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ijege-13_bs-ferrari-et-alii.pdf
tion velocities which render any warning equipments
useless. A reliable forecast of trajectories, velocities,
bounce heights and kinetic energies of potential fall-
ing blocks is fundamental in hazard mapping and ter-
ritory management; although the prediction of mo-
tion parameters is a quite difficult task, because of
their intrinsic randomness.
been developed, but their applicability is restricted by
the lack of numerous experimental data, concerning
the parameters which govern the rockfall motion.
have been compared with those obtained from experi-
mental field tests, which have been carried out on an
Italian talus slope. Firstly, geomechanical surveys of
the release area of blocks have allowed recognizing
the rock volumes prone to failure and the modalities
of detachment. Afterwards the kinematic simulations
of the blocks to test have been performed, using two
different approaches and models.
the protection measures against rockfalls cannot
be adequately designed unless the comprehensive
understanding of rockfall phenomenon. Some ex-
perimental rockfall tests have been performed on a
talus slope in Grosina Valley (northern Italy), with
the aim to check the reliability of common simula-
tion methods and to analyse the motion of falling
blocks. First, a-priori kinematic simulations have
been performed, and, after the rockfall tests, the
results have been compared with the real stopping
positions of blocks. Afterwards, the recorded trajec-
tories of falling blocks have been analysed, allowing
the calculation of the motion parameters of falling
blocks. The motion of blocks was mainly character-
ized by rebounds, therefore particular attention has
been paid to restitution coefficients, which describe
the loss of energy during the impact and greatly af-
fect the results of rockfall simulations. Although
the talus slope features are quite constant, an unex-
pected wide range of restitution coefficients results
from the movies: the variability is greater than that
one of bibliography, moreover normal restitution
coefficients are extremely high (they often overpass
the unit). The qualitative relationships between res-
titution coefficients and slope features, falling block
characteristics and pre-impact motion conditions
have been searched and described.
slope which constitutes the transition and deposition
zone of blocks. This scree cone, having a mean slope
gradient of 35°, develops from the bottom of the cliff
and, after two road crossings, reaches the Roasco Riv-
er, at the valley floor (Fig. 1).
to the superimposition of gravitational, glacial and,
in the lower part alluvial events too; however large
blocks are more frequent at the bottom of the slope
and the cone can be classified as a fining-upward scree
slope. The talus slope, with absence of trees, except
seedlings in the lower part, forms a preferential corri-
dor for rock blocks which fall down from the cliff and
are free to reach the roads or also the Roasco River, as
happened in autumn 2010. Laterally, beyond the cone,
where the forest is present, the falling blocks fall stop
behind trees, which are mainly spruces and larches.
to 290° in the western part, and a medium dip of 55°,
which reaches also 80° in its higher part.
task in kinematic simulation modelling is the choice
of restitution coefficients (K), which quantify the loss
of energy occurring during the impact.. These param-
eters are generally derived from literature, without the
local specific outcropping material features are tak-
ing into account; indeed no standard methods exist to
estimate K from field evidences. In the study area K
values have been initially computed as the mean of
bibliographic values; afterwards they have been cali-
brated, using a back-analysis approach, and used to
perform kinematical simulations of blocks to test.
thrown down the slope by a caterpillar. The trajectory
of each block has been recorded, the analysis of mov-
ies allowed to calculate, for each impact, velocities,
K, energies, heights of bounce and impact angles. The
comparison between forecasting models and the ob-
served stopping points, as well as the measured mo-
tion parameters, is discussed in the paper.
ley, an Italian Alpine valley, situated in Lombardy
Region (province of Sondrio). Grosina Valley is a
transverse of Valtellina and is a small glacial valley,
with west-east orientation.
and is characterized by a thrust system which over-
laps the Grosina-Tonale System, to the Campo-Ortles
System. The former includes the Grosina Valley For-
mation, which outcrops in the study area and consists
mainly of paragneisses and micaschists; the latter is
mostly characterized by gneisses.
Slope Deformation, 2 km
Mount Farinaccio Slope Side.
ous blocks. The release area of blocks is a steep cliff,
about 70m high; its activity is witnessed by numerous
melting period; only the set k2 shows oxidation traces,
which can explain the greater weathering process suf-
fered from this set.
blocks, but also their predisposition to failure, which
depends on the orientations of joints and slope face.
nuity planes detected on the cliff and comparing them
with the circle of the peak friction angle along discon-
tinuities, whose value, equal to 39°, has been computed
applying the B
veys. Adding the great circle of mean dip and dip direc-
tion of the cliff, it is possible to note that the failure of
blocks can occur both for sliding and toppling of wedg-
es. Indeed the point of intersection between k2 and k4
great circles lies between the friction angle circle and
the great circle of the slope face. Furthermore the top-
pling phenomenon, can occur along k3, which has a dip
close to slope dip, but the opposite dip direction. The
analysis of each side of the scarp shows that the slid-
ing of wedges predominates in the Eastern side of cliff,
while the toppling occurs especially in its Western part.
tions (of block volumes and starting velocities, accord-
ing to the detachment modality) in rockfall simulations.
ods can be employed to forecast trajectories, bounce
geomechanical surveys have been performed in the
source area, according to the ISRM suggested methods
(I.S.R.M., 1977), with the aim to provide the quantita-
tive description of the discontinuities in rock masses,
which allows to, determinates both the features of the
instable blocks and their detachment modality.
neiss, with rare levels of quartz and amphibolite.
ondary joints have been subdivided in three main sets
(k2, k3 and k4), whose representative orientations are
reported in Table 1.
of their orientation) is comprised between 6 and 20
cm, with values usually smaller than 50 cm, only one
measure resulted slightly higher than 1 m. The mean
spacing of discontinuities, which is very important to
evaluate block volumes, ranges from 47 cm for k1
(the closest set) to 145 cm for k2 (the most spaced
set). The persistence is high for both k1 and k2, me-
dium for k4 and low for k3. Especially k2 and k4 sets,
accompanied by k1, are responsible to isolate blocks,
whose mean volumes are nearly 0.7 m
medium estimated value of 1.5 m
mum instable volume observed on the cliff has been
estimated equal to about 20 m
cm for the closest set (k1), and 7 cm for the most open
one (k2), whose values often exceed 10 cm; these
wide apertures facilitate the detachment of blocks,
as well as the smoothness of discontinuities planes,
whose Joint Roughness Coefficient (JRC) ranges from
6 to 8, indicating very smooth discontinuities.
slightly weathered, sure enough the average Joint
wall Compressive Strength (JCS), determined using
the Schmidt hammer, is about 58 MPa for k2, while it
ranges from 70 to 77 MPa for all the other sets.
proach: the falling boulder is considered dimension-
less (i.e. a point). In addition to the topography, the
input data include some parameters related both to
the detachment of blocks (location of release areas,
number and mass of blocks to simulate, starting ve-
locities and angular deviations), and to their motion:
limit angles, restitution and of dynamic rolling friction
(μ) coefficients, which are used to simulate the loss of
energy during bouncing and rolling, respectively.
profile, adopting a rigid-body approach and so taking
into account also the shape of blocks (always with
circular sections), and their dimensions. Also this
program requires the input data relative both to the
detachment points and the motion parameters (K and
μ), adding the roughness (ε).
topographical, geomechanical surveys and also pho-
togrammetrical analysis, those related to motion are
particularly difficult to infer, in fact neither direct field
procedures nor empirical correlations exist to estimate
these parameters, which can be derived performing
in situ rockfall tests. If rockfall tests cannot be per-
formed, motion coefficients can be hypothesized, aris-
ing from bibliographical values, or back-calculated,
analysing the past rockfall events occurred in the area;
this last procedure can be applied only if the stop-
ping positions of fallen blocks are exactly known,
numerous problems arise when the blocks have been
removed or buried, without mapping their locations.
is a common practice to subdivide the study area in
some homogenous regions.
and the presence, density and kind of vegetation cov-
er; at each zone motion parameters (Kn, Kt, μ and ε)
have been assigned.
liographic values, obtained in similar geological and
geomorphological contexts (P
tachment, a block can continue its motion by free
falling, bouncing, rolling and sliding. The free fall is
modelled by the ballistic parabola physics law, know-
ing the initial velocities; after this phase, the block
impacts to the soil, at the point described by the inter-
section between the trajectory of block and the slope
surface. Then the block firstly rebounds and farther it
can start to roll. The rebounds can be described us-
ing the normal and tangential restitution coefficients
(Kn and Kt), expressed by the ratio between the ve-
locity after and before the impact, respectively normal
and tangential to the slope. Kn and Kt quantify the
loss of energy which occurs during impacts, and their
values depend basically on the outcropping material
and the presence of obstacles. On the apex and on the
upper part of the talus slope, as a whole, the motion
can be simulated using rebound models, which can be
separated in two types: lumped-mass and rigid body
approaches; the former models the block as a single
material point, the latter accounts for the block shape.
In this study, both methods have been tested.
more it is accurate, better the results will be. Two dif-
ferent approximations of the slope topography exist:
the 2D slope profile and the 3D grid, which typically
is a rasterized Digital Elevation Model (DEM).
(CRSP, P
3D grid, while the latter utilises the rigid body model,
with a 2D section. Unluckily, as it often happens, the
detailed topographic base of Mount Farinaccio has
not available, but only the DEM with 10m resolu-
tion, consequently, Rotomap has been initially em-
ployed, being a 3D model well-adaptable for studies
at regional scale with also a smoothened topography
(F
slope, has been chosen and used to model in 2D the
rockfall, with CRSP; this section should be the most
critical of the whole talus slope. In addition, also the
most dangerous section derived from Rotomap re-
sults, has been individuated and compared with the a
priori chosen section.
ping points of blocks. This uncertainty could be re-
duced considering the silent witnesses, i.e. the signs
produced by the passage of blocks (tree and surfaces
hits), which allow to reconstruct the travel path of
the block and its features. This process cannot be ap-
plied in the study area, being these signs neither well
identifiable nor attributable to a specific block. So in
order to evaluate the uncertainty related to the cali-
bration process, the results of simulations have been
compared with those of the in situ tests, performed
in May 2011. These tests have been carried out with
the aim to remove some instable blocks stopped
on the terrace at the bottom of the cliff during the
last rockfall event, therefore the sizes and shapes of
blocks to test were exactly known, as well as their
precise starting location. Using these initial motion
condition and the back-calculated motion coeffi-
cients, a new set of kinematic simulations has been
performed, before the test execution.
in the study area in autumn 2010. Indeed in the simu-
lations all blocks have reached the Roasco River and
some of them have been able to go up the slope beyond
the river (Fig. 3a), while during the 2010 event some
blocks stopped on the road and on a terrace situated at
the bottom of the cliff, which had been deliberately cre-
ated to hold the falling blocks. It follows that the bib-
liographical values, although carefully selected from
similar contexts, should always be calibrated (F
der to shorten the travel distances of blocks, Kn and Kt
have been reduced, while ε has been raised (Tab. 2).
The back-calculated parameters obviously fit well with
the stopping points of the 2010 event (Fig. 3b).
ling, it cannot be done in areas where the previous
events are mainly unknown and their features not
identifiable. If only the stopping points of blocks
are known, but not the precise location of the re-
lease areas (such as in the case of study), caution-
ary results have been obtained using the bottom of
the cliff as the source point. An ulterior problem in
the calibration is related to the fact that, if several
homogeneous units are involved, infinite different
combinations of motion coefficients will lead to the
same stopping positions, implying a big uncertainty
Considering geomechanical survey results, priority has
been given to rocks with a nearly parallelepiped shape
and volume approximately equal to almost 0.8 m
the road during the 2010 event. Each block has been
measured along its three dominant axes, making pos-
sible the calculations of volumes and masses. The block
volumes are in good accordance with the volumes com-
puted from geomechanical survey data, although the
spacing of the set k1 is slightly underestimated.
been painted using different colours with the aim to
allow their recognition during and after the tests.
of each block has been recorded using both lateral
fixed cameras and a frontal mobile one. The lateral
cameras have recorded the block movements in the
upper part of the talus slope, and the frontal camera
the entire path.
ther continued to roll or mainly took one two bounces
and went into flight. If the stone was larger than the
materials over which it moved, its angular momentum
increased until two basic factors began to diminish
its velocity: a flatter portion of the slope, and larger
materials of substratum (r
lide against common pieces, losing energy. With this
deceleration process, the stone was soon trapped in
voids between stones of its own size, resulting in a
segregation of materials, observed on the talus slope.
pared with simulation results.
hazard classes H4, H3 and H2, related respectively to
falling blocks. In the 3D model all blocks, which have
not been subject to fragmentation along their paths,
have stopped in the area individuated as hazard class
H4, whilst the fragments of blocks, have been able to
reach farther location than those forecasted by simula-
tions, although they have been carried out with 1000
blocks, knowing the precise starting position and di-
mension (or mass in lumped-mass method) of blocks.
steepest profile has been taken into account; moreo-
ver in CRSP all the blocks have a circular section,
while in reality they have prismatic sections, and so
a smaller motion efficiency.However the results of the
back-analysis process revealed to be very useful and
reliable to forecast the trajectories of blocks, but more
efforts should regard the problem of block fragmenta-
tion and especially the angular deviation of fragments.
process, takes into account only the stopping positions
of blocks, without considering their kinematic, which
can be evaluated using both field experiments and lab-
oratory tests, although the latter are difficult to extend
to field processes due to the difficulties encountered
when defining similitude rules (B
paths, the lateral videos have been studied frame by
frame, extracting 30 frames per seconds. The frames
have been referenced in the space, using the gradu-
ated rope fixed along the slope, through the distance
among known points. In each frame the barycentre of
falling block has been individuated, as a point, and
the set of points represents the trajectory of the block
(Fig.4). The points have been initially referred to the
global xy Cartesian coordinate system, where x is the
horizontal axis and y is the vertical axis; afterwards a
second (local) nt system has been determined, with di-
rection n normal and t tangential to the slope surface.
Knowing both the coordinates of barycentres and the
interval of time Δt between two following frames, the
displacements of barycentre S and the translational ve-
locity V vectors (in terms of direction and magnitude)
have been calculated along the path of block.
(B
one, if the overall K (Ko) is computed, as the ratio
between the post- and pre-impact total translational
velocities (without considering the factorization in
normal and tangential velocities), it results always
below one, which is coherent with the energy dissi-
pation occurring during the impacts. Kn values high-
er than the unit can therefore occur, provided that Ko
is smaller than the unit.
block and the slope during the impact, and to the ro-
tational motion established at the impact point. Actu-
ally applying the law of the conservation of energy, it
is possible to see that the impact causes the increasing
of the rotational energy (between the 3 and 16% of
the total energy) at the expense of the translational
total energy, which has components related to the
velocities tangential and normal to the slope. While
the contribution of the former, after the impact, al-
ways decreases (between the 8 and 35%), the latter
increases (between the 4 and 19%).
lengthened block, if impacts with its major axis about
perpendicular to the slope, rotates and its barycentre
becomes higher than those of a block which impacts
puted applying the following formulas (et alii, 2002):
predominant kind of motion, Kn and Kt have been
computed, as the ratio between translational veloci-
ties (normal and tangential to the slope respectively)
after and before the impact.
ture. Nevertheless Kt values are in quite good ac-
cordance with common bibliographic values for bare
talus slopes, which generally range from 0.55 to 0.80,
whilst the computed Kn values are extremely high,
with a mean value bigger than one, although the unit
is often seen as an upper boundary for K in numerical
codes. Actually, K equal to one corresponds to a per-
fect elastic collision, K below one defines an inelastic
collision, and K nought means that the block instan-
taneously stops at the surface without bouncing, with
a perfectly plastic behaviour (G
gains translational velocity during the impact, which
is unlikely. Nevertheless experimental evidences show
that Kn values above the unit sometimes occur, be-
ing measured both in field tests (a
model, with rigid-body approach, has proved to be
more cautionary than the 3D lumped-mass model.
by test movies, using image analysis techniques.
The resulting tangential restitution coefficients agree
with literature, whilst the normal ones are uncharac-
teristically high (often above the unit). So high nor-
mal restitution coefficient are mainly related to the
geometry of the block at the impact point, but also to
the outcropping material grain size, slope angle and
to parameters linked with the kinematics of block be-
fore and during the impact.
in an area with the quite constant features (a bare talus
slope). These coefficients change within the same ho-
mogenous unit, going downward the slope. Therefore
the common practice in rockfall modelling which
considers motion parameters constant inside each ho-
mogenous area has proven to be too much simplistic.
Inside each homogenous zone it should be better to
consider not a constant value but a range of variation
of these coefficients. Additionally the subdivision in
homogenous areas should be more detailed, consider-
ing also small grain size and slope angle variations,
which have proven to affect the restitution coefficients.
and to find the quantitative relationships to estimate the
restitution coefficients from field evidence.
sibility to perform the tests, Erika De Finis and Andrea
Merri for the help during field surveys, but also Ales-
sio Conforto and the Professor Marco Masetti.
ally the barycentre of a lengthened block is subjected
to a bigger displacement in the direction normal to the
slope than that of an equilateral one. If a lengthened
block impacts with its corner, the arm of the angular
velocity along the direction normal to the slope can be
strongly greater than the arm of the angular velocity
along the direction translational to the slope and con-
sequently Kn can overpass the unit, even though the
loss of kinetic energy produced by the impact is saved
(F
slope angle, and consequently small incidence angle (in
this study Kn above the unit has been measured with
incidence angle smaller than 15°). Actually steeper the
slope is, smaller the impact angle will be, hence Kn
increases with the decrease of impact angle or equally
with the increase of slope angle. Moreover smaller the
normal translational impact velocity is, higher Kn will
be (in this study Kn above the unit has been measured
with normal impact velocity below 10 m/s).
son between kinematic simulations and test results.
culate unitary rock volumes prone to failure, and to
individuate the possible detachment mechanisms. The
motion parameters firstly have been calculated aver-
aging out the literature values, and then they calibrated
through a back-analysis process, this step has revealed
to be of fundamental importance. The so derived mo-
tion parameters have been used to simulate the falling
of the blocks selected for the tests. The comparison
between a-priori simulation results and real stopping
points of tested blocks are close only if the block is
All.2/9 Milano, Italy.
The issue 16 volume 01 has been published