We present field evidence and a kinematic study of a rock
block mobilized in the Ponti area by a
Active faulting, rock fracturing and high rates of seismicity contribute to
a high rockfall hazard in Greece. Rockfalls damage roadways and
houses (Saroglou, 2013) and are most often triggered by rainfall and,
secondly, seismic loading. In recent years, some rockfalls have impacted
archaeological sites (Marinos and Tsiambaos, 2002; Saroglou et al., 2012).
The Ionian Islands, which include Lefkada island, experience frequent
On 17 November 2015, an
Map of Lefkada island, Greece, with the location of the study site (Ponti) and
epicenters of recent earthquakes (stars) in 2003 (
On the south side of Lefkada, near the gulf of Vasiliki, a seismically triggered rockfall in Ponti village was responsible for one of the two deaths caused by the earthquake (Fig. 1). Of particular interest is the very long travel path of the rock block, which was about 800 m in plan view from the point of detachment to the end of its path. Near the end of the rockfall path, the block impacted a family residence, penetrated two brick walls and killed a person in the house. The block exited through the back of the house and came to rest in the property's backyard.
The Ponti village rockfall site is a characteristic example of how seismically induced rockfalls impact human activities. It also provides an opportunity to evaluate 2-D and 3-D rockfall analysis to predict details of the rockfall trajectory, based on field evidence. In order to create a highly accurate model of the rockfall propagation in 2-D and 3-D space, the rock path and the impact points on the slope were identified by a field survey. The study was performed using an unmanned aerial vehicle (UAV) with an ultrahigh definition (UHD) camera, which produced a high-resolution orthophoto and a digital terrain model (DTM) of the slope. The orthophoto was used to identify the rolling section and the impact points of the rock along its trajectory, which were verified by field observation. The high-resolution DTM made it possible to conduct kinematic rebound analysis and a 3-D rockfall analysis.
Orthophoto of case study. The total length of the trajectory shown with a yellow line is 800 m.
The locations of the epicenters of the 2003 and 2015 events, as well as the
location of the rockfall case study, are shown in Fig. 1. The southwest
coast of Lefkada is part of the Triassic to Eocene age Paxos zone and
consists of limestones and dolomites that are covered by Neogene clastic
sedimentary rocks, mostly sandstones and marls. Figure 1 also shows faults
and high-rockfall-hazard areas as identified by Rondoyanni et al. (2007).
The rockfall at Ponti is not located in an identified high-rockfall-hazard
area. Based on measurements conducted at one location along the rockfall
path using the multichannel analysis of surface waves method, the in situ
shear wave velocity of the top layer was estimated to be around 800 m s
The slope overhanging Ponti village (shown in Fig. 2) has a maximum height
of 600 m and an average slope angle of 35 to 40
The rockfall release area was at an elevation of 500 m, while the impacted
house (shown in Fig. 3) was at an elevation of 130 m. The volume of the
detached limestone block was approximately 2 m
A quadrotor UAV (Phantom 3 Professional) was deployed to reach the uphill
terrain that was practically inaccessible. The UAV was equipped with an
ultrahigh definition camera mentioned earlier and had the capacity to collect
4K video. The sensor was a 1/2.3
The first objective of the UAV deployment was to find the initiation point of the rock and then identify the rockfall path (shown in Fig. 2). A particular focus on that part of the task was the identification of rolling and bouncing sections of the rockfall path. In addition, to generate a high-resolution orthophoto of the rockfall trajectory, aerial video imagery was collected, and the resulting digital surface model (DSM) and digital terrain model were used to perform rockfall analysis.
The aerial survey was conducted by capturing 4K video along a gridded
pattern covering the area of interest at a mean flight altitude of 115 m
above the terrain resulting in image frames of a mean ground sampling distance
of 4.97 cm pixel
The structure-from-motion (SfM) methodology was implemented to create a 3-D point cloud of the terrain and develop a 3-D model. The methodology is based on identifying matching features in multiple images, and thus imagery overlap of at least 70 % is required. Compared to classic photogrammetry methodologies, where the location of the observing point is well established, SfM tracks specific discernible features in multiple images and, through nonlinear least-squares minimization (Westoby et al., 2012), iteratively estimates both camera positions, as well as object coordinates in an arbitrary 3-D coordinate system. In this process, sparse bundle adjustment (Snavely et al., 2008) is implemented to transform measured image coordinates to three-dimensional points of the area of interest. The outcome of this process is a sparse 3-D point cloud in the same local 3-D coordinate system (Micheletti et al., 2015). Subsequently, through an incremental 3-D scene reconstruction, the 3-D point cloud is densified. Paired with GPS measurements of a number of control points (for this site, 10 fast-static GPS points were collected) at the top, middle and bottom of the surveyed area, the 3-D point cloud is georeferenced to a specific coordinate system, and, through the post-processing of a digital surface model, a digital terrain model and orthophotos are created. The SfM methodology was implemented in this study using the Agisoft PhotoScan software. Precalibrated camera parameters by the SfM software (PhotoScan) were introduced and then optimized during the matching process and the initialization of ground control points (GCPs).
Damage from the falling rock on the impacted house in Ponti, Lefkada, Greece.
Schematic illustrating the overlap between pictures in the study site using SfM methodology.
Top view orthophoto denoting rolling section, bouncing positions and indicative closeups of impact points.
In addition, the accuracy of the model has been examined by using portions of the ground control points and developing DTMs of differencing between different models, an investigation that is described by Manousakis et al. (2016). Finally, a comparison was made of the DTM developed by the UAV against the satellite-based DTM used for the Greek cadastre. The two surfaces were found to be very similar, as discussed subsequently.
A 5 cm pixel size orthophoto was generated based on the methodology outlined earlier. As shown in Fig. 5, the rolling section and the bouncing locations of the rock block throughout its course were identified. The rolling section was easily discerned as a continuous and largely linear mark left in the vegetated terrain. Impact points that are part of the bouncing section of the rock were identified as circular to ellipsoidal bare-Earth craters with no disturbance in between. The last bouncing point before impacting the house is clearly identified on the paved road. The plan view ortho-imagery, along with the original footage of the video collected, was crucial to the qualitative identification of these features. The alternative, i.e., land-based, conventional field reconnaissance was physically impossible to perform throughout the vegetated and steep terrain.
A profile section and a 10 cm digital surface model were then developed (Manousakis et al., 2016), allowing the identification of features such as structures, slope benches or high trees, which could affect the rock's path downhill. Subsequently, this resolution of the DSM proved to be not only unnecessarily high and thus difficult to manipulate in subsequent rockfall analyses, but also caused numerical instabilities in the rockfall analyses. Therefore, a downscaled 2 m DTM was produced for the rockfall analysis as described next. This was implemented through the use of an aggregate generalization scheme where each output cell is assigned the minimum elevation of the input cells that are encompassed by that cell. In addition, noise filtering and smoothing processing were implemented to reduce the effect of vegetation in the final rasterized model. Note that this resolution is still higher than the resolution of DTMs that are often used in rockfall analyses.
To create the DTM, algorithms for vegetation removal were executed using
the Whitebox Geospatial Analysis Tools (GAT) platform (Lindsay, 2016). The
process involves point cloud neighborhood examination and digital elevation model (DEM) smoothing
algorithms. Firstly, a bare-Earth DEM was
interpolated from the input point cloud LAS file, by specifying the grid
resolution (2 m) and the inter-point slope threshold. The algorithm
distinguished ground points from non-ground points based on the inter-point
slope threshold. Thus, the interpolation area was divided into lattice
cells, corresponding to the grid of the output DEM. All of the point cloud
points within the circle containing each grid cell were then examined as a
neighborhood. Those points within a neighborhood that have an inter-point
slope with any other point and are also situated above the corresponding
point are attributed as non-ground points. An appropriate value for the
inter-point slope threshold parameter depends on the steepness of the
terrain, but generally values of 15–35
Further processing of the interpolated bare-Earth DEM was executed to improve vegetation and structures' removal results by applying a second algorithm to point cloud DEMs, which frequently contain numerous off-terrain objects (OTOs) such as buildings, trees and other vegetation, cars, fences and other anthropogenic objects. The algorithm works by locating and removing steep-sided peaks within the DEM. All peaks within a subgrid, with a dimension of the user-specified OTO size, in pixels, were identified and removed. Each of the edge cells of the peaks were then queried to check if they had a slope that is less than the user-specified minimum OTO edge slope and a back-filling procedure was used. This ensures that natural topographic features such as hills are not recognized and confused as off-terrain features (Whitebox GAT help topics).
The final DTM model had a total RMS error after filtering for six GCPs that was
0.07 m, while the total RMS error for four checkpoints was 0.20 m. When compared to
a 5 m DEM from the Greek National Cadastre with a geometric accuracy of RMSE
The epicenter of the earthquake according to the National Observatory of Athens Institute of Geodynamics (NOA) is located onshore near the west coast of Lefkada. The causative fault is estimated to be a near-vertical strike-slip fault with dextral sense of motion (Ganas et al., 2015, 2016). Based on the focal mechanism study of the earthquake, it was determined that the earthquake was related to the right lateral Kefalonia–Lefkada Transform Fault, which runs nearly parallel to the west coasts of both Lefkada and Kefalonia island, in two segments (Papazachos et al., 1998; Rondoyanni et al., 2007).
A strong motion station recorded the ground motions in the village of Vasiliki located at a distance of 2.5 km from the Ponti rockfall site. The ground motion characteristics of the recording are summarized in Table 1 and are presented in Fig. 6 (ITSAK, 2016).
Accelerometer recordings.
Acceleration time history recording at the Vasiliki site (ITSAK, 2016).
Peak ground acceleration along the rock slope is estimated from the
PGA of the base (PGA
The initial horizontal velocity of the block, at the time of detachment, was
calculated considering equilibrium of the produced work and the kinetic
energy according to Eq. (1).
The initial horizontal velocity was calculated equal to 0.67 m s
In order to estimate the possible rock paths and design remedial measures, simulation programs based on lumped-mass analysis models are commonly used in engineering practice. The trajectory of a block is modeled as a combination of four motion types: free falling, bouncing, rolling and sliding (Descoeudres and Zimmermann, 1987). Usage of the lump-mass model has some key limitations – the block is described as rigid and dimensionless, with an idealized shape (sphere); therefore, the model neglects the block's actual shape and configuration at impact, even though both affect the resulting motion.
The most critical input parameters are the coefficients of restitution (CORs), which control the bouncing of the block. In general, the coefficient of restitution is defined as the decimal fractional value representing the ratio of velocities (or impulses or energies, depending on the definition used) before and after an impact of two colliding entities (or a body and a rigid surface). When in contact with the slope, the block's magnitude of velocity changes according to the COR value. Hence, COR is assumed to be an overall value that takes into account all the characteristics of the impact, including deformation, sliding upon contact point and transformation of rotational moments into translational moments and vice versa (Giani, 1992).
The most widely used definitions originate from the theory of inelastic
collision as described by Newtonian mechanics. For an object impacting a
rocky slope (Fig. 7), which is considered as a steadfast object, the
kinematic COR (
Coefficients of restitution.
Two different mechanisms participate in the energy dissipation process;
energy loss normal to the slope is attributed to the deformation of the
colliding entities and loss in the tangential direction is due to friction
between them. Therefore kinematic COR has been analyzed for the normal and
tangential component with respect to the slope surface, defining the normal (
Normal and tangential CORs have prevailed in natural hazard mitigation design via computer simulation due to their simplicity. Values for the coefficients of restitution are acquired from values recommended in the literature (e.g., Azzoni and de Freitas, 1995; Heidenreich, 2004; Richards et al., 2001; RocScience, 2004). These values are mainly related to the surface material type and originate from experience, experimental studies or back analysis of previous rockfall events. This erroneously implies that coefficients of restitution are material properties. However, COR values depend on several parameters that cannot be easily assessed. Moreover, values suggested in the literature vary considerably and are sometimes contradictory.
A total of 23 impact points were identified on the slope surface (Fig. 8). Their
coordinates are presented in Table 2, along the block's path starting from the
detachment point (where
Plan view and cross section along the block's path (units in m); 2-D rockfall trajectory analysis results are plotted with the green and blue line.
Out-of-plane geometry.
The apparent dip of the slope at impact positions was measured from the DTM;
on each impact point a line was set with a length twice the block's mean
dimension, oriented according to preceding trajectory direction. Moreover,
the impact point was expanded on the DTM to a rectangular plane with a side
twice the mean dimension of the block (Fig. 9). This plane was then
oriented so that one side coincides with the strike direction and its
vertical side towards the dip direction. Thus, direction difference,
Having a detailed field survey of the trajectory path, a back analysis according to the fundamental kinematic principles was performed with the intent to back-calculate the actual COR values.
The 23 impact points identified on the slope comprise a rockfall path of
22 parabolic segments. The vertical and horizontal length of each segment is
acquired by subtracting consecutive points. Since no external forces act
while the block is in midair, each segment lays on a vertical plane and is
described by the general equation of motion as
Parabolic segment.
Since no evidence can be collected regarding launch angle and velocity,
innumerable parabolas satisfy Eq. (5). However,
For the case presented in Fig. 11 (the first parabolic segment) it is shown
that for the majority of the release angles, initial velocity variation is
low and ranges between 7.2 and 12 ms
Given the minimum initial velocity and the critical release angle for each parabolic segment, the impact velocity and impact angle can be calculated. Subsequently, normal and tangential velocity components according to the apparent dip of the impact area are calculated in order to evaluate COR values. Results are summarized in Table 3.
It is observed that
For the cases where
Impact points characteristics.
Release angle versus initial velocity for the first parabolic section
(
Normal COR versus impact angle.
The wide scatter of the normal COR implies that the restitution coefficient cannot be a material constant. Yet, in most relevant software, the normal COR is defined solely by the slope material. Moreover, normal COR values higher than one were calculated in 11 out of the 15 remaining impacts. Normal CORs higher than one have been observed in both experimental (e.g., Spadari et al., 2011; Buzzi et al., 2012; Asteriou et al., 2012) and back-analysis studies (e.g., Paronuzzi, 2009) and are related to irregular block shape and slope roughness, as well as to shallow impact angle and angular motion. A more detailed presentation of the reasons why the normal COR exceeds unity can be found in Ferrari et al. (2013). However, in rockfall software used in engineering practice, normal COR values are bounded between 0 and 1.
As shown in Fig. 12, the normal COR increases as the impact angle reduces, similarly to previous observations by Giacomini et al. (2012), Asteriou et al. (2012) and Wyllie (2014). The correlation proposed by Wyllie (2014) is also plotted in Fig. 13 and seems to describe consistently, but on the nonconservative side, the trend and the values acquired by the aforementioned analysis and assumptions.
Parabolic paths characteristics for the minimum release velocity.
Soil types for 3-D rockfall analysis (according to Rockyfor3D). The yellow line showing the path of the trajectory is 800 m.
A deterministic 2-D rockfall analysis was first performed using RocFall
software (RocScience, 2004). According to Asteriou and Tsiambaos (2016) the
most important influence is posed by the impact configuration, which is
influenced by slope roughness and block shape. In this study, roughness has
been fully taken into account (considering the block's dimension scale) by
the high resolution of the cross section used in the analyses (more than
1500
Considering an initial velocity of 0.67 m s
Note that for this analysis the friction angle was set to zero. A standard
deviation for the coefficients of restitution, the friction angle and
roughness of the material on the slope was not used for this deterministic
analysis. For friction equal to 32
Additional analysis was also performed, with lower coefficients of
restitution that are representative of the talus material on the slope
(
Restitution parameters for Rockyfor3D.
In order to more closely simulate the actual trajectory, various
combinations of restitution coefficients and friction angle were considered.
The closest match occurred for
Even in this case, the modeled trajectory is significantly different from the
actual one. The main difference is that the block rolls up to 200 m
downslope while the actual rolling section is 400 m (as shown in Fig. 8).
Furthermore the impacts on the ground in the bouncing section of the
trajectory are considerably fewer in number (14 versus 23) and in different
locations compared to the actual ones. Finally, the bounce height of some
impacts seems unrealistically high. For example, the second bounce has a
jump height (
The rockfall trajectory model Rockyfor3D (Dorren, 2012) has also been used in order to validate the encountered trajectory and assess the probability that the falling rock (from the specific source area) reaches the impacted house.
The 3-D analysis was based on the down-scaled 2 m resolution digital terrain
model that was generated from the 10 cm DSM. The following raster maps
were developed for the 3-D analysis: (a) rock density of rockfall source;
(b) height, width, length and shape of block; (c) slope surface roughness; and
(d) soil type on the slope, which is directly linked with the normal coefficient
of restitution,
Reach probability graph calculated from 3-D rockfall analysis.
The slope roughness was modeled using the mean obstacle height (MOH), which
is the typical height of an obstacle that the falling block encounters on
the slope at a probability of 70, 20 and 10 % of the trajectories
(according to the suggested procedure in Rockyfor3D). No vegetation was
considered in the analysis, which favors a longer trajectory. The
parameters considered in the 3-D analysis for the different formations are
summarized in Table 4. The spatial occurrence of each soil type is shown in
Fig. 13 and the assigned values of
The energy line angles were recalculated from the simulated trajectories and
it was determined that the energy line angle with highest frequency (39 %)
was 30–31
Lateral dispersion is defined as the ratio between the distance separating the two extreme fall paths (as seen looking at the face of the slope) and the length of the slope (Azzoni and de Freitas, 1995). According to Crosta and Agliardi (2004) the factors that control lateral dispersion are (a) macro-topography factors, which are factors related to the overall slope geometry; (b) micro-topography factors controlled by the slope local roughness; and (c) dynamic factors, which are associated with the interaction between slope features and block dynamics during bouncing and rolling. Based on an experimental investigation, Azzoni and de Freitas (1995) noted that the dispersion is generally in the range of 10 to 20 %, regardless of the length of the slope, and that steeper slopes exhibit smaller dispersion. Agliardi and Crosta (2003) calculated lateral dispersion to be up to 34 %, using high-resolution numerical models on natural rough and geometrically complex slopes.
Three-dimensional trajectory analysis (from Rockyfor3D analysis). The yellow line shows the actual trajectory. Black lines show the simulated trajectory.
Lateral dispersion cannot be defined from the actual rockfall event in Ponti since only one path is available. Using the simulated trajectories from Rockyfor3D, which are in the 3-D space (Fig. 15), a lateral dispersion of approximately 60 % is shown in the middle of the distance between the detachment point and the house. This is significantly higher dispersion than the findings of Azzoni and de Freitas (1995) and Agliardi and Crosta (2003). The lateral dispersion computed by Rockyfor3D is extremely pronounced and most likely due to the topography effect of the area of detachment. Specifically, the origin of the rock block is located practically on the ridgeline, facilitating the deviation of the rockfall trajectory from the slope line.
Asteriou and Tsiambaos (2016) defined deviation (
Figure 16 illustrates the relationship of deviation with direction
difference. It is noted that, for parallel impacts (
Deviation as a function of direction difference.
UAV-enabled reconnaissance was successfully used for the identification of the origin of the detached rock, the rockfall trajectory and the impact points on the slope, and especially for discerning the rolling and bouncing sections of the trajectory. A UAV with an ultrahigh definition camera was deployed to reach the inaccessible, steep and partly vegetated uphill terrain. A high-resolution orthophoto of the rockfall trajectory, a 10 cm DSM and a 2 m DTM were generated and formed the basis for an analytical 2-D kinematic analysis and a comparison with the outcomes of 2-D and 3-D rockfall analysis software.
The findings from this study indicate that UAV-based photogrammetry can be a low-cost alternative to lidar surveying for developing DTMs. Acquisition of a UAV with a high-resolution camera is significantly less expensive than the acquisition cost of a lidar or a total laser scanner unit that generates similar (i.e., point cloud) data. In addition, deployment of UAVs is simpler and less expensive. Among the many advantages of UAV-enabled SfM is the ability to access areas that are relatively inaccessible. This advantage is particularly important in emergency response and reconnaissance following natural disasters such as landslides, floods, earthquakes and hurricanes.
However, experience is necessary to generate data of appropriate quality (spatial distribution and resolution), as data quality is significantly affected by the sensor data as well as the flight characteristics. Ground control points are critical to properly scale the point clouds and reduce distortions.
The initial velocity of the detached rock was estimated based on site conditions and amplification of the ground acceleration due to topography. It was found that the initial velocity of the blocks plays a significant role in the accurate reproduction of the rockfall trajectory.
Based on the computational analysis performed, it was found that the coefficients of restitution cannot be directly connected to the material type, nor can they be considered material constants. The impact angle seems to influence the normal COR, which has been also observed in other recent studies but has not been incorporated yet on analysis models.
It was proven impossible to replicate the actual trajectory of the rockfall by performing a 2-D rockfall analysis with the recommended set of parameters indicating limitations in the present formulations. In an attempt to match the actual rock path to the analysis output, the friction angle of the limestone slope was considered equal to zero. However, the falling rock still rolled on the slope and stopped much earlier than its actual runout distance while the impacts on the ground in the bouncing section of the trajectory were considerably different in number and in location compared to the actual ones.
Using the 3-D analysis software and recommended input parameters, rock trajectories better approximated the actual trajectory, indicating that the 3-D analysis can be more accurate than the 2-D analysis.
Based on the aforementioned analyses it becomes evident that engineering judgement and experience must accompany the usage of rockfall software in order to acquire realistic paths. The recommended set of parameters should be used with caution since field performance can differ significantly, as demonstrated by this case study.
The UAV data are available upon request from the authors.
The authors declare that they have no conflict of interest.
This article is part of the special issue “The use of remotely piloted aircraft systems (RPAS) in monitoring applications and management of natural hazards”. It is a result of the EGU General Assembly 2016, Vienna, Austria, 17–22 April 2016.
The US collaborators were partially supported by the National Science Foundation (NSF), Division of Civil and Mechanical Systems, under grant no. CMMI-1362975 and USGS National Earthquake Hazards Reduction Program (NEHRP) grants G17AP00088, as well as an internal grant from the University of Michigan (MCUBED 2.0). Any opinions, findings, conclusions, and recommendations expressed in this paper are those of the authors and do not necessarily reflect the views of the NSF, USGS, or the University of Michigan. Edited by: Daniele Giordan Reviewed by: Marco Piras and two anonymous referees