NHESSNatural Hazards and Earth System SciencesNHESSNat. Hazards Earth Syst. Sci.1684-9981Copernicus PublicationsGöttingen, Germany10.5194/nhess-18-3145-2018Brief Communication: Measuring rock decelerations and rotation changes during short-duration ground impactsRock accelerations and rotationsCaviezelAndrinandrin.caviezel@slf.chhttps://orcid.org/0000-0001-6249-4913GerberWernerWSL Institute for Snow and Avalanche Research SLF, 7260 Davos Dorf, SwitzerlandSwiss Federal Institute for Forest, Snow and Landscape Research WSL, 8903 Birmensdorf, SwitzerlandAndrin Caviezel (andrin.caviezel@slf.ch)23November201818113145315128March201816May201813November2018This work is licensed under the Creative Commons Attribution 4.0 International License. To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/This article is available from https://nhess.copernicus.org/articles/18/3145/2018/nhess-18-3145-2018.htmlThe full text article is available as a PDF file from https://nhess.copernicus.org/articles/18/3145/2018/nhess-18-3145-2018.pdf
Rockfall trajectories are primarily influenced by ground contacts, causing
changes in acceleration and rock rotation. The duration of contacts and its
influence on the rock kinematics are highly variable and generally unknown.
The lack of knowledge hinders the development and calibration of physics-based rockfall trajectory models needed for hazard mitigation. To address
this problem we placed three-axis gyroscopes and accelerometers in rocks of
various sizes and shapes with the goal of quantifying rock deceleration in
natural terrain. Short ground contacts range between 8 and 15 ms,
longer contacts between 50 and 70 ms, totalling to only 6 % of the runtime. Our
results underscore the highly nonlinear character of rock–ground
interactions.
Introduction
A detailed understanding of object penetration into matter is essential
from both a fundamental physics and geophysical point of view. The
relevant timescale spans from high-speed impacts of kilometers per second in planetary
science to centimeters per second or millimeters per second in laboratory experiments of intruder sinking into
granular beds. There are many studies on penetration of objects
into granular media or coefficients of restitution (see
, and references therein). However,
there is little understanding of processes arising from altered impact
conditions, such as deviations from normal impact configurations, high
rotational speeds of the impacting object, etc. Consequently, the
understanding of the mechanics of rock–ground interactions poses a
longstanding problem in rockfall engineering. This interaction defines the
speed, jump height and dispersion of falling rocks in natural terrain.
Because ground interaction controls rockfall runout distances and energy
levels, it is the core problem when developing physics-based dynamic models
for rockfall hazard mitigation and planning .
One approach to address the impact problematic is to use
dendrogeomorphic techniques to asses rockfall frequency and distribution
and/or trajectory reconstruction via impact
analysis . Hardly any data exist that
directly measure rock–ground interactions during a rockfall event. A
possible method to characterize ground impacts is to study surface scars left
by falling rocks. For example, translational rock velocities can be
determined by measuring the distance between ground contacts and the relative
slope angle between the contact points. For an initial estimation it can be
assumed that the jump height will be about 1/10 of the jump distance on the
slope. Based on such an assumption, a flight parabola is determined and the
relevant velocities can be calculated . If different jump
heights are assumed, e.g., 1/8 or 1/12, the maximum velocities shortly
before ground impact will change by less than 10 %. In many cases, this
method suffices to obtain a rough estimate of the dissipative character of
the ground interaction.
The problem with many approaches is that ground scarring is often difficult to
physically interpret, especially if the rock is in a fast rotating, rolling
motion. In this case the distances between ground contacts are extremely
short and provide little information concerning the true velocity of the
rock. Although the depth of the ground scar is an indication of the rebound
mechanics at work, scar depths are highly variable, especially if the rock is
“skipping” on the ground surface. Moreover, the analysis of rockfall traces
provides little information of the mechanics of ground interaction,
particularly if the relationship between the translational and rotational
kinematics of the rock are unknown.
Newer studies in penetration studies make use of emerging microelectronic
mechanical sensors to directly track the occurring motion
. Note that to date the major drawback
of available multi-degree-of-freedom inertial measurements units (IMUs) is the
range restriction to low accelerations (few tens of g). Because the major
application for such IMUs is unmanned aerial vehicle (UAV) flight control,
resistance to and measurement capabilities of heavy impacts is not the main
focus of chip makers.
In this paper, we present novel and detailed in situ measurements of
high-impact ground interaction contact times, decelerations and changes in
rock rotations using sensors inserted inside the rock. The resulting
three-dimensional measurements yield detailed insights into how rocks behave,
both in flight and upon contact with the ground. The measurements guide
towards how experimental field campaigns can be constructed to obtain the
necessary data needed to calibrate constitutive relationships for dynamic
rockfall models.
However, before any conclusions can be reached or any further calculations
made based on the results, the measurements must be subjected to a quality
check and verified. At present we have little idea of the degree of
acceleration reversal and change of rotational speed during impact, making it
difficult to judge the accuracy of the measurements. Simple kinematic
requirements must be fulfilled. For example, the acceleration measurements at
rest must correspond to the value of gravitational acceleration and indicate
a value of zero in free flight. The purpose of this brief communication is
therefore to elaborate on measurement frequencies and methods needed to
capture the physical information required to study rock–ground interaction in
natural terrain. We believe this information is necessary to develop better
trajectory models for rockfall hazard mitigation.
Methods of measurement and evaluationField studies
The rockfall tests were performed in natural terrain. The test site, located
near Tschamut in the canton of Grisons, is a slope 50 m high with a maximum
inclination of 42∘, running down to a horizontal surface. The surface
vegetation consists mainly of grass, with a few scattered shrubs in the
upper, steeper part of the slope. The absence of tall vegetation and
relatively smooth terrain allow a clear observational view and make the
Tschamut site ideal for conducting rockfall experiments and filming the
rocks' movements. A release point at the top of the slope was selected,
measured and used to release the rocks by simple dropping (no or little
initial translational velocity and initial spin). The release point was
selected to accommodate the transport of rocks, facilitating experimental
data sets of more than 50 releases on a single day (i.e., with the same ground
conditions including temperature and moisture content).
We present the results of one out of more than 50 trajectories captured in a
test series specifically designed to investigate the role of rock shape on
runout and dispersion; see . In this
particular measured run, an artificially manufactured concrete block with an
0.3 m edge length and a mass of 44 kg was released. The symmetric and
well-defined block shape was used as a control geometry in the rockfall
experiments. The rock's corners and edges were pared back a quarter to
make the block less dice shaped. A hole 68 mm in diameter was drilled through
the block to accommodate the sensor. The block's mass and volume (0.019 m3) make it equivalent to a sphere with a radius of 0.165 m and a
circumference of 1.04 m with a rock density of 2315 kg m-3.
Sensor
In view of developments in consumer electronics for devices including
tablets, mobile phones and UAVs, the measurement
ranges and performances of available miniaturized motion sensors are steadily
increasing. In situ data were recorded using a dedicated low-power sensor
node, dubbed StoneNode (Fig. a); see
. The main components of StoneNode v1.0, which was
used to record the data presented here, are a triaxial accelerometer with a
measurement range of 400 g and an InvenSense three-axis gyroscope recording up
to 4′000∘ s-1 (22.2π rad s-1). Analysis of frequency measurements yielded
values of 400 Hz during acceleration and 487.5 Hz for rotation. A
micro-controller manufactured by Texas Instruments hosts the sensors and was
selected for its low power consumption (roughly 3.6 mW at 3 V). Thus, a
1100 mA h LiPo battery can gather 56 h of data. Efficient data retrieval
is ensured using a plug-and-play USB device. For detailed information on the
sensors used and comparison with other systems, see and
.
(a) An exposed micro-controller board hosting all the MEMS
sensors, microSD card and a USB connector powered by a 1100 mA h battery
(both covered by the board). (b) Sensor data stream showing absolute
rotational velocities and acceleration values during the 20 s movement phase
(from 54 to 74 s), the rectangle indicating range with one saturated axis.
(c) Slope distance of the projected trajectory of the stone with its
location and slopes. (d) Absolute rotational velocities and acceleration
values, plus mean acceleration values within the intervals of impacts (white
dots) for calculating eccentricity.
Mean values of absolute rotational and acceleration data for calculating eccentricities.
Time (s)59.0–59.759.9–61.061.2–61.9Rotation (∘ s-1)369035014098Acceleration (m s-2)16.2014.0118.9Eccentricity (m)0.0040.0040.004Eccentricity (mm)3.913.753.70Quality analysis
Before the measurements can be processed, the raw data need to be verified.
Assuming that the sensors are functioning properly, the raw data should be
checked for the following criteria:
The measuring range of each individual sensor should not be exceeded.
When at rest, the rotational velocity should equal zero and the acceleration values should equal 1,
corresponding to gravitational acceleration.
During free fall, the rotational velocity should remain constant, with zero absolute acceleration; this
analysis must be performed when there is relatively little rotation, the influence of centripetal acceleration
will grow at higher rotational velocities.
Theoretically, when rotational velocity is constant, if there is an offset with the sensors and the center
of mass, the phenomenon of centripetal acceleration should result in the measurement of higher values.
During free fall, the rotational velocities and acceleration values can then
be correlated, representing the eccentrically fitted sensor as the rock's
center of gravity. In physical terms, this relationship can be expressed by
the formula Eq. ():
Re=aZω2,
where Re is the sensor's eccentricity (m), aZ the centripetal
acceleration (m s-2) and ω angular velocity (rad s-1). In theory,
rotational differences should result in the same eccentricities.
ResultsGeneral
The raw data comprise measurements starting from when the sensor was switched
on until the block's deposition some 74 s later. The effective start of the
rockfall occurred after around 54 s. During this period, 8000 acceleration
values for all three axes (x, y and z) and 9750 rotational values were
measured. During the 20 s rockfall from release to deposition, the block
covered a horizontal distance of 147 m and negotiated a height difference of
49 m. The maximum inclination on site was -42∘, dropping to zero and even
+4∘ on the upslope of the depositional area. The effective fall
trajectory's slope length was 162 m (Fig. c).
Ground contacts are very clearly indicated by sharp peaks in the acceleration
measurements and changes in rotational velocities. In steeper terrain, higher
velocities and larger jump lengths lead to significantly fewer ground
contacts than in the runout zone with roll-out behavior. Absolute rotation
increases from an initial value of zero to 4′500 degrees per second (∘ s-1)
before falling back to zero.
The maximum absolute acceleration value measured was 225 g (at second
62.0). The rest of the measured values range below 140 g, and many were even
less than 50 g (Fig. b).
(a) Duration of ground contacts. (b) Absolute
rotational and acceleration values for the ground contact at 55.24 s lasting
42 ms, (c) at 57.62 s lasting 28 ms, (d) at 58.72 s lasting 68 ms,
(e) a double contact from 63.13 s onward lasting 13 ms and 8 ms, (f) and at 70.81 s lasting 13 ms.
The error on individual measurements is smaller than the
plotted marker size.
Quality analysis procedure
The absolute rotational velocities and acceleration values were calculated
and presented in the preceding section. The peak values of the individual
measurements were checked. Due to the symmetry braking caused by the sensor
hole, a main rotational axis exists that reaches the saturation limit
between 62 and 64.6 s. This causes the resultant trace to predominantly feature
the oscillating mode of the two remaining axes highlighted with the box in
Fig. b.
The sensors are specified to high-resolution capabilities of 0.122 ∘ s-1
in the
case of the gyroscope and 0.195 g for the accelerometer. These values hold
only when maximum sensitivity settings are used. In the used case, full-scale
range is needed for both sensors; thus the measured deviations increase
significantly. As described in these main deviations can be
corrected via a linear correction function f(x)=c0+c1⋅x for
each sensor axis. If applied, c0 is the dominant correction term for the
accelerometer in the order of 0.15 to 3 g. For the gyroscope, c1 is
dominant, being of the order of 0.09 % to 0.35 % from the ideal value of 1.0.
Note that the measured offsets lie below 1 % of the full-scale
range and thus can be neglected. For the presented trajectory the actual
sensor offset at rest amounts to 4.5±0.1∘ s-1 and 1.17±0.48g as
opposed to the ideal value of 1 g.
The free-fall analysis of the measurements began immediately after the
initial motion, at 54.5 s. At this time its rotation is relatively low (180.5 ∘ s-1) and its influence on the acceleration value small. Equation () yields
aZ=Re⋅ω2=0.165⋅180.5360⋅π2=0.41ms-2.
Eccentricity was analyzed between 59.0 and 61.9 s, ignoring data from the two
intervening ground contacts (Fig. d). The mean
acceleration values within these three intervals are used to feed Eq. () and to determine the eccentricity radius, which is virtually
identical for all three time intervals, equalling 0.004 m (Table ).
Duration of ground contacts
Ground contacts are clearly recognizable from the measured rotational and
acceleration values. Very short ground contacts last 8–15 ms, medium-length
contacts 20–40 ms and lengthy contacts 50–75 ms. During the first 2–3 s
after the rock has been set in motion, the duration of ground contacts
increases very quickly to the peak values and then drops back to values of
10–30 ms, remaining at this level on flat terrain (Fig. a). This corresponds to the intuitive understanding of more
excessive scarring, that is deeper and longer ground penetration, of rocks
with higher kinetic energy for a given soil softness. Remarkably, the total
contact times that determine the trajectory kinematics amount only to 14 %
of the total trajectory time of 21 s, or if the roll-out section after the
last recorded impact is excluded, to only 6 % of the total runtime.
Details of individual ground contacts
Individual results on absolute rotational and acceleration values during
ground contacts are presented below. Here, we classified a contact as the
temporal evolution between two plateaus in angular velocity. A typical
contact during the acceleration phase is shown in Fig. b.
Rotational velocities increase with almost every – relatively short – ground
contact, as at 55.24 s. This contact lasted 42 ms at a maximum acceleration
of 45.6 g and increased rotation from 683 to 1′087∘ s-1. This typical
behavior in steep terrain implies that the rotation change is a function of
the inclination of the slope. Here, the rotation increases with slope angles
higher than 38∘ and decreases under an inclination lower than
20∘.
The ground contact featured in Fig. c (which lasted 28 ms,
starting at 57.62 s) exhibits larger accelerations of 90.0 g while the
rotation tipped from 2′921 to 2′766∘ s-1, indicating an opposed faced
obstacle within the acceleration path. Both ground contacts shown above have
clear maxima in the accelerometer data. However, some contacts with two or
even more maxima were also recorded. A relatively long ground contact
occurred at 58.72 s, lasting 68 ms (Fig. d). During this
time, two main acceleration maxima were measured: 33.4 and 30.4 g,
respectively. During this ground contact, rotation increased steadily from
2758 to 3696 ∘ s-1.
If the angular velocity between two acceleration peaks remains constant,
neither steadily rising nor falling, it indicates that two separate ground
contacts occur, similar to those occurring at 63.13 and 63.15 s shown in
Fig. e. Here, the contact times are very short (lasting 13 and 8 ms) and the acceleration maxima differ (138.6 and 34.3 g). During
these two contacts, rotation increased from 4′186 to 4′387∘ s-1, with
a constant intermediate value to 4′334∘ s-1. Interestingly, the maximum
rotation of 4′709∘ s-1 occurred during the first contact, subsequently
decreasing to the intermediate value.
Towards the end of the trajectory, the decrease in rotation occurred at much
shorter time intervals than the increase on steeper terrain. A typical
example thereof is presented here, a relatively short ground contact at 70.81 s, lasting 13 ms. During this time,
rotation decreased from 1'831 to
1′539∘ s-1, reaching a local minimum of 1′458∘ s-1 in between. The maximum
acceleration for this ground contact was 72.5 g (Fig. f).
Discussion
Because the acceleration and rotation sensors exhibit very small inherent
offsets, a correction is not mandatory – but feasible if desired. The
constant offsets being smaller than 0.1 % for the gyroscope and 0.8 % for the
accelerometer with respect to the full range capacity of each individual
sensor undermines the high-quality sensor stream. An evaluation of the
sensor's centrical installation in the block indicated a very small
eccentricity of 4 mm. This shows that a careful manual placement is
sufficient for accurate results.
In this experiment, ground contact duration was shown to vary considerably,
ranging from a minimum of 8 ms to a maximum of 75 ms. These measurements show
that longer contacts occurred on steeper terrain and shorter ones on flatter
terrain. However, no precise characterization is possible yet because the
spatial data cannot be linked to the temporal data within the needed
accuracy.
Temporal information on the block's flight duration between ground contacts
can be used to calculate the jump height of the flight parabola
. A temporal and/or spatial link could be used to calculate
the jump distance on the slope, but no such link has been established yet.
The measurements suggest very different forms of contact, both in terms of
acceleration and rotation. For very short contacts of less than 10 ms, the
individual measurements are not quite as reliable as the quality control
purports. To measure such short contacts, the measurement frequency would
have to be increased, which is achieved by updating to StoneNode v1.1,
which has an increased sampling rate of 1 kHz for the accelerometer and
gyroscope .
Conclusions
These measurements show that high-quality, detailed and reliable analyses of
rotational and acceleration data for rocks hitting the ground are possible.
The applied sensors and measurement techniques provide a logistically simple
but effective tool to obtain kinematic data for falling rocks. The measured
data provide insight into highly dynamic impact processes, but additionally
raise new questions, primarily concerning the spatial relation of the rock to
the surface of the terrain. For example, the rock's velocity vector at the
onset of a contact relative to the slope of the surface should be known to
evaluate the response of the ground material. Clearly the rock-based sensors
must be combined with high-resolution external remote-sensing methods such
as photogrammetry, lidar or radar to obtain the needed information. Most of
these techniques are well adapted and tuned to quasi-static conditions, that
is difference mapping and/or long-term monitoring. Extending these
time-of-flight measurement techniques to track a rockfall trajectory in real
time fails to date due to insufficient range, resolution and/or frame rate
capabilities . Possible solutions are a high frame-rate,
simultaneously triggered multi-camera setup and subsequent stereographic
reconstruction of the trajectory, or a highly specified time-of-flight camera
such as a scannerless lidar system capable of tracking motions as fast as
100 km h-1 in single-reflection mode over large distances. For experimental
purposes, being interested in direct flight kinematics, these approaches
might be favored over seismic signal analysis .
We have mainly gathered and processed temporal information from the rockfall
sensors. A connection to the spatial extent of the trajectory is still
missing. An approach involving the projected longitudinal profile is
available, but the exact connection to the inclination of the terrain or the
assignment of slopes to each ground contact is not yet possible. This
information would provide a better explanation of the general increases and
decreases in rock rotation.
The sensor data are ideal to calibrate constitutive relationships, which are
at the kernel of the RAMMS rockfall software module
. The combination of real-terrain
measurements coupled with non-smooth modeling approaches opens many new
possibilities to investigate how terrain influences rock motion. Because
terrain is seldom homogeneous and rock shapes far from symmetric, in situ
measurements are needed to measure the forces at play at any given time and
impact, but also for every possible rockfall trajectory. Simulated results
can now be calibrated to measured data to provide a calibration methodology
for rockfall simulation codes.
Data are available via EnviDat (https://www.envidat.ch), the environmental data portal developed at the WSL.
Under 10.16904/envidat.37 () a data archive is found containing site-specific geographical data such as DSM and
orthophotos
as well as the deposition points of manually induced rockfall by releasing differently shaped boulders with 30–80 kg of mass.
Additionally available are all the StoneNode v1.0 data streams for rocks equipped with a sensor.
The scrutinized data stream presented here is labelled “EOTA_RF05_r6”.
Both authors contributed equally to the conception of the experiment, the data analysis and the paper preparation.
The authors declare that they have no conflict of
interest. Edited by: Jean-Philippe Malet
Reviewed by: François Noël and one anonymous referee
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