Historic subsurface dimension stone quarry and the stability of its galleries as a function of pillar width and thickness of cover bed

Abstract

There are historic subsurface dimension stones in the capital of Hungary (Budapest) that were excavated in porous limestone. The stability of these subsurface openings is important, since most of them are located in urban areas, where existing buildings or new structures are planned to be built. The paper presents a detailed study considering the geometry of the system and the mechanical parameters of the limestone. The geometry of the cellar system was obtained using terrestrial laser scanning (TLS). The cover beds are few meters in thickness, and the width of the pillar is between 2.50 and 3.98 m, according to the measurements. The rock mass parameters which were used in the calculations were obtained from laboratory tests. A finite element (FEM) software Rocscience (RS2) were applied to model the stability of the galleries. Calculations were made for various geometries taking into account the thickness of cover beds and the width of pillars. Altogether 70 models were made. A surface load of 150 kN/m2 was also applied to model the buildings. New relationships between cover bed thickness, pillar width and displacements are outlined to compare these results to previous works. The strength reduction factor was also calculated for all geometries, indicating the changes in the stability of these underground quarries and pointing out the importance of cellar geometries.

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Environmental Earth Sciences (2022) 81: 414
https://doi.org/10.1007/s12665-022-10539-x
THEMATIC ISSUE
Historic subsurface dimension stone quarry andthestability ofits
galleries asafunction ofpillar width andthickness ofcover bed
JalalZenah1· PéterGörög1· ÁkosTörök1
Received: 23 December 2021 / Accepted: 25 July 2022 / Published online: 16 August 2022
© The Author(s) 2022
Abstract
There are historic subsurface dimension stones in the capital of Hungary (Budapest) that were excavated in porous limestone.
The stability of these subsurface openings is important, since most of them are located in urban areas, where existing build-
ings or new structures are planned to be built. The paper presents a detailed study considering the geometry of the system and
the mechanical parameters of the limestone. The geometry of the cellar system was obtained using terrestrial laser scanning
(TLS). The cover beds are few meters in thickness, and the width of the pillar is between 2.50 and 3.98m, according to the
measurements. The rock mass parameters which were used in the calculations were obtained from laboratory tests. A finite
element (FEM) software Rocscience (RS2) were applied to model the stability of the galleries. Calculations were made
for various geometries taking into account the thickness of cover beds and the width of pillars. Altogether 70 models were
made. A surface load of 150kN/m2 was also applied to model the buildings. New relationships between cover bed thick-
ness, pillar width and displacements are outlined to compare these results to previous works. The strength reduction factor
was also calculated for all geometries, indicating the changes in the stability of these underground quarries and pointing out
the importance of cellar geometries.
Keywords Subsurface quarry· Porous limestone· Stability modelling· FEM· Displacement
Introduction
The stability of engineering structures is an important topic
in engineering practice; in some urban areas, cavities are
serious challenges affecting the engineering design and con-
struction activities, whether they are natural or man-made.
There are several cities around the world that have areas
that are undercut by cellars and cavities, which are suffer-
ing from stability problems caused by these openings. Such
kind of issues exists in different European countries, such
as in French Jura (Smeray etal. 2000), in Spain (Fuentes
etal. 2010), and in Emilia-Romagna Region (Italy) (Tinti
etal. 2015). The problem of pillar design have been studied
in literatures the studies focused on the design of the pillar
in coal mines (Wagner 1980), and room and rib pillar in
Granite mine (Peila etal. 2008). Several known cellars and
cavities exist in Budapest, Hungary (Hajnal 2006; Görög
etal. 2013). The origin date of the cellars in Hungarian cit-
ies are representing various ages from the Middle Age to
the nineteenth century (Gálos etal. 1981). In most cases,
these cellars are cut in soft rocks, such as porous limestone
(Görög etal. 2013) and tuffs (Vincze and Görög 2016; Moc-
sár-Vámos etal. 2015).
The usage of the cellars changed through the time; most
of them related to previous mining activities, the host rocks
of them were proper dimension stone. There are some
which were built for wine cellars, or because of defence.
Nowadays, some of them are using as wine storage (Fuentes
etal. 2010), mushroom production, hosting events, as water
sewer system (Marasović etal. 2014), and some of them are
neglected. The areas which are affected by cellars located
in a residential area; therefore, the cavities present hazards.
If they are not in use, their state is not monitored regularly,
This article is part of a Topical Collection in Environmental Earth
Sciences on “Building Stones and Geomaterials through History
and Environments – from Quarry to Heritage. Insights of the
Conditioning Factors”, guest edited by Siegfried Siegesmund, Luís
Manuel Oliveira Sousa, and Rubén Alfonso López-Doncel.
* Ákos Török
torok.akos@emk.bme.hu
1 Department ofEngineering Geology andGeotechnics,
Faculty ofCivil Engineering, Budapest University
ofTechnology andEconomics, Budapest, Hungary
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they cause several problems such us surface settlements or
collapse. Therefore, one of the serious geotechnical issues
of these areas is to determine the stability of cellars and
cavities; investigation the rock masses; displacement meas-
urements and calculations; regular monitoring of them to
monitor the effect of these cavities on the structure above
and under the ground.
Subsurface quarries are common worldwide, and nowa-
days, the areas above these subsurface quarries are develop-
ing continually; those reasons led to study these subsurface
quarries and evaluate their stability conditions of it. Subsur-
face quarries can be found in almost all countries, with some
examples from, India (Vandana etal. 2020), China (He etal.
2016) and in Italy (Bartolo and Salvini 2019), and it used as
construction material such as the Marble quarry which used
to build the Milan Cathedral (Oggeri and Oreste 2015), lime-
stone quarry in Germany (Siegesmund etal. 2010). Tunnels
cut in limestone also have similar openings and their stabil-
ity depend on several factors, such as the physical properties
or accidental fire (Martínez Ibáñez etal. 2021).
These types of dimension stone quarries are known from
many parts of the globe and have been described from Italy
(Negri etal. 2015) (Bartolo and Salvini 2019), France (Al
Heib etal. 2015), as well as in Hungary.
The stability of these openings are always in question,
especially when they are used as tourist attractions (Rybár
etal. 2017). Construction activity above these abandoned
quarries and galleries causes the additional load, which lead
to further stability problems to these openings (Zenah etal.
2019; Zenah and Görög 2021). Therefore, a detailed geo-
technical investigation is necessary in such cases. It should
start with the geometry measurements, which can be done
with conventional geodetic tools. Since the geometry of
these cellars is usually not regular, only a detailed measure-
ment is appropriate to get the real geometry. The terrestrial
laser scanning (TLS) method is able to measure the real
geometry with imperfections (Zhao etal. 2019), reduced
the time required for the field measurement (Kordić etal.
2019), monitoring the changes on coastal cliff faces (Rosser
etal. 2005), or slopes in civil engineering works (Miščević
etal. 2020), and can be the base of the numerical model of
the cellar.
The second step of the stability analysis is to measure and
evaluate the properties of the rock masses around the cavity.
It can be done with conventional rock mechanical methods:
core drillings, samplings, measurements of discontinuities
and rock mass classification. The rock mass of this kind of
cavities can be easily described, since the cellars are acces-
sible, and there is no lining system, so the rocks are visible.
There are several software codes dealing with geotechni-
cal analysis, such as MATLAB (Mollon etal. 2010; Janič
etal. 2019), Rocscience (RS2 Bukaçi etal. 2016; Zenah
etal. 2019), Examine (Andersson etal. 2004)), FLAC3D
(Emad 2017), Abaqus (Sharma etal. 2018). The stability
of this kind of cavities depends on several factors, such as
material and rock mass properties, changes in the stress and
geometrical characteristics (Cała etal. 2016). The effect of
geometrical factors such as pillar width and cover thickness
to the stability of cellars are investigated in this paper. The
effect of the cover thickness was investigated by researchers
using tunnels that are located at different depths (shallow
to deep) (Sharma etal. 2020). The stability of the pillars
controls the cellar/tunnel stability.
The aim of this paper is to evaluate the stability of cellar
system under surface load, to protect valuable areas and new
construction ones.
Numerical modelling gives the possibility to build dif-
ferent models and investigate the stability of cellars with
different geometry and compare the results. The results may
help to have clear scenarios about displacement, failure and
safety of such cavities which lead to more understanding the
structural behaviour of the cellars and safer design for the
structures above.
Geological overview andhistorical quarries
ofporous limestone inBudapest
Budapest is located in the central part of Hungary (Fig.1).
The topography of capital city is divided into two parts by
the river Danube. On the west side of the river are the Buda
Mountains and on the east side is the Pest Plain. The mor-
phology of the Buda Mountains is governed by faults and
thrust belts, while the Pest Plain is filled with alluvial sedi-
ments (Bodnár etal. 2011). The stratigraphy of Budapest is
very complex, with the oldest exposed Triassic carbonates
to the youngest fluvial sediments of the Holocene period
(Fig.2). Sedimentary rocks prevail in the area of Budapest.
From sedimentary rocks, various limestone types are the
ones that are used mostly in moments. Besides the Trias-
sic Dachstein limestone, Eocene Nummulitic limestone,
Miocene porous limestone and Pleistocene travertine form
the available stone resources. The present study focuses on
the Miocene porous limestone. The study area is located in
the southern part of Budapest (Buda side) and is covered
by Miocene limestone (Fig.1),. This limestone is under-
lain by clayey silty sediments and overlain by silty clay and
evaporitic beds that are not exposed to the surface (Fig.2).
The Miocene carbonates (limestone) are the most common
dimension stones of the entire sequence and the youngest
dimension stones besides travertine. The exploitation of this
limestone was first from surface quarries, then due to wine
cultivation, subsurface galleries were cut, and limestone was
extracted from those. This quarrying activity led to the exca-
vation of thousands of square meters of underground cellars
and left quarry yards, too (Fig.3). The total length of these
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cellars is more than 100km. The cellars have different cover
depths depending on the quality of porous limestone, since
stone extraction followed the best quality limestone banks.
As a consequence, the depth of galleries, the width of pil-
lars are also variable. Part of the studied cellar system are
presented in Fig.4., showing the modelled cross section. The
hatched areas represent the pillars.
Materials andmethods
The research plan and the applied methodology is sum-
marized in Fig.5. The history of quarrying and geological
setting is given in the previous section (Section“Geologi-
cal overview and historical quarries of porous limestone
in Budapest”), while all other methods are described here.
The study area is covered of Miocene limestone, porous
limestone which has different quality of layers. The most
common type, which was the target of quarrying activity,
is an ooidal limestone. The main components are carbonate
grains that are ooids and micro-oncoids. The well to mod-
erately rounded ooids and micro-oncoids are of 0.2–1.0mm
in diameter. The calcite is the main cement that forms cir-
cumgranular cement rims around the grains. Bioclasts such
as gastropods, bivalves and foraminifers also form part of the
rock. The stone is highly porous and the porosity is mainly
related to intergranular pores (Fig.6). Further description
of this The pore-size distribution was previously studied in
detail (Török and Szemerey-Kiss 2019). The micro-facies
of the rock is ooid–micro-oncoid grainstone to packstone.
This material was one of Budapest's most widespread
construction materials in the past centuries (Török 2003).
Emblematic buildings, such as the Parliament building,
Citadella and Mathias Church in Budapest was constructed
from this stone (Török etal. 2007). Similar Miocene porous
limestone was used in other countries, such as Austria (Bed-
narik etal. 2014), Czech Republic (Valtice) (Přikryl and
Přikrylová 2004; Török etal. 2004), Belgium (De Kock
etal. 2017), France (Beck and Al-Mukhtar 2008), Italy
(Pappalardo etal. 2016), Cyprus (Modestou etal. 2016),
Malta (Cassar 2002; Rothert etal. 2007; Grøntoft and Cassar
2020), Cologne Cathedral in Germany (Graue etal. 2011).
The historic bridge of Mostar, Bosnia and Herzegovina
was also made of limestone (Čorko etal. 2001). Extensive
research on other limestones and evaluations of their prop-
erties were made in the past years in Turkey (Ozguven and
Ozcelik 2013), in Slovakia (Laho etal. 2010), and in Sri
Lanka (Jayawardena 2017). Despite this, there are several
types of this rock with very different mechanical properties,
so its investigation is essential in every case.
Fig. 1 Map of Hungary with a simplified geological map of Budapest showing main rock types and the porous limestone quarries. Red circle
refers to the location of the studied dimension stone quarry
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Fig. 2 Stratigraphic of Buda-
pest, showing the Miocene
porous limestone with subsur-
face quarries that are now used
as cellars
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The geometries of the cellar were determined using Ter-
restrial Laser Scanner (TLS), which is a useful and effective
method for measuring the real geometry of the cellars (Her-
rero etal. 2015), geometry of the buildings (Herrero etal.
2015) and the geometry of slopes (Török etal. 2016; Kordić
etal. 2019). We used a phase-based terrestrial laser scanner
(Faro Focus 120S) (Fig.7) with ± 2mm ranging accuracy
and 120m maximum measurement range.
Our TLS measurements signify that the cellar consists of
a main corridor with seven side corridors to the right side
and six air ventilation shafts (Fig.8). The studied investi-
gated cellar has almost no support system; there are only
some separated brick and limestone masonry arches to
avoid falling blocks. The result of TLS scan geometry was
imported to 2D model that includes the hots rock and cover
bed. The layered structure of the Miocene limestone was
mapped through the ventilation shafts. The area is covered
with topsoil with a thickness of around 0.1m. It is underlain
by a weathered porous limestone which has a thickness of
1.5m. The cellars were cut in the high quality limestone
layer (Fig.9). The thickness of coverbed and the presence
of covering weathered limestone was also proved historical
archive by core drilling data.
The studied cross section is located far from the axis of
the main corridor by 21m and parallel to it. The width of
the pillars between (2.50—3.98) m, the depth is around 6m
as the surface above the cellar is almost flat according to
the studied cross section. The area above the cellar system
is large. It is a new construction area, with some buildings.
The load of the planned buildings according to the static
design is 150 kN/m2.
Specimens were obtained from the cellar and tested under
laboratory conditions. Several rock physical tests were done
according to national standards, such as American Society
for Testing and Materials (ASTM) and European Stand-
ards (EN): the dry density was calculated according to
EN 1936:2006. The uniaxial compressive strength (UCS)
test and Brazilian tests for dry conditions were performed
Fig. 3 Former porous limestone quarries that are now used as housing or cellars
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according to ASTM D7012-14e1 with correcting the UCS
value for (L/D = 2, D = 50mm) (Gálos and Vásárhelyi 2006).
The ultrasonic wave propagation velocity test made follow-
ing the guidelines given by EN 14,579:2004. Altogether 32
specimens were tested in the laboratory as in Table1. The
sampling locations are marked by red circle in Fig.8.
Rocscience (RS2) program was used for the calculations,
one of the roc-science software packages; it is a 2D finite
element program for soil and rock applications.RS2 can
be used for: excavation design, slope stability, groundwater
seepage, probabilistic analysis, consolidation, and dynamic
analysis capabilities (Zenah etal. 2019; Bukaçi etal. 2016).
Those calculations were done in different cases. First, in the
current state of the cellar and second with a variable cover of
the cellar and with variable width of the pillar. The dimen-
sions of the cover and pillar width of the existing cellar net-
work (Fig.10). The current cover is 5.5m, and it is reduced
by 0.5m till 2.5m in every calculation step; the width of
the pillars was also reduced from the original 2.5m with
0.5m increments down to 0.5m. These calculations were
made for one surface load of 150 kN/m2 in dry condition
only. To conclude, 70 different models were generated with
7 different cover thicknesses, and for each of five different
widths of the pillar were modelled under two different loads.
Every model was run twice, once for calculating the strength
reduction factor (SRF), and the second time to calculate the
maximum displacements.
In this case, long-term stability is established when the
safety factor is higher than 1.35. However, during the evalu-
ation of the results, the cellar was considered stable if the
stress reduction factor (SRF) was bigger than 1.00, if it is
smaller than this value, the collapse of the cellar will happen.
Results anddiscussion
According to the on-site measurements, there was only
one main joint direction with dip direction = 90° and dip
angle = 74°, and the joint spacing is about 20m, according
to that the GSI = 80.
Results oflab tests
The results of laboratory tests are presented in Table2,
Fig.4 Studied cellar system—the red colour refers to the studied cross section, the hatched area represents the pillars
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Fig. 5 Methodology and major
steps of stability calculations
Fig. 6 Host rock of historic subsurface quarries, the porous oolitic limestone, a well sorted ooid grains, b thin section image of micro-oncoid–
ooid grainstone
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The input parameters for the stability calculations in the
models, were the parameters of the specimen which has the
lowest UCS value as following:
gdry
=1.580 g∕cm
3
, Intact UCS
dry
=2.46 MPa, E
dry
=
1.298 GPa.
The generalised Hoek–Brown failure criterion was used
(Hoek etal. 2002) for the material model, the parameters
for Hoek–Brown were partly obtained from laboratory tests
(UCS) and from site survey (GSI):
The following Hoek–Brown’s parameters are calculated
by modelling program (RS2):
The UCS reduced by 20% for the weathered limestone,
because the rock at this depth is weathered and fractured,
similarly to former studies of this area (Zenah etal. 2019)
(Fig.9).
Results ofmodelling
After running all the 70 models the results of strength reduc-
tion factor (SRF) and the displacements of the roof of one
branch of the cellar are given in Tables3 and 4, respectively.
Beside Tables3 and 4, Fig.11 shows the results of roof
displacements for load 150 kN/m2. Under load 150 kN/m2
pillar's width under 1.0m is not acceptable in term of dis-
placements and SRF, while for pillar's width 1.0m the bor-
der between safe and collapse area is not clear and it’s not
preferable to have this width.
We considered the SRF > 1 is acceptable, so the previ-
ous discussion accepted the SRF equals one or more, and
rejected SRF which is less than one.
For deeper understanding of changing the displacements
(maximum and roof) in the models both displacements
Intact Rock Constant(mi)=10, Disturbance Factor =0.
mb=4.895,
s
=0.108,
a
=0.5.
Fig. 7 Used TLS device, while it is working inside the cellar system
Fig. 8 Cellar system, with the entrance and the branches obtained from TLS, the sampling locations is marked by red circle
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maximum and roof (the point where the roof displace-
ments were measured is shown in Fig.12, the graphs of the
displacements for pillar width 2.5m and 1.5m drawn in
Fig.13; from Fig.12, it’s clear that the maximum displace-
ments happened in the weathered limestone layer, this idea
could be more clear in Fig.13 with the graphs, the maximum
displacements are much more higher in values than the roof
displacements till the weathered limestone layer is removed
by decreasing the cover of the cellar.
For each pillar's width the SRF is increasing with the
increasing of the cellar's cover; the displacement is increas-
ing with shallowing the depth.
Other results match with these ones such as the results of
Vu etal. (2015), where the effect of building deep founda-
tion’s load on the settlement of the ground surface above a
tunnel, the results showed that in granular and cohesive soils
the maximum settlements increase with the decreasing the
cover thickness in different rates according to the soil types.
The graphs after (Vu etal. 2015) study and this paper’s
graphs (with pillar width 2.5m) can be found in Fig.14.
The two graphs have the same shape if we consider the
increase in displacements because of the weak upper layer.
The graphs in Vu etal. (2015) work are calculated from
equations. In that work (Vu etal. 2015), the horizontal rep-
resent the cover value, while the vertical axes represent the
maximum settlements of the ground surface.
The effect of shallow depth and deep depth studied by
Gao (2012) the results were similar to our results, the shal-
low depth studied done for depth 0.6m (model 1) and 5.0m
(model 2) and from the graph of the roof displacements it
easy to obtain that the displacements are increasing from
around 0.01 to 0.12m when the depth decreased from 5.0m
to 0.6m.
The effect of pillar width studied for coal pillar under road
load by Le Quang etal. (2020) done for 8 widths between
4 and 20m, it showed that the vertical displacements are
increasing with reducing the width of the pillar as the same
results that we got from this paper.
The thickness of the cover is very important, and it has
a major effect on the stability of the cavities; the difference
between the stability of shallow cavity and deep cavities
was studied by Gao (2012), the study recommended to find
Fig. 9 Geological layers in the
studied area with the cellar
Table 1 Test methods and number of tested specimens
Property Code of the test procedure Number of
specimens
Density EN 1936:2006 32
US-wave velocity EN 14,579:2004 32
UCS ASTM D7012-14e1 8
Brazilian strength ASTM D3967-16 7
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the optimal depth of the cavities. According to our study the
optimal depth (the minimum cover remains after drilling
the ground) of cellar is 4m if we have pillar width 1.5m
(Fig.11).
The width of the pillar affects the stability of the pillar
and then for sure the stability of the cellar. Le Quang etal.
(2020) studied the role of the pillar width on the stability
and displacements of the cellars under road load. Rahaman
and Kumar (2020) studied singular and twin horse-shoe
tunnels in the rock mass, and this study described the dif-
ferences in stability of the tunnels under loading (load fac-
tor) with changing cover/width ratio the (H/B) of the tunnel
Fig. 10 Studied A–A cross section with the modelled cover and pillar geometries (cover: 2.5–5.5m), (pillar width: 0.5–2.5m)
Table 2 Laboratory results in dry condition
Density (kg/m3) UCS (MPa) Brazilian tensile strength (MPa)
Max Min Mean Standard deviation Max Min Mean Standard deviation Max Min Mean Standard deviation
1710 1520 1630 0.05 6.66 2.46 5.24 1.615 2.11 1.03 1.56 0.45
Table 3 Strength reduction factor (SRF) with changing the cover and
the width of pillars
SRF Pillar's width (m)—150 kN/m2
Cover (m) 2.5 2 1.5 1 0.5
5.5 1.64 1.49 1.32 1.08 0.68
5 1.58 1.49 1.30 1.08 0.79
4.5 1.60 1.50 1.33 1.09 –
4 1.62 1.39 1.31 1.01 –
3.5 1.67 1.48 1.32 1.05 –
3 1.55 1.48 1.29 1.03 –
2.5 1.60 1.45 1.19 1.02 –
Table 4 Displacement of the roof (mm) of the cellar with changing
the cover and the pillar's width
Roof dis Pillar's width (m)—150 kN/m2
Cover (m) 2.5 2 1.5 1 0.5
5.5 4.54 4.87 5.44 7.09 1210.00
5 4.50 4.83 5.36 8.14 –
4.5 4.46 4.77 5.30 7.47 –
4 4.50 4.81 5.31 8.39 –
3.5 4.56 4.96 5.55 7.99 –
3 4.75 5.22 5.99 17.60 –
2.5 5.78 5.70 7.48 16.7 –
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in between 1 and 6. They used a generalized Hoek–Brown
(GHB) failure criterion, and the computer modelling code
to perform the finite element limit analysis was written in
MATLAB. They have found that increasing cover/width
ratio increased the stability (magnitude of load factor) of the
twin tunnel. If one has a given width of the cellar, the cover
thickness influences the stability of the cellar and the SRF
is not proportional with the thickness of the cover, Table3.
In this study, we focused on the differences in pillar width
and its effect on deformations under a given load. These
results suggest that maximum displacement was reached
when the cover was thin; but increasing cover thickness did
not cause a gradual decrease in displacement, but from a
cover of 4–4.5m, the displacements were increasing with
increasing cover thickness. Compared to elliptical shape sin-
gle natural cavities (Benito Olmeda etal. 2020), it was found
that strength and condition of rock mass, thickness of the
cover, width and value of the load were found to be the most
affected parameter on the bearing capacity of the foundation.
In summary, similarly to our study the bearing capacity of
the foundation under fixed foundation load is increasing with
the increase of the cover of the cavity in the studied range.
Similarly to the study of Benito Olmeda etal. (2020) in
which a natural cavity with significant dimensions were
Fig. 11 Roof displacements for all depths and pillar's widths under load 150 kN/m2
Fig. 12 Displacements in the cross section, where the cover = 5.5m and pillar width = 2.5m, with showing the roof displacements’ point
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studied using FLAC3D computer code to calculate the bear-
ing capacity of a foundation the pillar width and the thick-
ness of the cover are the main control factor of the stability
according to our results (Tables3 and 4). However, they
have also emphasized that the thickness of the cover, the
eccentricity of the load, the rock type (mi) and strength and
condition of rock mass are also important parameters on the
bearing capacity of the foundation.
In dual squared tunnels in a rock mass with surface load
(Xiao etal. 2019) the displacements were modelled by
Plaxis 2D. They demonstrated that for shallow depth, the
stability number increases with increasing the space between
the tunnels to diameter (L/B) value till it reaches the upper
limit. The same results were obtained from the graphs, while
the ratio (H/B) increased. Yamamoto etal. (2011) studied
single shallow circular tunnel in soil with surface load; the
study covered changes in cover to diameter ratio (H/D) and
soil properties to find the stability number of the tunnel.
Their results showed that for good soil properties (such as
ϕ = 30°) the stability number increased with increasing the
(H/D) ratio, in another words: if we fix the dimension of the
diameter (D) so the increasing of H increase the stability
number, as the result of our study, Table3.
The collapse of subsurface galleries can also be attributed
to natural processes and not necessarily by human activ-
ity linked an increase in surface load. Several examples are
known, where limestone quarries are collapsed due to pillar
instability, such as a mine in Pennsylvania (Esterhuizen etal.
2018). Newly formed sinkholes can also lead to the collapse
of abandoned shallow underground limestone quarries, such
as the ones in Belgium (Van Den Eeckhaut etal. 2007).
Conclusions
Porous limestone was intensively quarried for dimension
stone from the nineteenth century in the Budapest region.
Similarly to France, Italy and other countries of the Mediter-
ranean region, it is one of the major construction materials
of the monuments of the city.
The limestone was quarried in subsurface areas forming
an extended network of cellar side corridors. These sub-
surface galleries pose a high risk due to the thin cover, and
building load often collapse.
To estimate the risk of collapse, geometries of cellars
were measured and used in computer modelling with vari-
ous geometries, including cover thickness width of pillars.
Calculations with a 2D finite element program (RocSci-
ence2) software were performed using input parameters of
the mechanical properties of porous limestone obtained from
laboratory tests and cellar geometries measured by TLS.
As a result of 70 different scenario modelling, the safety
factor increases, and the displacement decreases with the
increasing cover of the cellars to a certain depth. However,
the trend is not uniform, and it turns, namely, the cellars that
are located deeper than 4m show larger displacements and
reduced factor of safety. It suggests that rock stresses due
to rock load become more crucial at deeper cellar settings.
Fig. 13 Maximum (M) and roof (R) displacements for pillar width 2.5m and 1.5m as a function of the cover
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Environmental Earth Sciences (2022) 81: 414
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Page 13 of 15 414
Based on these model results, it is possible to determine
the critical depth and critical width of pillars under critical
load for this type of porous limestone. It is necessary to
emphasize that these results are valid for dry conditions,
and water saturation reduces the strength of limestone
almost to half; thus, inundation of cellars often lead to
failure and roof collapse.
Acknowledgements The research reported in this paper is part of
project no. BME-NVA-02, implemented with the support provided
by the Ministry of Innovation and Technology of Hungary from the
National Research, Development and Innovation Fund, financed under
the TKP2021 funding scheme.
Funding Open access funding provided by Budapest University of
Technology and Economics.The research was partly funded by project
Fig. 14 Displacement as a function of cover thickness: a previous works (Vu etal. 2015) and this study; b enlarged graph showing the results of
this study
Content courtesy of Springer Nature, terms of use apply. Rights reserved.

Environmental Earth Sciences (2022) 81: 414
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414 Page 14 of 15
no. BME-NVA-02 (Ministry of Innovation and Technology of Hungary
from the National Research, Development and Innovation Fund), under
the TKP2021 funding scheme.
Declarations
Conflict of interest All authors declare that they have no conflict of
interest.
Open Access This article is licensed under a Creative Commons Attri-
bution 4.0 International License, which permits use, sharing, adapta-
tion, distribution and reproduction in any medium or format, as long
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