Constraints on Long-Term Seismic Hazard from Vulnerable Stalagmites for the Surroundings of
Vacska cave, Pilis Mountains of Hungary
European Geosciences Union General Assembly
23-28 April 2017, Vienna, Austria
Session NH4.2/SM3.11 - Seismic Hazard and Disaster
Risk: Assessment, Testing, and Implementation
X4.366
K. GRIBOVSZKI (1, 2), G. BOKELMANN (1), K. KOVÁCS (2), P. MÓNUS (2), P. KONECNY (3, 4), M. LEDNICKA (3), A. NOVÁK (2)
(1) Department of Meteorology and Geophysics, University of Vienna, [email protected] (2) Geodetic and Geophysical Institute, Research Centre for Astronomy and Earth Science, Hungarian Academy of Sciences
(3) Institute of Geonics, Academy of Sciences of the Czech Republic (4) Planetarium Ostrava, Faculty of Mining and Geology, VSB-TU of Ostrava, Czech Republic
ABSTRACT: Damaging earthquakes in central Europe are infrequent, but do occur. This raises the
important issue for society of how to react to this hazard: potential damages are enormous, and
infrastructure costs for addressing these hazards are huge as well. Obtaining an unbiased expert
knowledge of the seismic hazard (and risk) is therefore very important.
Seismic activity in the Pannonian Basin is moderate. In territories with low or moderate seismic
activity the recurrence time of large earthquakes can be as long as 10,000 years. Therefore, we cannot
draw well-grounded inferences in the field of seismic hazard assessment exclusively from the seismic
data of 1,000- to 2,000-years observational period, that we have in our earthquake catalogues.
Long-term information can be gained from intact and vulnerable stalagmites (IVSTM) in natural
karstic caves. These fragile formations survived all earthquakes that have occurred, over thousands of
years - depending on the age of them. Their “survival” requires that the horizontal ground
acceleration has never exceeded a certain critical value within that time period.
Here we present such a stalagmite-based case study from the Pilis Mountains of Hungary.
Evidence of historic events and of differential uplifting (incision of Danube at the River Bend and in
Buda and Gerecse Hills) exists in the vicinity of the investigated cave site. These observations imply
that a better understanding of possible co-seismic ground motions in the nearby densely populated
areas of Budapest is needed. A specially shaped (high, slim and more or less cylindrical form), intact
and vulnerable stalagmite in the Vacska cave, Pilis Mountains was examined. The method of our
investigation includes in-situ examination of the IVSTM and mechanical laboratory measurements of
broken stalagmite samples.
The used approach can yield significant new constraints on the seismic hazard of the
investigated area, to show that tectonic structures close to Vacska cave could not have generated
strong paleoearthquakes in the last few thousand years, which would have produced a horizontal
ground acceleration larger than the upper acceleration threshold that we can determined from the
intact and vulnerable stalagmites. A particular importance of this study results from the seismic
hazard of the capital of Hungary.
2. THE INVESTIGATION METHOD OF STALAGMITE
The method of our investigation is
the same as before (Gribovszki et
al., 2017):
– the natural frequency and the
geometrical dimension of IVSTM
was determined by in situ nondestructive observations;
– in the theoretical calculation
(Eq1 and 2) the results of our
earlier mechanical laboratory
measurements (the density, the
dynamic Young’s modulus and the
tensile failure stress of broken
stalagmite samples) have been
used;
– the value of horizontal ground
acceleration resulting in failure
and the theoretical natural
frequency of IVSTM were
assessed
by
theoretical
calculations in static case,
resonance (dynamic amplification) was not taking into account
(Cadorin et al., 2001);
– age determination of drilled
Figure 2. Photo of IVSTM3.3m (the stal. behind
core
samples
(earlier
age
the one at the front was investigated in detail)
determination results from Vacska
cave are available).
1. THE LOCATION OF VACSKA CAVE IN THE PILIS MOUNTAINS OF HUNGARY
The Vacska cave is located in the Pilis
Mountains, Hungary (Fig. 1). This cave
is close to the capital of Hungary
(Budapest is located 15 km to the
southeast) and the incision of Danube at
River Bend (at 10 km distance), where
uplifting occurs.
In this cave three intact vulnerable
candlestick-type stalagmites (IVSTM)
with palm-tree trunk shape stand;
among them the most vulnerable is the
3.3 m long one (IVSTM3.3m, Fig. 2-4).
In this study we try to find the
answer to the question:
What is the upper limit of the size of
earthquakes
occurring
in
the
Figure 1. The location of the investigated cave, Vacska in the Pilis
surrounding of the cave? In other words:
Mountains, Hungary, near the capital of Hungary, the active faults
What is the highest ground motion that
(Horváth et al., 2004) and the felt and registered earthquakes
this tall and vulnerable IVSTM3.3m
can survive?
3. NON-DESTRUCTIVE IN-SITU EXAMINATIONS OF THE INTACT AND
VULNERABLE STALAGMITE (IVSTM)
Considering that in situ measurements of slim and high
stalagmite had to be done non-destructively, we confined
ourselves only to determine their dimensions (Table 1)
and natural frequencies (Table 3). In case the investigated
IVSTM is slim enough, resonance effect can occur during
an earthquake [Lacave et al., 2000].
In order to measure the natural frequency and harmonic
oscillations of IVSTM3.3m, horizontal LF-24 geophones
were fastened on the stalagmites, and it was excited by
small amplitude forced vibration obtained by a gentle hit
(Fig. 4).
Name
Place
IVSTM
(3.3m)
Vacska
cave
Height
(m)
(cm)
H/
D
3.3
the upper 30 cm of the
stal. heavily grows
narrower
average max.: 12.5
(average min.: 10.4)
Diameter
26
(32)
Table 1. Results of non-destructive in-situ examinations of the
intact, vulnerable stalagmite I.: dimensions
It can be seen in Table 3, that the
natural frequency of IVSTM (two
peaks at ~9 Hz, Fig. 6-7, Table 3) is
below 20 Hz. This means that the
eigenfrequency
falls
into
the
frequency range of
nearby
earthquakes. If the natural frequency
of stalagmite is below 20 Hz then
resonance can occur.
Figure 5. The recorded vibration of IVSTM3.3m
5. OSCILLATION OF STALAGMITES BY THEORETICAL CALCULATIONS
The natural frequency of a stalagmite
The horizontal ground acceleration
resulting in failure of a stalagmite
1 3ED 2
(Eq. 1)
r u
f0 
4
ag 
(Eq. 2)
π 16 H
2
2 H
D: diameter
measured at the horizontal section of the cylindrical shaped stalagmite,
r: radius
H: height of the stalagmite, : density of the stalagmite, E: dynamic Young-modulus,
u: tensile failure stress of the stalagmite
Cadorin et al. 2001
NAME
IVSTM
(3.3m)
measured
theoretical
f 0 (Hz)
f 0 (Hz)
a g (m/s2)
a g (m/s2)
~9
6.6
(5.5)
0.86 (height = 3m)
using the mechanical properties
of stal. from Detrekői-zsomboly
theoretical
2.30 (height = 3m)
using the mechanical properties
of stal. from Baradla cave
theoretical
Table 4. The measured and calculated natural frequencies and horizontal ground accelerations resulting in failure
obtained by theoretical calculations
Figure 7. The vibration and Power
Spectral Density of IVSTM3.3m
Figure 6. The vibration and Power Spectral Density of
IVSTM3.3m along the recorded signal of the excited stalagmite
Figure 3. Sketch
of IVSTM3.3m
Our theoretical calculations (equations by using cantilever beam theory, see Chapter 5) did not
take into consideration the phenomenon of resonance, which means that in reality the IVSTM
would have broken at a lower value of horizontal acceleration than the computed ones.
SUMMARY
• Stalagmites are useful for
giving upper bounds of
maximum credible earthquakes in the present and
the past;
• Our preliminary investigation determined almost
the same value for the
critical horizontal ground
acceleration as the SHARE
model for 10% probability
of exceedance in 50 years
(0.072g).
4. MECHANICAL PROPERTIES OF STALAGMITES
Since the mechanical laboratory measurements (MLM) of broken samples from the Vacska
cave did not finish till the EGU2017, therefore we used only our earlier results of MLM in the
calculations (eigenfrequency and horizontal ground acceleration equations, Eq1-2.). Our
earlier results came from Baradla cave, Hungary and from Detrekői-zsomboly, Slovakia (Table
2). Table 3 shows us that the previously determined mechanical properties of stals. from
different caves does not yield the same results of eigenfrequency as what we got from in situ
measurements in Vacska cave. The differences between the measured and calculated values is
less then 30%.
Baradla cave, Hungary
Detrekői-zsomboly,
Slovakia
density,  [kg/m 3]
dynamic Young’s modulus, E [MPa]
tensile failure stress, u, [MPa]
2 394 ± 155
20 813 ± 5 921
1.62 ± 0.48
1 940.5 ± 6.4
25 181 ± 3 917
0.51 ± 0.13
Table 2. Results of mechanical laboratory measurements of stalagmites originated from Baradla cave, Hungary and Detrekőizsomboly, Slovakia
Name
Place
theoretical
IVSTM
(3.3m)
Vacska
cave,
Hungary
6.6 (height = 3m)
using the mechanical properties of
stal. from Detrekői-zsomboly
f0
Figure 4. Recording the vibration of
IVSTM3.3m, the photo was taken from the
abyss below it
6. DEPTH OF THE CAVE
For this kind of study stalagmites are most suitable if they are at shallow depth, since seismic
waves are progressively attenuated with depth. The depth of the hall, where the investigated
stalagmite stands, is ~45-50 m beneath the surface. (The detailed vertical profile is not
available so far.) At this depth and in case of limestone rock type the seismic waves cannot be
attenuated considerably (Shimizu et al., 1996).
(Hz)
theoretical
f0
(Hz)
5.5 (height = 3m)
using the mechanical properties of
stal. from Baradla cave
measured
f0
(Hz)
two peaks at
~9
Table 3. Results of non-destructive in-situ examinations of the intact, vulnerable stalagmite II.: measured natural
frequencies of IVSTM3.3m, and the calculated eigenfrequencies (Eq. 1)
Figure 6. SHARE Model for rock site, 10% probability of exceedance in 50 years (Giardini et al., 2013)
and our previous results (PGA from stal. investigations), the red star shows the location of Vacska cave
REFERENCES
Cadorin, J. F. , et al., 2001, Netherl. J. of Geosci., 80, 3–4, 315–321.
Giardini, D., et al., 2013, Seismic Hazard Harmonization in Europe
(SHARE):
Online
Data
Resource,
http://portal.shareeu.org:8080/jetspeed/portal/
Gribovszki, K., et al, 2013, Acta Cars. Slo., 51 (1), 5-14
Gribovszki, K., et al., 2017, Journal of Seismology
Horváth, F., et al., 2004, Atlas of the present-day geodynamics of
the Pannonian basin: Euroconform maps with explanatory text
Lacave, C., et al., 2000, Proc. of the 12th World Conf. on Earthq.
Engin. (30.01.– 04.02. 2000, Auckland, New Zealand), paper 2118.
Shimizu, I., et al., 1996, Engin. Geol., 43, 107-118.