This research deals with the analysis of rockfall motion and the importance of kinematic
simulations as well as in situ tests in designing of protection measures.
The study area is a talus slope located in Northern Italy (Provence of Sondrio), where
rockfalls frequently occur. The positions and dimensions of fallen blocks were measured and
used in the calibration process, performed through the back-analysis approach. The calibrated
values of restitution coefficients were compared with those obtained from in situ tests, which
were carried out on the examined slope. Looking at the resulting rock fall hazard, the bidimensional
kinematic simulations were performed in order to individuate the most suitable
location and dimensions of mitigation measures

F. Ferrari

G.P. Giani

T. Apuani

AIR Universita degli studi di Milano

1 Università degli Studi di Milano, Dipartimento di Scienze della Terra Ardito Desio, via Mangiagalli 34, 20133 
Milano (I), gianpaolo.giani@unimi.it  
2 Università degli Studi di Milano, Dipartimento di Scienze della Terra Ardito Desio, via Mangiagalli 34, 20133 
Milano (I), federica.ferrari@unimi.it  
3 Università degli Studi di Milano, Dipartimento di Scienze della Terra Ardito Desio, via Mangiagalli 34, 20133 
Milano (I), tiziana.apuani@unimi.it  
ROCKFALLS: IN SITU TEST, KINEMATIC SIMULATION AND 
MITIGATION MEASURES – SASSO FARINACCIO CASE STUDY 
Gian Paolo Giani1, Federica Ferrari2, Tiziana Apuani3 
 
This research deals with the analysis of rockfall motion and the importance of kinematic 
simulations as well as in situ tests in designing of protection measures.  
The study area is a talus slope located in Northern Italy (Provence of Sondrio), where 
rockfalls frequently occur. The positions and dimensions of fallen blocks were measured and 
used in the calibration process, performed through the back-analysis approach. The calibrated 
values of restitution coefficients were compared with those obtained from in situ tests, which 
were carried out on the examined slope. Looking at the resulting rock fall hazard, the bi-
dimensional kinematic simulations were performed in order to individuate the most suitable 
location and dimensions of mitigation measures. 
 
Keywords: rock falls, calibration process, mitigation measures, restitution coefficients. 
 
INTRODUCTION  
Rockfalls constitute a significant hazard in mountain areas or villages with abrupt topography, 
where it is not usually economically feasible to stabilise all the areas that may be sources of 
rockfalls [1]. Hence, the passive mitigation measures are widely diffuse in alpine areas 
subjected to rockfalls. The choice of the most effective location and mitigation design 
measures requires the analysis of possible block trajectories, by using kinematic mathematical 
models [2].  The fall path that a single block follows during in situ test, it was also proved 
that, for slopes with a fairly simple geometry, it is possible to obtain reasonable statistical 
distributions of rock trajectory endpoints [3], [4]. Actually, the kinematic simulations, furnish 
the expected values of kinetic energies, bounce height and travel distance of blocks prone to 
failure, computed using a statistically significant number of falling blocks. Of course, the 
simulations are a useful tool in any rock fall engineering planning, but they are reliable only if 
adequately calibrated, with the specific site location features [5]. 
This note reports an example of case study, which staring from an historical rock fall event 
define the possible future rock fall scenarios, which, using the simulations, are the basis of 
mitigation measures planning.  
 
GEOLOGICAL CONTEXT 
The area of study is a talus slope (0.13km2 extended), located on the left hydrographical side 
of the western Grosina Valley, 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. Regarding the geological-structural context, this area 
pertains to the superior Austro-Alpine domain and is characterized by a thrust system, 
overlapping the Grosina-Tonale System to the Campo-Ortles System. The former includes the 
Grosina Valley Formation, which outcrops in the study area and consists mainly of 
paragneisses and micaschists. 
	    
IN SITU OBSERVATIONS 
The last rockfall event occurred in the study area in autumn 2010. Numerous blocks detached 
from the steep cliff located on the top of talus cone. Some blocks stopped near the bottom of 
the cliff, where a terrace was built some years ago to capture falling blocks. With the time, the 
fallen debris and blocks piled, reducing the terrace effectiveness, and during the 2010 event, 
some blocks were able to overpass the terrace and reach the road and the Roasco River (one 
block). The locations of accessible fallen blocks were mapped (Figure 1), noting their 
dimensions. No fresh blocks, stopped along the talus slope, were recognizable. 
 
Figure 1 – Stopping locations of blocks fallen in autumn 2010 
A detailed geomechanical survey was carried out on the cliff, according to the suggested 
methods for the quantitative description of discontinuities in rock masses [6]. One main sub-
horizontal discontinuity set, related to the gneissic orientation of minerals, was individuated, 
together with three less persistent secondary sets. The orientations, accompanied by joint set 
spacing, give an average rock block volume of 1.5m3. This volume is comparable with the 
dimensions of blocks fallen in 2010, and is the expected volume of future. Hence, it was used 
in the kinematic simulation for the analysis of possible future scenarios. 
The comparison among the orientations of discontinuity sets, cliff, and the friction angle, 
computed according to the Barton & Choubey equation [7], show two different detachment 
mechanisms [8]: the sliding of block prevails on the Western side of the cliff, while the rock 
toppling on the Eastern side [9]. 
  
KINEMATIC SIMULATIONS AND BACK-ANALYSIS 
Kinematic simulations are useful to study the propagation of blocks along a slope, being able 
to estimate the trajectories, bounce heights and energies of falling blocks. After the 
detachment, a block can continue its motion by free falling, bouncing, rolling and sliding. The 
free falling phase is modelled by the ballistic parabola physics law, while the rebound is 
commonly described using normal and tangential restitution coefficients, expressed by the 
ratio between the velocity after and before the impact, respectively normal and tangential to 
the slope. Roll and slide phases are mainly controlled by the friction angle between the falling 
rock and slope surface. Models that analyse rock block trajectories need to incorporate all 
these kind of motion. The models can be classified in lumped mass (i.e. the rock mass is 
	    
concentrated in its centre of gravity) and rigorous models (block shape and volume are 
considered). In this study, both methods were tested, using respectively CRSP [10] and 
Rotomap [11]. Regarding the topographic base, the former considers the 2D slope profile and 
the latter the 3D grid. Whatever is the simulation approach chosen, a big influence on the 
results is given by the topography, more it is accurate, better the results are. 
Since the detailed topographic base of study area was not available, but only the DEM with 
10 metres resolution, Rotomap was initially employed to calibrate motion parameters, using a 
back-analysis approach. Initially, a set of coefficients was derived averaging out bibliographic 
values, obtained in similar geological and geomorphological contexts [2], [12], [13], [14]. At 
a later stage, these values were arranged until the best match with the stopping position of 
blocks, mapped for the 2010 rockfall event (Figure 1), was found (Figure 2).  
 
  
Figure 2 – Comparison between the 3D rock fall path obtained using the bibliographical values (a) and the back-
calibrated parametres (b). The values of the used normal and tangential restitution coefficients (respectively Kn 
and Kt), the dynamic rolling friction coefficient (µ) and the roughness (ε) are reported on the table on the right. 
 
When numerous kinds of outcropping materials are considered, infinite different 
combinations of motion coefficients lead to the same stopping positions, implying a big 
uncertainty in the calibration of models based only on the stopping points of blocks. This 
uncertainty could be reduced by comparing the results of the numerical simulation with those 
of in situ tests [9].  
  
Camera Parameter Estimated value Measured value 
 
Upper camera 
Mean velocity [m/s] 8.47 5.07 
Maximum velocity [m/s] 14.12 12.45 
 
Lower camera 
Mean velocity [m/s] 14.83 15.15 
Maximum velocity [m/s] 22.92 20.13 
Table 1 – Comparison between the estimated and measured velocity values 
 
 
Even if the interpretation of the in situ tests, give some unusually high restitution coefficients 
[14], the velocities near the camera, estimated through 1000 simulations with CRSP, fit very 
well with the measured velocities [Table 1]. On the contrary, the bounce heights are 
overestimated by simulations. The section used to perform the simulations with CRPS, was 
chosen in the centre of the talus slope, according to maximum slope angle. Since for the 
design of mitigation measures accurate results are necessary, with the aim improve them, 
 bibliography back-analysis 
Unit Kn Kt µ ε Kn Kt µ ε 
Rock 0.57 0.73 0.64 0.35 0.60 0.80 0.20 0.35 
Scree 0.41 0.65 0.62 0.30 0.40 0.63 0.65 0.60 
Wood 0.28 0.49 0.73 0.90 0.20 0.40 0.70 0.90 
River 0.30 0.65 0.60 0.40 0.20 0.40 0.60 0.70 
Road 0.40 0.90 0.55 0.05 0.40 0.90 0.20 0.45 
Grassland 0.29 0.48 0.58 0.15 0.40 0.50 0.30 0.35 
	  
	    
some GPS points were measured along the chosen topographical section, and they were used 
to construct a more detailed slope profile. 
  
MITIGATION MEASURES 
The detailed analysis of the motion along the 2D profile indicate that the best position to put a 
rockfall net is at the top of talus slope, near the edge of the terrace. Actually, if a block 
overpasses the terrace, its probability to reach the road is equal to 1, due to the steepness of 
the talus slope and the absence of trees. Moreover, the estimated velocities and energies near 
the road are bigger than those near the terrace are. Near the terrace, the estimated mean 
kinetic energy is equal to 540 kJ, while near the road the mean value is equal to 1100 kJ. It 
follows that it is necessary to stop the blocks on the terrace, being a more delimited area than 
along the road. The best solution therefore will be a high energy rockfall fence on the edge of 
terrace and a low energy barrier fence along the road. This could be useful considering that 
after an impact the fence lost the 60% of its effectiveness and should be replaced. 
 
CONCLUSIONS 
In this note an example of rockfall case study was presented. The kinematic simulations gave 
an important support in the design of mitigation measures. The parameters describing the rock 
fall motion were calibrated, through a back-analysis process, using the stopping positions of 
blocks. Although the restitution coefficient measured in field, during in situ tests, are higher 
than those estimated by back-analysis, the estimated and measured velocities are comparable. 
 
REFERENCES  
[1] ALEJANO L.R., PONS B.,  BASTANTE F.G., ALSONSO E., STOCKHAUSEN H.W. (2007) Slope 
geometry design as a means for controlling rockfalls in quarries. International Journal of Rock Mechanics and 
Mining Sciences, 44: 903-921 
[2] GIANI G.P., GIACOMINI A., MIGLIAZZA M., SEGALINI A. (2004) Experimental and theoretical studies 
to improve rockfall analysis and protection work design. Rock Mechanics and Rock Engineering, 37: 369-389 
[3] RITCHIE A.M. (1963) The evaluation of rockfall and its control. Highway Research Record, 17: 13-28 
[4] PIERSON L.A., GUILLIXSON C.F., CHASSIE R.G. (2001) Rockfall catchment area design guide. Final 
report SPR-3 (032)  
[5] FERRARI F., GIANI G.P., APUANI T. (2012) Mount Farinaccio rockfall: comparison between kinematic 
simulations and experimental field tests. Rendiconti online della Società Geologica Italiana, 19: 40-41 
[6] International Society for Rock Mechanics I.S.R.M. (1977) - Suggested methods for the quantitative 
description of discontinuities in rock masses. International Journal of Rock Mechanics and Mining Science and 
Geomechanical Abstract, 15 (6): 319-368 
[7] BARTON N., CHOUBEY V. (1977) The Shear Strength of Rock Joints in Theory and Practice Rock 
Mechanics. Rock Mechanics 10 (1/2): 1-54 
[8] MARKLAND J.T. (1972) A useful technique for estimating the stability of rock slopes when the rigid wedge 
sliding type of failure is expected. Imperial College Rock Mechanics Research Report, 19 
[9] FERRARI F., GIANI G.P., APUANI T. (2013) Towards the comprehension of rockfall motion, with the aid 
of in situ tests. Italian Journal of Engineering Geology and Environment, 6: 163-171 
[10] PFEIFFER T., BOWEN T. (1989) Computer simulation of rockfalls. Bulletin of the Association of 
Engineering Geologists, 26 (1): 135–146 
[11] SCIOLDO G. (1991) Rotomap: analisi statistica del rotolamento dei massi. Guida informatica ambientale, 
Patron, 81-84 
[12] PITEAU D.R., CLAYTON R. (1987) Computer rockfall model. Proceedings of Meeting on Rockfall 
Dynamics and Protective Works Effectiveness, 123-125 
[13] AZZONI A., ROSSI P.P., DRIGO E., GIANI G.P., ZANINETTI A. (1992)  In situ observation of rockfall 
analysis parameters. Proceedings of 6th International Symposium on Landslides, 307-314 
 [14]	  FERRARI F., GIANI G.P., APUANI T. (2013) Why can rockfall normal restitution coefficient be higher 
than one? Rendiconti online della Società Geologica Italiana, 24: 122-124 


ROCKFALLS: IN SITU TEST, KINEMATIC SIMULATION AND MITIGATION MEASURES &#8211; SASSO FARINACCIO CASE STUDY

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ROCKFALLS: IN SITU TEST, KINEMATIC SIMULATION AND MITIGATION MEASURES – SASSO FARINACCIO CASE STUDY

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ROCKFALLS: IN SITU TEST, KINEMATIC SIMULATION AND MITIGATION MEASURES &#8211; SASSO FARINACCIO CASE STUDY

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ROCKFALLS: IN SITU TEST, KINEMATIC SIMULATION AND MITIGATION MEASURES – SASSO FARINACCIO CASE STUDY