station (D = 0.05 m2 s−1, see auxiliary material for details). As the frequency of fluctuation increases, the depth to which surface pressure fluctuations penetrate the bed sediment decreases.

6. Summary and Conclusions

[72] Using an in situ sensor network installed in the headwaters of a natural catchment, we measured flow and bed properties for six debris-flow events during which significant entrainment of channel bed sediment occurred. Regardless of the pre-flow volumetric water content of bed sediment and flow magnitude, entrainment always occurred in a progressive fashion from the bed-sediment surface downward.En massefailure of the full thickness of sediment along the sediment-bedrock interface never occurred.

[73] When a force plate measuring total normal stress at the sediment bed-rock interface was covered by more than 5 cm of bed sediment, measurements of total normal stress due to an overriding flow were narrowly distributed around the mean stress that scaled with the static flow weight. In contrast, when the force plate was free of bed sediment or only thinly covered, high-frequency fluctuations of stress were measured. These high-frequency fluctuations had magnitudes a factor of ten larger and smaller than the mean stress. The short length scale over which high-frequency stress fluctuations attenuated indicates that near-surface bed sediment experienced significant deformation, as well as concomitant fluctuations in Coulomb frictional resistance, irrespective of the influence of pore fluid pressure or fluctuations in shear stress. Thus, these normal-stress fluctuations might facilitate entrainment by momentarily reducing local normal stress.

[74] As channel bed sediment was overridden by debris flows, pore pressure fluctuations having a range of frequencies and magnitudes were generated in the near-surface bed sediment. These pressure fluctuations propagated through the bed sediment in a subsonic, diffusive manner. Regardless of whether the pore fluid was dominantly air or water, low-frequency pore pressure fluctuations having magnitudes of approximately 1 kPa were measured through the entire thickness of bed, and were tightly correlated with increases in total normal basal stress and flow depth. In contrast, if the near-surface bed sediment was wet or getting wet, high-frequency pore pressure fluctuations having magnitudes as large as 12 kPa were measured, but these high-frequency fluctuations were measured only to shallow depths below the bed-sediment surface due to rapid attenuation. Entrainment of the near-surface sediment was commonly correlated with the occurrence of these high-frequency, larger-magnitude pressure fluctuations, which brought the near-surface sediment toward a liquefied state. Frequency-dependent attenuation of pore pressure fluctuations and the diffusive mode of propagation indicates that the depth to which significant excess pore fluid pressures can propagate, and hence the depth to which high pore pressures can weaken the bed sediment and promote entrainment, scales as (D/fi)0.5, in which D is the hydraulic diffusivity and fi the frequency of fluctuation. The fact that this length scale is commonly much less than the bed thickness likely explains why en masse failure of the entire sediment thickness was not observed.

[75] Measured rates of bed sediment entrainment varied strongly with pre-flow volumetric water content, as did total event volumes when the dependence on event duration was removed. When bed sediment was near saturation before flow arrival, entrainment rates were 1.1–14 cm s−1. When pre-flow volumetric water content was near zero, entrainment rates were 0.2–0.5 cm s−1. Rates of sediment entrainment remained constant during dense granular surges as well as during less dense water-rich, inter-surge flow, despite changes in flow depth, density, and velocity. The entrainment rates of initially dry bed sediment were largely limited by the rate at which water could infiltrate into the sediment.

[76] The observations of the mechanisms by which granular stresses and pore fluid pressures propagate through bed sediment when overridden by a debris flow provide useful constraints for mechanistic models of bed-sediment entrainment. In addition, the observation that pre-flow volumetric water content of bed sediment is a strong predictor of entrainment rate indicates that debris flows moving over initially saturated bed sediment will grow more rapidly and attain larger total volumes than flows moving over dry bed sediment. Incorporating bed-sediment properties into future debris-flow hazard assessments and sediment-transport models could increase accuracy of predicted sediment delivery to downstream environments.

Notation
A

cross sectional area, m2.

Ai

amplitude of the ith frequency component of p′(z = 0), Pa.

Cm

matrix compressibility, 1/Pa.

Cf

pore fluid compressibility, 1/Pa.

D

hydraulic diffusivity, m2/s.

Ėes

average entrainment rate determined from direct measurement with the erosion sensor, m/s.

Ėf

average entrainment rate determined from the force excursion method, m/s.

Ėt

average entrainment rate determined from the temperature perturbation method, m/s.

fi

frequency of the ith frequency component of p′(z = 0), 1/s.

FOS

factor of safety of bed sediment.

g

gravitational acceleration, m/s2.

h

bed-normal flow height, m.

Hbedes

bed sediment height determined from direct measurement with the erosion sensor, m.

Hbedf

average bed sediment height determined from the force excursion method, m.

Hbedt

average bed sediment height determined from the temperature perturbation method, m.

K

hydraulic conductivity, m/s.

k

intrinsic permeability, m2.

Le

diffusive e-folding length scale forp′, m.

n

matrix porosity, %.

P

characteristic pressure scale, Pa.

p

total pore fluid pressure, Pa.

p

fluctuating component of pore fluid pressure, Pa.

I

ratio of Λgd.

Ss

specific storage, 1/m.

inline imagec

timescale for pore contraction, s.

inline imaged

timescale for pore pressure diffusion, s.

t

time, s.

tb

time at the beginning of a flow event, s.

te

time at the end of a flow event, s.

ū

surge front velocity, m/s.

ug

velocity of sediment grains in sheared layer, m/s.

V

total event volume passing the upper station, m3.

inline image

event-averaged volumetric yield per unit time, m3/s.

z

bed-normal depth beneath the sediment surface, m.

zs

bed-normal depth beneath the sediment surface at near-surface pressure sensor, m.

α

bed inclination, degrees.

Δt

length of time between two stage measurements, s.

δ

grain diameter, m.

θ

volumetric water content, %.

Λd

rate of pore pressure decrease via diffusion, Pa/s.

Λg

rate of pore pressure generation via pore contraction, Pa/s.

μ

dynamic viscosity of pore fluid, Pa s.

ρ

wet bulk density of bed sediment, kg/m3.

ρf

wet bulk density of flow, kg/m3.

ρpf

density of pore fluid, kg/m3.

σ

total normal basal stress at the bedrock interface, Pa.

σf

total normal stress due to the flow only, Pa.

σs

total normal stress due to static bed sediment, Pa.

inline image

median of σin a 101-point moving window, Pa.

ϕ

internal angel of friction of the bed sediment, degrees.

Acknowledgments

[77] This research was supported by the National Science Foundation (NSF) Graduate Fellowship, NSF grants EAR 0643240 and EAR 0952247, and the USGS Landslide Hazards Program. R. M. Iverson and the Associate Editor J. J. Major are particularly thanked for their insightful and critical reviews that significantly improved the manuscript, as are the reviewers M. Berti, O. Hungr, and V. Manville. Randy Amen provided invaluable guidance during the design and construction of the force plate and William Kean helped design the erosion sensor. We would like to thank Joe Gartner for field assistance and Jonathan McKenna for conducting the grain size analysis.

Ancillary