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Numerical analysis of the behavior of a karst cave at Castellana-Grotte, Italy

The present paper discusses the behavior of a natural
cave within a stratified rock mass, which is
subjected to slow and progressive loosening of the
roof and then to sudden detachments of either single
rock slabs or entire roof portions. The cave studied,
generated by karst processes in a horizontally
bedded carbonate rock mass of Cretaceous age, is
located at Castellana-Grotte, in the Apulian karst of
Southern Italy. This research is focused on the
behavior of one of the caverns (namely, the so-
called “Civetta”), which can be considered as
representative of the behavior of most of the caverns
in the cave system. The observed behavior of the
carbonate rock mass within the cave shows gradual
propagation of fractures through the horizontal rock
strata at the roof, until portions of the ceiling,
ranging in thickness from a few centimeters to more
than one meter, suddenly fall. This rock mass
behavior at the top of large excavations or natural
caves has been documented in the literature as the
result of the transition for the lower strata at the roof
from continuous elastic beam behavior to Voussoir
beam behavior; the stability of the roof formed of
vertically jointed beams is then controlled by the
eventual formation of a sufficiently thick arch
compression (Evans 1941, Diederichs & Kaiser
1999a, b, Hatzor et al. 2002). Most of these previous
works have focused on large man-made excavations
within stratified rock masses, which behavior is in
part different from that of the natural caves here
analyzed. However, the long-term behavior can be
considered similar for both cases.
The aim of this research is to investigate the
mechanism that leads to the long-term progressive
collapse of portions of the cave roof. A numerical
analysis has been therefore carried out by means of
3.10 distinct element code (ICG 1999). The
process of formation of cracks normal to the bedding
planes due to tensile strength degradation of
weathered limestone with time has been studied; in
addition, the reason for asymmetric collapse of the
cave roof, as observed in situ, has been also dealt
with. Then, the response of a numerical model,
which includes new vertical joints as an effect of
tensile failure, has been evaluated.
The Castellana-Grotte cave system was formed by
karst processes in a stratified limestone of Upper
Cretaceous age (Calcare di Altamura formation)
(Parise & Reina 2002). Its current configuration
derives from the combination of the effects of
different stages in the karst process evolution, and of
the related instability mechanisms, which caused
both the widening and the upward enlargement of
many rooms. Thus, nowadays the cave consists of
wide rooms, with height ranging from about 10 to 60
m, connected by narrow and high corridors (Figure
Numerical analysis of the behavior of a karst cavern at Castellana-Grotte,
P. Lollino & M. Parise
National Research Council, IRPI, Bari, Italy
A. Reina
Technical University, Bari, Italy
ABSTRACT: The present paper concerns the numerical study of the behavior of natural karst caves at
Castellana-Grotte (Apulia, Southern Italy) by means of the Discrete Element Method. The caves have been
formed by karst processes in a stratified calcareous rock mass and consist of wide caverns, which are
connected by narrow and high corridors. The observed behavior of the carbonate rock mass in the caves
shows gradual failures of slices from the ceiling due to propagation of tensile joints, followed by sudden fall
of slabs with thicknesses ranging from few centimeters to more than one meter. The factors controlling the
loosening of the cave roof with time and the consequent failure mechanism have been investigated. In
addition, both the influence of structural features on the roof stability and the reason for asymmetric collapse
of the roof have been assessed.
Figure 1. Longitudinal cross-section of the Castellana-Grotte karst system.
The huge cavern (“Grave”) at the entrance of the
cave system is open at the top due to the collapse of
the roof, which is the extreme consequence of the
upward propagation of the instability mechanisms.
A detailed geo-structural survey has been carried
out within the Civetta cavern. This room is strongly
controlled by two main structural features at its
lateral boundaries, as generally observed for
carbonate rocks by Fookes & Hawkins (1988). It is
in fact elongated according to the main direction of
development of the cave (that is NW-SE). The
typical shape of the current configuration of the
cavern is shown in the two cross-sections in Figure
2. Thickness of the sub-horizontal bedding planes,
dipping less than 10 degrees toward the east and the
south-east, is not regular and locally the rock mass
has a massive aspect: mean thickness of the bedding
planes ranges between 15 and 65 cm at the top of the
cave, but the strata may be as thick as 150 cm along
the lower areas of the sidewalls. Three sets of
vertical or sub-vertical persistent joints have been
identified at the Civetta cavern. The main set (set 1),
which seems to control the configuration of the
room, is oriented N140W. A second, less defined,
set (set 2) is about perpendicular to the first one,
while the third (set 3) has a mean direction of
N90W. Their mean frequency is quite moderate
(mean spacing approximately equal to 80 cm for set
1 and 120 cm for set 2). The strike of the joint sets
as mapped in the areas of the two cross-sections in
Figure 2 are shown in the same figure. Additional
non-persistent vertical joints with higher frequency
(spacing ranging from 50 to 80 cm) have been
recognized at the cavern roof; they can be
considered as the result of initial fracturing and
stress relaxation, as discussed in the following.
White & White (1969) explain that processes of
cavern breakdown are responsible for both the initial
enlargement of a cave and its following upward
extension. Evidences of such processes exist at the
Civetta cavern in terms of both small-scale features,
as block, slab and chip breakdowns, and large-scale
features, as terminal breakdowns and major ceiling
collapses. In particular, terminal breakdowns consist
of collapses of rock ledges along the upper part of
the two sidewalls due to breakage of the rock
bridges sustaining them. On the other hand, major
ceiling collapses derive from the gradual
propagation of tensile cracks, which are
perpendicular to the roof, and from the eventual
instability of greater thickness of stratified vertically
jointed slabs with wide span. The latter process
usually results in recurring bell shapes of the cross-
sections of the cavern (Fig. 2). The evolving
configuration of the Civetta cavern and, in general,
of many caverns in the karst system at Castellana is
presumed to be the consequence of the cyclic
occurrence of these two instability processes
(tension ceiling collapse and rock ledge detachment
from the sidewalls). The different stages of this
process within the Castellana karst system have
resulted in different heights of the rooms (Fig. 1).
Figure 2. Cross-sections of the Civetta cavern.
The instability process within stratified hard rock
masses has been widely discussed by Diederichs &
Kaiser (1999a, b), according to the traditional
Voussoir beam theory (Evans 1941), suitably
revisited by them. In particular, they suggest that
timing for roof collapse is often controlled by
residual tensile strength available along the existing
rock bridges (Diederichs & Kaiser 1999b).
According to the Authors, the tensile strength
degradation due to humidity and chemically assisted
stress corrosion can be responsible for failure of
spans that have remained safe for very long term.
Therefore, the transition from systems of stratified
continuous beams to systems of stratified voussoir
beams due to time-dependent tensile strength
degradation as an effect of weathering processes,
and the following collapse of the stratified blocky
roof, is thought to be the process occurring at the
Civetta cavern and, in general, at the Castellana-
Grotte cave system.
Water infiltration from the ground surface, which
may produce significant weathering effects, is
evident within the Civetta cavern, as well as in the
whole karst system at Castellana-Grotte. An intense
activity of limestone solution, and the successive
deposition of calcite in the cavern, can be
recognized at the Civetta cavern. In addition, all
along the cavern boundaries it is possible to identify
karst conduits and voids at various heights produced
by the enlargement of original fissures and/or
bedding planes.
The Calcare di Altamura is generally classified as
hard rock and is characterized by both a cristalline
texture and an isotropic structure at the laboratory
specimen scale. At the mass scale, it can be
classified as anisotropic rock due to moderately
spaced bedding planes.
Laboratory tests on intact rock samples have been
carried out to derive both index properties and
strength properties of the limestone. The unit weight
is found to be between 2.65 and 2.72 g/cm
Unconfined compression tests have been performed
to determine both the unconfined compressive
strength, σ
, and the elastic parameters of the rock.
The mean value of the compressive strength resulted
to be about
= 149 MPa. The value of the modulus
of elasticity, E, deduced as the slope of the
unloading-reloading curve, ranges between 24000
and 48000 MPa, whereas the mean value of the
Poisson ratio is 0.3. Flexural tests on cylindrical
beam samples indicated a mean value of the flexural
strength of about 14.5 MPa and the tensile strength,
, has been derived accordingly (
= 4.8 MPa). The
mean values of the data as resulted from the
laboratory tests are summarized in Table 1. As no
data from triaxial compression test were available,
the shear strength of the intact rock has been
assumed according to the literature data (Goodman
Table 1. Rock and joint properties at Castellana-Grotte.
Intact rock properties:
γ σ
E’ ν S
φ σ
MPa MPa MPa ° MPa
2.7 149 37000 0.3 15 38 4.8
Joint properties:
MPa ° °
8-10 54 46 31
In situ tests have been carried out on exposed
joint surfaces along the sidewalls of the Civetta
cavern to determine the roughness and the
compressive strength of the joint walls. Over forty
joint profiles have been tested by means of a
profilometer in the Civetta cavern and the mean JRC
value is estimated at 8-10, according to ISRM
standards (ISRM 1978). The mean value of the joint
wall compressive strength, JCS, as deduced by
means of Schmidt hammer tests, performed
according to ISRM suggestions, is about 74 MPa for
unweathered surfaces and reduces to about 34 MPa
for joints subjected to significant weathering
processes. The residual friction angle of the joints,
, has been deduced by means of tilt tests
performed on natural joint planes as found in the
field, and the corresponding mean value ranges
between 28° and 34° (Table 1). In order to assess the
peak friction angle,
, the empirical criterion of
Barton has been used, and the resulting value ranges
between 43° and 49°.
A two-dimensional plane-strain DEM analysis has
been carried out by means of
3.10 code (ICG
1999) to investigate the collapse mechanism and the
factors controlling the evolution in the Civetta
code, which adopts an explicit
solution scheme, is in fact suitable for problems
involving caves in jointed rock masses since it
allows for both stress analysis of deformable blocks
and simulation of large displacements along the
discontinuities. The initial configuration of the
geometry modeled is shown in Figure 3.
It is
characterized by an 11 m span horizontal roof,
which underlies continuous rock beams delimited by
persistent bedding planes. This configuration
can be
considered as representative of an intermediate
stationary stage of the evolution process of the
cavern, before that vertical joint openings and
breakdowns take place within the roof. A finer
schematization of the domain, with lower spacing of
the bedding planes than the rest of the domain, has
been modeled just above the roof to reproduce
structural features closer to reality. Three monitoring
points have been chosen along the cave roof to
assess the trend of block displacements with
timesteps (Fig. 3). A linear elastic perfectly plastic
constitutive model with a Mohr-Coulomb failure
criterion fitting the peak strength envelope assumed
and a tension cut-off reproducing the tensile strength
as measured in the laboratory tests has been adopted
for the intact rock. A Mohr-Coulomb failure
criterion with tensile strength equal to zero has been
also assumed for the joint behavior. Both the
stiffness and the strength parameters adopted for the
numerical analysis are reported in Table 1.
Figure 3. Initial configuration of the model (stages 1 - 3).
For problems involving caves within stratified rock
masses, Hatzor et al. (2002) indicate that two
different independent mechanisms should be
1 failure through intact rock elements, and
2 displacement of rigid blocks from the cave
They also highlight that in such cases the stability
analyses are usually based on either a completely
continuous approach, which allows for a precise
stress analysis, or a completely discontinuous
approach, which can define block kinematics
(Hatzor & Benary 1998). In the present analysis the
Distinct Element Method is used to integrate both
the two approaches and then to study both the
mechanisms, which are considered to be one the
effect of the other at Castellana-Grotte. Therefore, a
stress analysis of the original domain has been
performed to detect the areas subjected to tensile
failure and to propagation of vertical joints, as a
consequence of progressive degradation of tensile
strength of the limestone due to chemical and
humidity weathering processes. Later, the stability
analysis of a new model, with vertical joints in the
same position where tensile failures have occurred
in the previous stress analysis, has been investigated
by monitoring the displacements of the roof
elements according to a fully discontinuous
In brief, the whole numerical analysis has been
divided into four stages:
1 gravitational elastic equilibrium;
2 assignment of the real and unweathered material
properties (see Table 1);
3 gradual reduction of the tensile strength within
the elements above the cave roof;
4 analysis of the stability of a new model with
vertical joints at the roof.
Figure 4. Tensile failures after stage 2.
Numerical results and discussion
The model, which assumes real and unweathered
material properties under gravitational load (stage
2), results in a stable condition. Few tensile failures
appear just above the roof and within a distance of
about 2 m from it (Fig. 4). The model does not show
block displacements changing with timesteps.
Figure 5. Tensile failures after stage 3.
In the third stage of the analysis, a gradual reduction
of the tensile strength has been applied to the
elements above the roof and consequently tensile
failures start to propagate in the middle area of them.
The model assuming a tensile strength of
= 20 kPa
results in a large development of tensile failures
throughout the strata overlying the roof for a 5 m
thick area according to a “dome” pattern: short
joints develop along the whole span, whereas longer
persistent joints form in the middle area (Fig. 5).
This is consistent with the assumed transition from
continuous elastic beam behavior to vertically
jointed beam behavior, as already described in
section 2. Consequently, the stability conditions of
the new model in Figure 6 have been evaluated. In
this model the mean spacing between the vertical
joints has been assumed very low (about 40 cm) to
account for the worst conditions for stability.
The pattern of the calculated displacement
vectors, which extend for 3-4 m above the roof,
shows a clear deflection of the lower beams at the
midspan (Fig. 7). The “dome-shaped” stress-
loosened area, which is indicated by the opening of
the horizontal joints subjected to zero normal stress,
is also clearly shown in Figure 7. The plot of the
vertical displacements of the three monitoring points
with timesteps indicate that the model does not reach
a static configuration since the displacements do not
tend to a constant value (Fig. 8). This result implies
that, for the assumed structural conditions, a
sufficiently thick arch compression is not formed in
the jointed beams above the roof, and the cavern
ceiling will consequently tend to the collapse.
Figure 6. Configuration of the model in stage 4.
Figure 7. Displacement vectors and open joints after stage 4.
Figure 8. Vertical displacements versus timesteps for three
monitoring points during stage 4.
The influence of the ratio between spacing of the
horizontal bedding planes and the cave span at the
Civetta cavern has been also analyzed. Different
configurations assuming the same vertical joint
spacing (s
= 80 cm) and spacing of the horizontal
bedding planes equal to s
= 20, 30, 40 and 60 cm
have been modeled. The resulting midspan
deflections of the different models are reported
against numerical time in Figure 9. The figure shows
that, for the assumed joint friction angle value,
spacing greater than 20 cm ensures stable conditions
to the cave roof, whereas the model with s
= 20 cm
produces a deflection continuously increasing with
time, as for the case with s
= 40 cm. This implies
that with s
= 20 cm the vertically jointed beams are
too slender to form the arch compression, in
accordance with the guidelines by Diederichs &
Kaiser (1999a).
Y-disp (cm)
sh=60 cm
sh=40 cm
sh=30 cm
sh=20 cm
Figure 9. Midspan deflections versus timesteps for models with
different spacing of bedding planes.
Finally, the reason for a stronger tendency for
development of instability mechanisms at the
southwestern side, as observed at the Civetta cavern
(Fig. 2), has been explored. This phenomenon is
thought to be the effect of either a stronger
weathering process on that side due to the many
karstic conduits, or the presence of significant
structural features, as vertical joints and faults,
which enhance the loosening process at a greater
extent. In the first case, starting from the initial
configuration in Figure 3, a gradual reduction of the
tensile strength has been applied only at the left area
of the roof. The analysis shows tensile failures,
which propagate only at the left portion of the roof,
and the vertical displacements are mainly
concentrated at the same side (Fig. 10). The second
hypothesis which has been investigated is the
influence of persistent vertical joints along the left
sidewall of the cavern, with the whole roof area in
this case as subjected to uniform tensile strength
degradation. The numerical results show an
asymmetric pattern of the new tensile failures with
more persistent vertical joints developing on the left
area of the roof (Fig. 11).
Figure 10. Tensile failures and displacements vectors for a
model with asymmetric tensile strength degradation for rock.
Figure 11. Tensile failures for a model with asymmetric
structural features.
The numerical analysis discussed in this paper
suggests that the potentialities for such kind of
problems offered by the current implementation of
DEM method in
need to be increased to
simulate the opening of new fractures through intact
rock. From this point of view, an interesting
contribution can derive from the rock fracture
mechanics theory. Some suggestions for this
problem were given in the last years by some author
(Kulatilake et al. 1992), but the problem still needs
to be exhaustively investigated.
A preliminary numerical analysis aimed at
understanding the reasons for progressive collapse,
which affects the roof of the Civetta cavern at
Castellana-Grotte karst system has been carried out
by means of
3.10 discrete element code.
The numerical results have shown that the main
factor controlling the formation and the propagation
of vertical joints within the rock strata overlying the
cave roof is the gradual degradation of the tensile
strength of the limestone with time due to chemical
and humidity weathering processes of the rock mass.
This process is then responsible for the long-term
transition from continuous elastic beam behavior to
vertically jointed beam behavior, whose stability is
controlled by the beam geometry. Thus, it has been
found that 20 cm spaced bedding planes for an 11 m
wide span do not ensure stable conditions of the
roof, independently from the spacing of vertical
joints. Asymmetric loosening of the cave roof, as
observed in situ, has been demonstrated to be
produced by two possible factors: a stronger
reduction of tensile strength at one side of the roof
due to deeper weathering processes or the presence
of significant structural features along one sidewall
of the cavern.
An in situ monitoring campaign with instruments
logging the displacements of critical blocks and the
deformation of joints is considered necessary to
validate the interpretation of the failure mechanism
here proposed, as well as a further development of
the numerical analysis is required to investigate the
influence of joint friction angle on the roof stability.
This work has been funded by a research contract
with Grotte di Castellana s.r.l.
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... The karst system has a prevailingly sub-horizontal pattern, with wide caverns ranging in height from a few to some tens of meters, and intervening, structurally controlled corridors. The karst system at Castellana opens in the Upper Cretaceous Altamura Limestone formation, showing moderately spaced bedding planes [94]. The carbonate rock mass is fractured, with local arching and deformations in the strata, and thick weathered zones at the contact with clastic sediments or where the carbonates are wetted by trickling or condense water, and As in other sectors of the Apulian karst, and in many other karst areas worldwide [14,[80][81][82][83][84][85][86][87][88], the development, elongation, and spatial distribution of karst landforms in the Castellana area, both at the surface and underground, is strongly controlled by the main tectonic lineations [75,89]. ...
... The karst system has a prevailingly sub-horizontal pattern, with wide caverns ranging in height from a few to some tens of meters, and intervening, structurally controlled corridors. The karst system at Castellana opens in the Upper Cretaceous Altamura Limestone formation, showing moderately spaced bedding planes [94]. The carbonate rock mass is fractured, with local arching and deformations in the strata, and thick weathered zones at the contact with clastic sediments or where the carbonates are wetted by trickling or condense water, and weathered material is protected against mechanical erosion [95]. ...
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... The site of the Castellana Caves, located in the municipality of Castellana-Grotte (Apulia, southern Italy), has already been object of studies dedicated to structural analyses and evaluation of the characters of the local rock mass, with particular relation to instability [13,14]. In the occasion of the present work, the Grave has been analysed through a survey carried out by means of the laser scanner RIEGL VZ400 (figure 1). ...
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Knowledge of the geometrical and structural setting of rock masses is crucial to evaluate the stability and to design the most suitable stabilization works. In this work we use the Terrestrial Laser Scanning (TLS) at the site of the Grave of the Castellana Caves, a famous show cave in southern Italy. The Grave is the natural access to the cave system, produced by collapse of the vault, due to upward progression of instabilities in the carbonate rock masses. It is about 55-m high, bell-shaped, with maximum width of 120 m. Aim of the work is the characterization of carbonate rock masses from the structural and geo-mechanical standpoints through the use of innovative survey techniques. TLS survey provides a product consisting of millions of geo-referenced points, to be managed in space, to become a suitable database for the morphological and geological-structural analysis. Studying by means of TLS a rock face, partly inaccessible or located in very complex environments, allows to investigate slopes in their overall areal extent, thus offering advantages both as regards safety of the workers and time needed for the survey. In addition to TLS, the traditional approach was also followed by performing scanlines surveys along the rims of the Grave, following the ISRM recommendations for characterization of discontinuity in rock masses. A quantitative comparison among the data obtained by TLS technique and those deriving from the classical geo-mechanical survey is eventually presented, to discuss potentiality of drawbacks of the different techniques used for surveying the rock masses.
... This becomes even more complicated in the case of heterogeneous, and/or karstified, rock masses (Andriani and Parise 2015). However, these methods are generally not adequate to account for all the main factors governing the problem and therefore their use should be limited only to specific cases for which the schematization is acceptable, since they cannot account for variable geometries or heterogeneous deposits , as well as they cannot provide any information regarding the stress state, the strain level or the potential failure mechanism of the involved rock mass (Tharp 1995;Kaiser 1999a, 1999b;Liu et al. 2000;Hutchinson et al. 2002;Lollino et al. 2004;Suchorewska et al. 2012). In recent years, numerical modeling has A C C E P T E D M A N U S C R I P T 3 provided a powerful tool to explore the stress-strain state within the rock mass around the cave and the corresponding displacement field induced by a specific loading condition or a change in the boundary conditions, also adopting non-linear constitutive models for the rock material. ...
The assessment of stability of man-made underground caves, excavated in the past and later on abandoned, represents a serious challenge for land and urban planning operations, especially for the areas of possible interaction of the caves with overlying structures and infrastructures. Several areas of Southern Italy are characterized by the presence of abandoned underground quarries for the extraction of soft calcarenite rocks, which now threatens the overlying environment due to the risk of collapse and the consequent generation of sinkholes. This work presents a back-analysis of a sinkhole occurred in 2011 in the town of Marsala, caused by the collapse of an underground quarry, as a representative case study of these phenomena. Based on the available geometrical and geological dataset as well as the field observations of the phenomenon, in this article the assumptions and the results about the genesis of the 2011 sinkhole, as derived from a three-dimensional finite element back-analysis aimed at reconstructing the stress-strain evolution that brought to the ground failure collapse, is discussed. In particular, the 3-D numerical analyses have been performed in order to identify the factors responsible of the genetic mechanism of the sinkhole. The finite element analysis has been carried out by accounting for the geotechnical characterization of the Marsala calcarenites derived from both specific laboratory tests performed on samples taken from the site and literature data available on the same rock material; the numerical results have been then validated by means of the comparison with field observations and also compared with those achieved through a 2-D model of the same case study.
... To evaluate the sectors within cave systems mostly prone to further failures, the weathering processes in the rock mass must also be carefully examined (Fookes and Hawkins 1988;Hajna 2003;Lollino et al. 2004): these often cause strong reductions in the mechanical properties of the rocks, thus contributing to its overall decrease in strength, and facilitating its proneness to failures. ...
... They are typically preceded by formation of joints through the roof, which propagation leads to a complete or local failure mechanism. This process has been observed in artificial and natural caves; in these latter, it is characterised by falls in the central part of the roof, later followed Georisk 277 by failure of the remaining ledges along the sidewalls (Lollino, Parise, and Reina 2004;Parise and Trisciuzzi 2007). The resulting shape in the roof is generally circular or sub-elliptical (White and White 1969), with one or more rectilinear sides in case of strong tectonic control. . ...
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The procedure for evaluating the susceptibility to natural and anthropogenic sinkholes is aimed at contributing to mitigate the risk from the most common geohazard in karst. It develops from the identification and geographical location of the caves, and then proceeds with the speleological survey, before characterising the caves in terms of geological-structural data (highlighting all the existing discontinuities in the rock mass, of both stratigraphic and tectonic origin), and of all the features related to occurrence and development of instability processes. Laboratory tests and monitoring are also mentioned as further possible steps of the analysis. Eventually, the procedure results in a zonation depicting the sectors most prone to development of sinkholes.
... To evaluate the sectors within cave systems mostly prone to further failures, the weathering processes in the rock mass must also be carefully examined (Fookes and Hawkins 1988; Hajna 2003; Lollino et al. 2004): these often cause strong reductions in the mechanical properties of the rocks, thus contributing to its overall decrease in strength, and facilitating its proneness to failures. ...
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Karst is an extremely fragile natural environment. The geological, morphological, hydrological, and hydrogeological features of karst determine an overall high vulnerability to a number of potentially dangerous events. The delicate equilibrium of karst ecosystems can be dramatically and irreversibly changed, as a consequence of both natural and anthropogenic impacts. This contribution examines the main peculiarity of karst and discusses the main natural and anthropogenic hazards affecting karst. Sinkholes, mass movements, floods, and loss of karst landscape are dealt with and discussed also by means of description of some case studies. Actions to mitigate the hazard in karst are also treated, highlighting the necessity to protect karst, an environment that needs specific regulations to be properly safeguarded. In particular, the Karst Disturbance Index, to evaluate the degree of disturbance done by man to the natural karst, is discussed. Groundwater contamination is by the World Health Organization listed among the world’s severest problems. Globally, water resources are limited and under pressure from urbanization and climate change. Among available drinking water resources, groundwater from karst aquifers is progressively becoming more valuable for potable, irrigation, and other agricultural and industrial use due to its abundance (high flow rate springs up to some tens of m3/s) and relatively high quality of water. However, its efficient use and protection poses a great challenge to urban karstology due to the very high susceptibility to contamination. The concept of groundwater vulnerability and contamination risk assessment is presented as an alternative approach for source protection zoning and land-use planning in karst. Specifically, vulnerability assessment has in some countries already been adopted by some national water-related policies as it confirmed to be a practical tool for protection zoning. It offers balance between groundwater protection and economic interests. The resulting maps are useful for planners and developers dealing with the protection and management of karst groundwater. However, caution needs to be taken when selecting the appropriate method for vulnerability assessment and when interpreting the results. Karst groundwater protection mostly relies on the implementation of sanitary protection zones where different restrictions apply. A review of the relevant legislation of several European countries showed that the groundwater travel time is the most frequent criterion for the delineation of sanitary protection zones, where the horizontal travel time to the groundwater source is generally considered. As a result, some countries increasingly use groundwater vulnerability maps to define sanitary protection zones and to implement more stringent measures where groundwater is vulnerable. A step further in the optimization of the sanitary protection zone delineation approach is to include the travel time through the vadose zone and to take into account surface water flow to the ponor. The total travel time (ttot) is calculated to obtain the travel time from any point in the catchment area to the tapping structure. For the ponor catchment area, ttot is the sum of the surface water travel time to the ponor (ts) and the travel time from the ponor to the tapping structure, based on dye-tracing tests. For any point outside the catchment area of the ponor, the total travel time is the sum of the vertical (t v) and horizontal (t h) groundwater travel times. Apart from test results obtained using natural and artificial dye tracers, the vertical travel time can be estimated based on vulnerability assessment, while the horizontal time can be assessed by analyzing spring hydrographs. The vulnerability map produced on the basis of total travel time calculations can easily be converted into a map of sanitary protection zones, depending on national legislation. The Remediation of Groundwater in Karst section describes aggressive technologies currently being applied to remediate karst aquifers, including in situ thermal treatment, in situ chemical oxidation, in situ bioremediation, and pump and treat. The fundamentals of each technology are discussed, including design principles, failure mechanisms, and amenable contaminants. The authors first provide an overview of trends in the groundwater remediation industry, which is followed by thought-provoking discussion on the politics of remediation in karst. Special attention is given to the technical challenges presented by karst, such as conduit flow and dissolution features, which may make remediation impracticable. On the technical side, this chapter includes a demonstration of modeling tools to assist with remedial evaluation and design. For example, the authors illustrate the use of VS2DTI for heat transport modeling in thermal remediation design, and the conduit flow process (CFP) for pump and treat design. Each example illustrates the need to incorporate conduit geometry and flow in the remedial analysis, as the use of equivalent porous media (EPM) techniques would lead to poor remedial performance. The hydrogeology of the thick karstified carbonate regions is challenging not only theoretically but also from a practical point of view. In these systems different types of groundwater flow are operating on distinct timescales associated with different types of permeability. Practical and scientific concerns related to karst hydrogeology are often on a regional scale such as sustainable water management, contamination of aquifers, and geothermal utilization. It is key issue to understand the regional and hydraulically connected nature of carbonate systems and to find appropriate solution for these particular problems. The importance of the gravity-driven flow concept is that it helps to understand the common genesis of thermal flow. The paper presents a deduced generalized flow pattern for deep carbonate regions which can provide a basis for finding similarities between thermal springs connected to continental carbonates. The understanding of the scale effect is highlighted to resolve practical problems. An important consequence of the hydraulic continuity and relatively higher hydraulic diffusivity of karst is that the effects of natural or artificial stresses on the groundwater level can propagate greater distances and depths than in siliciclastic sedimentary basins. The Transdanubian Range, Hungary can give an “in situ example” for the operation of hydraulic continuity based on a “long-term pumping test.” The fact of hydraulic continuity operating on a different scale can be used also during the planning of geothermal doublet systems and in the necessity of the use of heat content of effluent lukewarm and thermal springs and wastewater of spas in discharge zones of thermal water. Inadequate management of transboundary aquifers can lead to various groundwater quality (changes in groundwater flow, levels, volumes) and quantity (dissolved substances) problems. These problems are more difficult to prevent, mitigate, and solve in an international context than in the case of national aquifers. International cooperation is necessary to ensure an appropriate assessment, monitoring, and management of transboundary groundwater resources. International agreements are made to prevent potential conflicts and to improve the overall benefit from groundwater. In practice, agreements, to be made and respected, require a sufficient knowledge on the resource, its current state, and the trends. This is often a challenge for invisible groundwater and especially in a complex hydrogeological environment like karst. Aquifers in karst are very vulnerable as well, asking for an additional attention of national and international water authorities. This chapter describes DIKTAS, a case study of transboundary aquifers in the Dinaric karst region; it addresses motivation for international water cooperation, methodological approach, achieved results, and current efforts.
... alla stabilità delle cavità in un mezzo continuo, laddove per i problemi che coinvolgono ammassi caratterizzati da un comportamento controllato da discontinuità strutturali si richiedono metodi specifi ci che contemplino la resistenza delle stesse discontinuità (si veda ad es., LOLLINO et al., 2004LOLLINO et al., , 2013. ...
... Some studies can be found in literature concerning mechanical strength variation when this type of stone is placed outdoors. Specifically it has been observed that in rocks such as calcarenite, the loss of strength between fresh and moderately weathered varieties may be as high as 50%-60% (Dearman 1995;Lollino et al. 2004). Andriani and Walsh (2007) have noticed that such a reduction of compressive strength is certainly more marked in the fine-grained variety, whereas Sperandio (2004) observed that the effects of deterioration mechanisms are more significant when these degrading actions occur as cyclic events and not steady state conditions. ...
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This work presents an account of the results of diagnostic analyses conducted by the authors on the portal of Palazzo dei Priori in Perugia, Italy. After summarizing the main events that may have affected the structural behavior of the portal in the course of time, this article describes the results of the finite element method (FEM) tests conducted on a three-dimensional model of the portal. The analysis of these results made it possible to investigate the origin of the surveyed crack pattern and to evaluate the seismic vulnerability of the portal also as regards its structural response to the seismic activity at the level expected for the Perugia area.
In salt mining, the salt caverns formed by solution mining may lead to collapse sinkhole disasters. Predicting and preventing this type of sinkholes is a real and urgent problem. In this paper, three collapse sinkholes at the Dongxing Salt Mine were taken as examples to investigate the collapse mechanism of overlying strata above salt caverns induced by solution mining. Geophysical exploration was firstly carried out, with results showing that the overlying strata dropped down layer by layer; the prediction measures concluded that whether the anhydrite roof is destroyed or not can be treated as a marker for the identification of a salt cavity anomaly. Then, a mechanical model for the anhydrite roof was established. According to the model, major factors that may affect the stability of the anhydrite roof were identified and qualitatively analyzed, including the pressure decrease of the brine, the strength decrease of the rock in the roof under the immersion of brine, and the increase of horizontal stress in the roof. Numerical simulation was carried out to further analyze the collapse process and the influencing factors. Some prevention technologies were drawn as follows: (1) Mining of salt formations should be prohibited within the impact scope of the weak structural zone; (2) As regards the protective layer, a certain thickness of salt formation above the salt cavity should not be mined to prevent the dissolution upward; (3) An oil pad should be adopted to reduce or even avoid the contact of brine and roof; (4) Appropriate brine pressure should be maintained to improve the stability of the salt cavity when it is abandoned. The above prediction and prevention measures are not only applicable for halite but also suitable for other minerals obtained by solution mining, such as natural soda, Glauber’s salt, and others.
As a foundation material, limestone differs from other rocks in that voids may be found at almost any depth within the rock mass. They may result directly from solution weathering near the surface and along discontinuities, or as specific cave systems at depths related to present or past groundwater levels. Reviews the processes involved in the weathering by solution of the crystalline limestones, typically of Palaeozoic age. It offers a tentative, simple engineering classification of the solution features characteristic of limestones; and presents case histories to illustrate some of the problems which may be encountered during construction in areas of limestone bedrock.-from Authors
To use the distinct element method, it is necessary to discretize the problem domain into polygons in two dimensions (2 D) or into polyhedra in three dimensions (3 D). To perform distinct element stress analysis in a rock mass which contains non-persistent finite size joints, it is necessary to generate some type of fictitious joints so that when they are combined with the non-persistent joints, they discretize the problem domain into polygons in 2 D or into polyhedra in 3 D. The question arises as to which deformation and strength parameter values should be assigned to these fictitious joints so that they behave as intact rock. In this paper, linear elastic, perfectly-plastic constitutive models with the Mohr-Coulomb failure criterion, including a tension cut-off, were used to represent the mechanical behaviour of both intact rock and fictitious joints. It was found that, by choosing the parameter values for the constitutive models as given below, it is possible to make the fictitious joints behave as intact rock, in a global sense.a) For both the intact rock and the fictitious joints, the same strength parameter values should be used. b) A joint shear stiffness (JKS) value for fictitious joints should be chosen to produce a shear modulus/JKS ratio (G/JKS) between 0.008 and 0.012 m. c) A joint normal stiffness/JKS ratio (JKN/JKS) between 2 and 3 should be chosen. The most appropriate value to choose in this range may be the Young's modulus/G value (E/G) for the particular rock. Some examples are given in the paper to illustrate how to use the distinct element method to perform stress analysis of rock blocks which contain non-persistent joints and to study the effect of joint geometry parameters on strength and deformability of rock masses.
The stability of two systems of bell-shaped caverns excavated some 1000 years ago at Bet Guvrin National Park is investigated. The caverns were excavated in a weak, anisotropic, and moderately discontinuous chalk. The cavern stability is considered based on two separate and independent methods: a continuum model framework—FLAC, used for stress analysis, and a discontinuous approach—block theory, used for critical key block analysis.The numerical stress analysis reveals that in the case of very large span openings, tensile fracture of intact rock may be responsible for instabilities, which may lead to global failure. Evidence of tensile rupture at margins of failed caverns is abundant at the Park.The discontinuous block theory analysis reveals that the moderate joint set spacing at Bet Guvrin, up to 45% of the roof area may be comprised of removable blocks. The removable keyblocks in the roof remain in place due to arching stresses, which develop through the roof material. The chalk at the roof can sustain the maximum loads in existing caverns, as predicted by the numerical stress analysis. However, local failures due to exceedingly high compressive stresses at the abutments or by tensile fracture at the roof, may lead to relaxation of arching stresses followed by keyblock displacement. Such a “mixed failure mode” process could eventually lead, over time, to global collapse. Indications that “mixed failure mode” processes are presently active in the studied caverns are substantiated by in-situ measurement of keyblock displacements.It is suggested that in weak and discontinuous rock environments where “mixed failure mode” processes may be active, long term stability evaluation should be based on both continuous and discontinuous stability analyses.
Classical assessment of instability potential in underground excavations are normally based on yield and rupture criteria for stress driven failure and on limit equilibrium analysis of structurally controlled failure. While it is true that ultimate failure and falls of ground can be an eventual consequence of stress fracturing and unfavourable structure within the rock mass, the timing of such failure is often controlled by the presence of residual tensile capacity, in the form of rock bridges separating joint segments and fractures and by the mechanisms of clamping and relaxation. Using crack and rock-bridge analogues in conjunction with an updated voussoir beam model, this paper explores the influence of residual tensile strength and boundary parallel relaxation on the failure process. The impact on support design is also examined. In underground hard rock mines with complex geometries and interacting openings, relaxation is identified as a key controlling factor in groundfall occurrence. Empirical stability assessment techniques for underground tunnels and for mining stopes are updated to account for relaxation.
The stability of a horizontally bedded and vertically jointed roof, referred to here as a laminated Voussoir beam, is studied using careful documentation of a historic roof collapse, which occurred in an ancient underground water storage reservoir dated back to ca. 1000 B.C. The roof of the opening failed immediately after the excavation leaving a dome shaped loosened zone, with a span of 7 m and height of 2.5 m, consisting of horizontal beds and vertical joints with mean spacing of 50 and 25 cm, respectively. The ancient engineers erected a massive pillar at the center of the dome in order to passively support the failed roof and the opening remained in service for several hundred years following the failure. Analysis of the roof using iterative Voussoir beam procedure [Beer, G. and Meek, J. L., Design curves for roofs and hanging walls in bedded rock based on Voussoir beam and plate solutions. Trans. Inst. Min. Metall., 1982, 91, A18–22.] shows that the roof was more sensitive to failure by shear along the abutments rather than by crushing at hinge zones and that the required friction angle (φreq.) for stability would have been 36°. The available friction angle is estimated between 38.6° and 46.4° and, therefore, the result of the iterative solution is considered unconservatively wrong. Results of DDA [Shi, G. -H. and Goodman, R. E., Two-dimensional discontinuous deformation analysis. Int. J. Numer. Anal. Methods Geomech., 1989, 13, 359–380; Shi, G. -H., Block System Modeling by Discontinuous Deformation Analysis. Computational Mechanics Publications, Southampton, 1993, pp. 209.] however indicate that φreq. must have been greater than 60°, a shear strength which was not available at the time of construction, thus the immediate failure. Using DDA we further demonstrate that φreq. is related to joint spacing (or block length) in a parabolic function: with increasing joint spacing φreq. decreases to a minimum value and than increases with further increase in joint spacing. This result is attributed to the interaction of two competing forces: one is the stabilizing axial thrust which increases with increasing moment arm in individual blocks (a function of joint spacing or block length), the other is the destabilizing vertical load which increases with increasing weight of overlying blocks.
The voussoir beam analogue has provided a useful stability assessment tool for more than 55 years and has seen numerous improvements and revisions over the years. In this paper, a simplified and robust iterative algorithm is presented for this model. This approach includes an improved assumption for internal compression arch geometry, simplified displacement determination, support pressure and surcharge analysis and a corrected stabilizing moment in the two dimensional case. A discrete element simulation is used to verify these enhancements and to confirm traditional assumptions inherent in the model. In the case of beam snap-through failure, dominant in hard rock excavations of moderately large span, design criteria are traditionally based on a stability limit which represents an upper bound for stable span estimates. A deflection threshold has been identified and verified through field evidence, which corresponds to the onset of non-linear deformation behaviour and therefore, of initial instability. This threshold is proposed as a more reasonable stability limit for this failure mode in rockmasses and particularly for data limited cases. Design charts, based on this linearity limit for unsupported stability of jointed rock beams, are presented here summarizing critical span–thickness–modulus relationships.