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ORIGINAL ARTICLE
Environmental Earth Sciences (2024) 83:566
https://doi.org/10.1007/s12665-024-11849-y
environmental issues such as water pollution (El Khalil et al.
2008), soil contamination (Montalván-Olivares et al. 2021),
loss of wild biodiversity (Murguía et al. 2016) or subsidence
(Hamdi et al. 2018; Mason et al. 2021). Consequently, there
is a need for new methodologies to improve mining prac-
tices and reduce environmental impact, as seen in initiatives
like the Responsible Research Innovation (RRI) from Hori-
zon 2020, which aims to make industries more inclusive
and sustainable (Iatridis and Schroeder 2016). In addition,
responsible mining has a positive impact on the economic
growth of the mining industry (Yousean et al. 2024).
Underground mining is particularly associated with sub-
sidence, aecting both mining infrastructure and inhabited
areas (Pipia et al. 2007; Perissin and Wang 2011; Solar-
ski et al. 2022). Subsidence can be classied as a direct or
indirect process; on the one hand, direct processes such as
post-mining voids to the surface; on the other hand, mining-
induced dewatering, which in some mining operations is a
key aspect and has typically been understudied (Guzy and
Witkowski 2021). Moreover, other indirect processes can
Introduction
The availability of mineral resources and the technological
capacity to obtain and use them are two primary determi-
nants of a nation’s prosperity and are essential for our soci-
ety’s development (Bascompta et al. 2022). However, the
improper exploitation of raw minerals can cause signicant
Nor Sidki-Rius
nor.sidki@upc.edu
Marc Bascompta
marc.bascompta@upc.edu
Lluís Sanmiquel
lluis.sanmiquel@upc.edu
Maria Teresa Yubero
maria.teresa.yubero@upc.edu
1 Department of Mining, Industrial, and ICT Engineering,
Polytechnic University of Catalonia, Av. de les Bases de
Manresa, 61, 73, Manresa, Barcelona 08242, Spain
Abstract
Subsidence is one of the main environmental impacts of underground mining worldwide. Besides, the increasing complex-
ity of underground mining due to greater depths and interaction with inhabited and environmentally sensitive areas can
lead to challenges that may threaten the viability of mining due to phenomena such as subsidence. This research aims
to increase the knowledge about surface subsidence due to underground mining, characterising the main factors that rule
mining subsidence utilising an actual mine that extracts potash. The calculation methodology was based on 74 sections of
the subsidence basin, using GPS measurements and the InSAR technique, with data collected over twelve nonconsecutive
years from 1995 to 2021. Thus, three dierent active areas and one residual area were determined. Average boundary
angles and their average distances of inuence for the active regions have also been determined. Furthermore, using the
least squares method, the subsidence basin curve was dened using a Gaussian function. The algorithm that governs the
subsidence process has been successfully calculated, allowing the approximation of the deformation of any point within
an area of interest. The novelty of this paper is twofold: the results obtained provide a detailed subsidence behaviour
and a prediction model of the case study. Furthermore, the methodology implemented can be applied to other subsidence
basins with mines in their area of inuence. Hence improving the surface mining area’s safety levels and managing the
environmental impacts.
Keywords Underground mining · Subsidence · InSAR · GPS · Environmental impact
Received: 31 January 2024 / Accepted: 6 September 2024 / Published online: 26 September 2024
© The Author(s) 2024
Denition of characteristic subsidence parameters. A case study in the
Catalan potassium basin
NorSidki-Rius1· MarcBascompta1· LluísSanmiquel1· Maria TeresaYubero1
1 3
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Environmental Earth Sciences (2024) 83:566
be found in subsidence due to mining-induced earthquakes
(Malinowska et al. 2018; Witkowski et al. 2024). Both types
of subsidence can be related to the extraction of essential
mineral resources, such as groundwaters or potash (San-
miquel et al. 2018; Figueroa-Miranda et al. 2018).
The main use of potash ore is as a fertiliser, and now-
adays, its use is essential for the continued production of
crops (Zörb et al. 2014). Therefore, it can be considered a
vital ore in reducing world hunger. For example, more than
828 million people worldwide suered from hunger in 2021
(FAO et al. 2022). Moreover, the United Nations stated in
2022 that 17 Sustainable Development Goals (SDG), espe-
cially the second SDG, “Zero Hunger”, and the fteenth
“Life on Land”, are completely linked to potash extrac-
tion. Potash extraction, often through deep underground
mining, poses signicant environmental challenges, espe-
cially related to subsidence (Broughton 2019; Ushakova et
al. 2023). Several environmental impacts on the surface of
the mine can be developed due to the mining works (War-
ren 2016; Ushakova et al. 2023). It is well-known that the
main impact of the construction of underground potash ore
deposits involves geotechnical challenges, mainly related to
time-dependent behaviour (Campos de Orellana 1996; Cor-
thésy et al. 2003; Marketos et al. 2015; Minkley et al. 2016;
Yubero et al. 2021) and subsidence processes (Yerro et al.
2014; Modeste et al. 2021). The eects of subsidence pro-
cesses appear mostly on the surface, such as cracks, changes
in the topography of the ground or even collapses (Baryakh
et al. 2016; Baryakh and Samodelkina 2018). Although
deposits deeper than 1,000 m are not common, there are
some examples, such as the Saskatchewan ore deposit
(Canada), which is one of the unique examples of long-term
potash mining at such depths (Van Sambeek 1997; Ong et
al. 2007; Samsonov et al. 2014; Baryakh et al. 2021). Nowa-
days, several deep potash mines are under construction or
have already been built in countries like Russia or Spain
(Baryakh et al. 2015, 2021; Sanmiquel et al. 2018; Sidki-
Rius et al. 2022), representing a challenge to reconcile their
exploitation with the needs of the surrounding ecosystem.
Numerous studies have investigated subsidence phenomena
and their environmental implications, primarily focusing
on subsidence basins due to soft ground tunnelling or coal
mining. One of the earliest geotechnical studies on ground
subsidence in clay soils was conducted by Terzaghi and
Peck (1948). In subsequent years, Schmidt (1969) examined
theories and methods to predict ground movement from soft
ground tunnelling. Clough and Schmidt (1981) discussed
geomechanical behaviour in soft clay excavations and tun-
nels. O’Reilly and New (1982) reviewed settlement and
ground movement measurements in UK tunnelling projects
covering various soil types. Rankin (1988) guided the esti-
mation of the eects of tunnel construction in urban areas
with soft soils, including empirical approaches for dening
subsidence zones, assessing surface movement, and propos-
ing risk classications.
Coal mining has historically caused subsidence, as has
the extraction of metalliferous ores, critical raw materials,
and overexploitation of groundwaters (Behera and Rawat
2023). Key works are reviewed to understand subsidence
management better. In 1975, the National Coal Board devel-
oped a method for characterising subsidence basin param-
eters after analysing several coal ore deposits in the United
Kingdom. Kratzsch (1983) presented the eects of surface
ground and shaft damage due to mining, outlining the basis
of knowledge of ground movement at that time. Using an
integrated approach, Peng (1992) dened and determined
subsidence basin parameters by analysing 110 cases from
major US coal deposits. Garrett (1996) highlighted the com-
mon techniques and risks in potash mining, emphasising the
need for case-specic analysis. Sheorey et al. (2000) ana-
lysed discontinuous subsidence processes in Indian coal-
elds using the inuence function methodology. Toraño et
al. (2000) used the prole function methodology to predict
subsidence from steep coal seam exploitation. Yan et al.
(2021a) applied theoretical analysis to study surface sub-
sidence boundaries due to horizontal coal seam mining. As
previously stated, other examples of subsidence caused by
the extraction of economically valuable ores, such as metal-
liferous or critical raw materials, can be found in works like
Contrucci et al. (2019), where the post-mining ground risk
was assessed in an iron ore deposit located in France. The
overburden of the area was found to be completely faulted,
which makes the monitoring inecient. Finally, GNSS
technology was identied as the best to monitor the area.
Furthermore, in the study of Murguía and Bringezu (2016),
a novel methodology was presented to measure the cumula-
tive area disturbed based on analysis of satellite images. The
authors analyzed several ore deposits, including Critical
Raw Materials (CRM), such as gold, silver, copper bauxite
and iron. Finally, focusing on subsidence caused by overex-
ploitation of groundwater, Abidin et al. (2008) developed a
study about the characteristics of land subsidence caused by
overexploitation of groundwater resources InSAR and GPS
technology. Their research suggests a framework for sus-
tainable subsidence monitoring that shares the same satellite
methodology as the current study. Other examples can be
found in the studies done in the city of Calcutta, where the
overexploitation of groundwaters produced subsidence of
11 mm/year in the south part of the city, and the vicinities of
the metropolitan area subsidence rate reached values of 5 to
6 mm/year (Behera and Rawat 2023; Chatterjee et al. 2006).
In recent years, research on infrastructure-related subsid-
ence processes, such as tunnels and roads, has increasingly
utilised technologies like Interferometric Synthetic Aperture
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Environmental Earth Sciences (2024) 83:566
Radar (InSAR) and the Global Navigation Satellite System
(GNSS). Yan et al. (2021b) examined subsidence impacts
from tunnelling at the Beijing-Zhangzhou railway, high-
lighting InSAR’s role in analysing subsidence in soft clay.
Bonì et al. (2015) monitored a severe subsidence process
over 20 years in the Alto Guadalentín area, Spain, using
DInSAR techniques due to aquifer overexploitation. Bitelli
et al. (2000) proposed a levelling network linked to a GPS
network to monitor subsidence in the southern Po Valley,
where anthropogenic activities increased subsidence rates.
Mancini et al. (2009) assessed subsidence in Tuzla, Bosnia
Herzegovina, due to solution mining of a salt deposit, nd-
ing a correlation between subsidence rate and salt mining.
Buzzanga et al. (2020) analysed subsidence in Hampton
Roads, Virginia, using a combination of InSAR and GPS.
Despite several contributions to the eld of land sub-
sidence, there is a lack of understanding regarding subsid-
ence processes in geological environments like potash ore
deposits. For example, Rucker et al. (2013) identied three
subsidence zones using InSAR following a brine well col-
lapse in New Mexico but did not quantify subsidence basin
parameters. Baryakh et al. (2021) studied subsidence from
deep potash mining in Russia using the Finite Element
Method (FEM) to improve boundary angle values, though
combining FEM with InSAR and GPS data could enhance
accuracy (Sidki-Rius et al. 2022). This highlights the impor-
tance of researching surface subsidence in potash mining
and underscores the need for accurate subsidence proles
and parameters for eective land management.
This study characterises the parameters governing sub-
sidence in the Catalan Potash Basin (CPB) from 1995 to
2021, aiming to improve land subsidence management. The
methodology employs advanced remote sensing techniques,
specically InSAR and GPS, to provide a detailed analysis
and understanding of the subsidence processes over time.
Furthermore, this research calculates and denes subsid-
ence proles in the study area, which leads to identifying
and quantifying subsidence parameters, including boundary
angle and the distance of inuence (Knothe 1957; National
Coal Board 1975). In addition, the characteristic subsidence
function has been approximated to the Gaussian function
using the least squares methodology.
Case study
The Catalan Potassium Basin (CPB) is located in the Ebro
Basin, Spain (Cendón et al. 2003). The CPB is 150 km2,
and it can be subdivided into east and west sides regarding
the main ore deposits, namely W-CPB and E-CPB, respec-
tively. The case study was carried out based on data from the
east side. Figure 1 consists of two complementary sections,
a satellite image showing the Ebro Basin and the Catalan
Potash Basin (CPB), which is further divided into eastern
and western segments as previously noted. Additionally, a
geological prole (A-A’) is provided to enhance the map’s
representation, illustrating the characteristic folded struc-
tures of the region.
All the layers of the deposit are stratied with the pres-
ence of clay minerals. The layers forming the deposit are
bent due to the tectonic forces experienced during the
Alpine orogeny and the well-known ductility of the salt
Fig. 1 The satellite image high-
lights the Ebro Basin in yellow
and the Catalan Potash Basin in
red. The case study is located on
the eastern side of CPB (E-side).
The white line indicates the
direction of the geological prole
(A-A’) depicted below the satel-
lite image (according to Vergés
1999)
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Environmental Earth Sciences (2024) 83:566
deposit is mined using the room and pillar method, with
extraction depths varying from 500 to 700 m. The average
prole size of the mining drifts is from 6 m to 15 m in height
and a width size ranging from 8 m to 10 m, with an aver-
age horizontal distance between tunnels of 9 m, in case of
materials (Campos de Orellana 1996). Figure 2 shows the
stratigraphic column of the main ore deposit of E-CPB. The
mining zone has two dierent mineable layers (layers A and
B), composed of sylvite and rock salt in between with an
intermediate layer consisting of salt (see Figs. 2 and 3). The
Fig. 3 Mine design options depend on the arrangement of the ore layers (after Sanmiquel et al. 2018)
Fig. 2 Stratigraphic column of the
study area (based on Campos de
Orellana 1996)
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Environmental Earth Sciences (2024) 83:566
believed to happen due to the propagation of post-mining
void; in the study area, there is no evidence that the subsid-
ence process is linked to an indirect impact, such as rock
mass drainage. The model was developed using classical
equations dening surface subsidence parameters (National
Coal Board 1975). For this purpose, the topographic char-
acteristics of the terrain were considered using measure-
ments carried out over non-consecutive twelve years from
1995 to 2021. In Table 1, a correlation between periods and
techniques employed is shown. The case study has been
monitored over an area of 46 km2 using GNSS and InSAR
technology. The set of GNSS control points has been used
to cover the whole area aected by the subsidence process.
Additionally, InSAR imagery has been used to comple-
ment the monitoring system. Although some urban regions
exist, the target area is dominated by forest and agricultural
land. GNSS and InSAR methods were employed due to
their reliability and accuracy in mining subsidence research
(Amelung et al. 1999; Rucker et al. 2013; Diao et al. 2019;
Modeste et al. 2021; Babayants et al. 2023). Only in the rst
periods, 1995 to 2003 and 2003 to 2008, were the measure-
ment campaigns developed by the mining company, and the
methodology used was classic total station topography. In
2008, the data was transferred to the research group, and a
new methodology was established using GNSS; in 2016, in
collaboration with an external company specialised in Inter-
ferometric technology, InSAR was coupled to GNSS as a
new subsidence monitoring method.
The GNSS method used is based on static dierential
GPS with dual frequency receivers, using four devices. This
way, two are considered bases, placing them in two well-
identied coordinate points. The other two devices are used
to measure the control points. The minimum measurement
time for each control point is 12 min. Thus, for each point,
it was possible to obtain the coordinates in the three axes,
X, Y, and Z, with a Root Mean Square Error (RMSE) of
two centimetres, taking into account that the methodology
used has an accuracy of one centimetre in planimetric and
altimetric coordinates. In addition, a double quality control
has been performed with the following steps: Firstly, dur-
ing the GPS post-process, using the Magnet Tools software
(version 6.1.0.), a warning is set o when an error higher
than two cm is detected when the error is detected, the point
is remeasured twice within a one-week gap. Secondly, some
points are randomly selected to be remeasured periodically
to control if there is any problem with the measurement.
InSAR technology combined with GNSS points has an
associated RMSE of two centimetres, making it a well-
established and reliable method (Sanmiquel et al. 2018).
The given approach used an average of 176 InSAR images
from the SENTINEL-1 satellite coupled with an average of
241 GNSS points; details are shown in Table 1.
a salt layer between A and B being thicker than 5 m, two
drifts are excavated to extract the potash ore, this type of
mining design can be located in the northern part of the ore
deposit (see Fig. 3). The extraction rate, depending on the
arrangement of the layers, ranges between 60% and 70%.
The average mineral excavation rate from 2015 to 2020 was
3 million tons.
Methods and materials
The following three sections will describe the methodology
used. Firstly, the database was created based on GNSS and
InSAR techniques. Following this, a specic methodology
was designed based on CAD software coupled with the
abovementioned methods. The denition of nine sections
allowed the study of 74 subsidence proles, which pro-
vided an accurate analysis of the selected area. Finally, a
hybrid methodology combining the methods proposed by
the National Coal Board (1975) and the approximation of
the subsidence curve by a Gaussian distribution using the
least squares method has been successfully applied.
Database creation
An analysis was carried out to identify the typical values
dening the surface of a subsidence basin, as well as the
angles and the governing function. An analysis was car-
ried out to identify the typical values dening the surface
of a subsidence basin, as well as the angles and the gov-
erning function. The total value of surface displacements is
Table 1 Correlation between periods and methodologies used
Initial
year
End year Techniques used in measurements
1995 2003 Surveying by total station. Measurement with
an average of 600 control points
2003 2008
2008 2010 Surveying by GNSS. Measurement with an
average of 1000 points
2010 2012
2012 2014
2014 2016
2016 2017 Surveying by GNSS and InSAR technology.
Measurement of 246 GNSS control points
combined with 201 images from SENTINEL-1
2017 2018 Surveying by GNSS and InSAR technology.
Measurement of 305 GNSS control points
combined with 142 images from SENTINEL-1
2018 2019 Surveying by GNSS and InSAR technology.
Measurement of 282 GNSS control points
combined with 142 images from SENTINEL-1
2019 2020 Surveying by GNSS and InSAR technology.
Measurement of 147 GNSS control points
combined with 175 images from SENTINEL-1
2020 2021 Surveying by GNSS and InSAR technology.
Measurement of 224 GNSS control points
combined with 220 images from SENTINEL-1
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Environmental Earth Sciences (2024) 83:566
can be formed in the case study (Sanmiquel et al. 2018) and,
therefore, it may be possible to detect a well-formed subsid-
ence base in all of them and see how progresses. According
to nine sections and the displacement surface for each indi-
cated period, 74 subsidence basin proles were analysed.
The proposed methodology allows the calculation of the
distance of inuence by establishing the start and end parts
of each subsidence prole and the total depth for each sub-
sidence prole. In Fig. 6, accumulative subsidence basin
proles of Sect. 01 are shown; each colour indicates a dif-
ferent period to observe its evolution over time; it can be
noticed that the subsidence prole becomes better dened
as the period increases, since with time, mining infra-
structure increases. The maximum subsidence recorded is
325 cm with an inection point of 150 cm. Although the
maximum subsidence depth ranges between 100 cm and
325 cm for the 74 proles mentioned, they all follow a simi-
lar proportion, with their inexion point around 40–50% of
their maximum subsidence. Considering the RMSE for both
The deployment of InSAR with GNSS data in a Geo-
graphic information system (GIS) software provides a
digital vertical displacement model for the whole period.
Consequently, utilizing the GIS software’s curvature anal-
ysis functionality, a detailed subsidence surface for each
period is feasible (Fig. 4).
Database management
AutoCAD and TCP-MDT software were used to analyse the
subsidence surfaces. Nine sections were selected in the area
aected by subsidence (Fig. 5); four of them cross the target
area from East to South West, identied with numbers (1
to 4), while ve vertical sections from North to South (A
to E). A Metric Point (MP) is considered every 10 m in all
sections of the twelve periods, showing the displacement in
the Z-coordinate. The calculation periods used to determine
each subsidence base are accumulative, using more than
ve years, which corresponds to 90% of the subsidence that
Fig. 5 The mining infrastructure
built from 2008 to 2020 is shown
in red, and the nine sections are
pink
Fig. 4 Methodology proposed to
calculate the subsidence surface
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Environmental Earth Sciences (2024) 83:566
The boundary angle is dened by the zero-subsidence
point and the total depth of the mining drifts. Considering
this denition, it can be calculated following the mathemati-
cal relationship stated by the National Coal Board (1975),
as shown in Fig. 7. Determining the characteristic boundary
angle for the area of interest was done through statistical
calculation. Finally, Fig. 8 shows the methodology used up
to the reaching point of the characteristic boundary angle
and distance of inuence.
Characteristic function of the subsidence basin
The eect of underground mining drifts on the surface
topography is inevitably associated with the resulting
ground movements in a subsidence basin. A considerable
amount of data is available from eld measurements of
techniques used, the accuracy of the subsidence basin pro-
les can be conrmed. Mining subsidence is a phenomenon
that is closely related to the mining excavation ratio, among
other geological and mining parameters (Hunt 1980; Salmi
et al. 2017; Sasaoka et al. 2015; Diao et al. 2019). Points in
red indicate zero subsidence (start and end point of subsid-
ence basin). Taking these points and the mining map into
account from 1995 to 2021, it was possible to determine the
distance of inuence, which is the shortest distance between
the point of zero subsidence and the nearest mining drift,
allowing the determination of the distance of inuence for
all subsidence proles. However, to calculate the total depth
from the surface to the drift, it was necessary to check the
cartographic maps available from the Cartographic and
Geological Institute of Catalonia (ICGC) since the depths
indicated on the mining map are referenced to sea level.
Fig. 7 Mathematic relationship
scheme
Fig. 6 Example of 11 subsidence basins from 2003 to 2021
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Environmental Earth Sciences (2024) 83:566
where Svmax is the maximum surface subsidence at the cen-
tre line of the tunnel or drift, Sv is the surface subsidence at
displacement distance x from the tunnel centre line, x is the
horizontal distance from the centre line, it is the horizontal
distance from the centre line to the inexion point in the
subsidence basin.
Alternatively, O’Reilly and New (1982), based on mon-
itoring data from several tunnels in the UK, were able to
prove that the horizontal surface displacements occur in the
transverse direction of the excavation axis and, assuming
that the resulting displacement vector is oriented towards
the tunnel, the horizontal movement can be expressed as
follows:
surface settlement proles on tunnels in clays. Figure 9
has been used to summarise the settlement trough adopted
from several research, where the surface vertical settlements
and horizontal stress and displacement are shown (Schmidt
1969; Peck 1969; National Coal Board 1975; Clough and
Schmidt 1981; O´Reilly and New 1982; Rankin 1988; Peng
1992). The green eld settlement prole, which can repre-
sent the prole of a subsidence basin over a single tunnel,
can generally be approximated by the error function or nor-
mal probability curve (also known as the Gaussian curve)
as follows:
S
v(x)=Svmax expexp
−x
2
2i
2
x
(1)
Fig. 9 Distribution of horizontal strain, surface displace-
ments, boundary angle and surface vertical settlements
trough (based on O´Reilly and New 1982)
Fig. 8 Methodology proposed to calculate the boundary angle and the distance of inuence
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Environmental Earth Sciences (2024) 83:566
Results and discussion
The following sections describe the results obtained. They
present the division between active and residual subsidence
areas, characteristic boundary angles, and distances of inu-
ence. In addition, they provide the characteristic parameters
of the subsidence basin function obtained from tting the
curve to a Gaussian distribution using the least-squares
method.
Active and residual areas in the Catalan Potash
Basin (E-CPB)
The methodology enabled the comparison of several sub-
sidence proles over a decade. Therefore, detecting the
progress of active and residual subsidence areas was pos-
sible. Four subsidence areas were determined in the E-CPB
and classied according to the cardinal directions. Three
of them, the northern, the southwestern, and the south-
ern regions, were dened as active areas. In contrast, the
eastern area was considered to be in a residual subsidence
process, given that there has been no mining activity since
2009. Non-cumulative proles were used to conrm the ten-
dency. An example of this trend is displayed in Fig. 11. The
sequence of proles A-A’, B-B’, C-C’ and D-D’, all from
the period of 2020–2021, shows that the subsidence basin is
stable in proles located in the eastern area, therefore, cate-
gorising them into a residual subsidence process in contrast
to the proles A-A’ and B-B’ which belong to an active one.
Characteristic boundary angle and distance of
inuence
The procedure discussed earlier achieved the criteria of
boundary angle and distance of inuence. Previous stud-
ies determined a general value of the subsidence angle of
35º (Sanmiquel et al. 2018). However, the proposed new
approach allowed the study of the specic areas of the
subsidence basin by means of 81 proles from 12 dier-
ent periods. In this regard, three values for the character-
istic boundary angle and distance of inuence have been
calculated. In Fig. 12, a graphical scheme of the target area
(shown in red), the selected sections (demonstrated in pink),
the characteristic average boundary angles
(α)
, and dis-
tance of inuence
(d)
are displayed (highlighted in green,
blue and yellow). The highest value of the boundary angle
is 71˚ in the northern zone, reaching its minimum value, 38˚,
in the southern zone. The distance of inuence is inversely
proportional to the boundary angle trend, and, therefore,
it experiences a value of 240 m in the north area while it
soared to 988 m in the south. Furthermore, as presented in
S
hx =
xS
v
(x)
z0
(2)
where z0 depth of the tunnel or drift centre line, Shx is the
horizontal movement at displacement distance x from the
tunnel centre line.
The horizontal displacement corresponds to the inec-
tion point of the subsidence basin. The horizontal defor-
mation can be calculated by deriving the aforementioned
expression (Eq. 2):
ε
hx (x)=Sv(x)
z0
x
2
i
2
x
−
1
(3)
Where the i parameter is the inection point of the subsid-
ence basin,
εhx
is the strain or horizontal deformation, and
Sv
is the surface subsidence at oset distance x from the
tunnel centerline.
In subsidence engineering, the terminology “deformation
or strain (ε)” is the change in length over a piece of ground,
expressed either as a dimension over the whole length or as
a fraction of the unit of length. The direction is always spec-
ied with extensions and compressions, indicated by a + and
– sign, respectively. Furthermore, the degree to which any
surface site may be expected to tilt as a result of subsid-
ence is calculated from the subsidence prole. Prediction
of deformation from curvature is a useful tool that can be
applied to any part of any prole.
The curvature can be calculated by dividing the subsid-
ence dierence by the distance between the observed sta-
tions (STN), which gives the slope (θ), determining the
curvature and the strain. An example can be seen in Fig. 10.
Fig. 10 Example of strain curvature (based on National Coal Board
(1975)
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Environmental Earth Sciences (2024) 83:566
drift was required, as the salt layer between the two potash
beds had a thicker less than 5 m. However, other mining and
geological factors might also aect it, as it is stated that the
rate of exploitation or the depth at which the mining gal-
leries are located can also be key factors in the subsidence
process (Hunt 1980; Sahu et al. 2017).
The main limitation of the study is the lack of under-
standing of the reason for the dierence between boundary
angles and inuence distances. Although it can be seen that
the geological structures or the mining designs used in the
study area could be inuencing parameters, future studies
will be required to conrm which has the most inuence on
the subsidence that occurred in the CPB.
the 3.1 section, the southeast zone corresponds to a stabi-
lised subsidence basin (highlighted in grey).
A possible explanation for the variation of the bound-
ary angle and the distance of inuence could stem from the
area’s geological structure. The case study (Section “Case
study”) showed that the area was folded due to alpine orog-
eny forces. Considering Fig. 13, in the northwestern part
of the study area, a thrust fault between the anticlinal and
syncline folds can be seen, which could be one of the factors
that cause the north and west boundary angles to be greater.
Another factor that might cause the dierence in bound-
ary angles and distances of inuence might be the design
of the mining drifts. In contrast, in the northern part of the
mine, two mine drifts were used to extract layers A and B,
and in the southern part of the ore deposit, only one mine
Fig. 11 (a–d) Sequence of proles A-A’, B-B’, C-C’ and D-D’, from 2020 to 2021
1 3
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Environmental Earth Sciences (2024) 83:566
obtained. From the values of parameter i, the horizontal
deformation was calculated following Eq. 3.
The average values of the strains are proportional to θ/l,
with horizontal deformation, have been determined within
reasonable limits of accuracy and are shown in the predic-
tion graph (Fig. 16). This gure provides a quantied rela-
tionship between deformation and θ/l, as follows (Eq. 4).
θ
l
=(deformation)
2
x
(4)
x (parameter dimensionless) varies between 0.018 and
0.012 from the proles shown in 2018 (θ/l), which gives the
dierential slope between two values with subsidence data.
In this case, a new algorithm has been tted more accu-
rately to all data between 1995 and 2021, obtaining all val-
ues in the proposed range in 2018 (0.018 and 0.012) but with
a higher concentration of x values between (0.015 − 0.013).
Eventually, it can be said that a new algorithm was success-
fully obtained, according to the eld data. Therefore, the
new algorithm calculates the horizontal ground deforma-
tions at any point of the subsidence basin. In addition, based
on the recently calculated limit, a lower deformation value
is suggested.
Approximation of the characteristic function of the
subsidence basin
In the study by Sanmiquel et al. (2018), four sections were
analysed beyond the zone of inuence from 2008 to 2016;
sixteen cross-settlement proles were measured in the four
sections. However, with this new approach, it has been pos-
sible to gather more subsidence data, as nine proles have
been dened in the period 1995 and 2020 (see Figs. 6 and
10), providing 99 transverse settlement proles, of which
74 have been analysed, this represents a more accurate
approach than in the previous study. Additionally, these
results have allowed us to compare them with the data
published by Sanmiquel et al. (2018), and consequently,
the tuning of the proposed algorithm has been improved.
An example of the transverse settlement proles 1–1’ from
1995 to 2021 can be seen in Fig. 14.
As in the London clay materials, in the saline materials,
the shape of the surface subsidence proles are reasonably
well represented by a Gaussian distribution, Eq. 1 (Mair et
al. 1993). The Gaussian curve was successfully tted to the
eld data using the least square method (Fig. 15).
The width of the settlement prole is dened by the
important parameter (i), which is the distance from the cen-
terline of the trenches to the inexion point of the trough
(shown in Fig. 15). This parameter has been obtained from
the Gaussian curve adjusted to the eld data, obtaining a
value of I for each transverse cross-section of the subsid-
ence proles. Seventy-four values of parameter “i” were
Fig. 12 Average boundary angle
and distance of inuence of the
active zones and the proles used
for the analysis
1 3
Page 11 of 16 566
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Environmental Earth Sciences (2024) 83:566
Fig. 14 Surface transverse settlement proles in the
section 1-1´
Fig. 13 Geological map of the
northwest part of the study area
(E-side in Fig. 1a), where a thrust
fault can be identied between
the anticline and syncline fold
1 3
566 Page 12 of 16
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Environmental Earth Sciences (2024) 83:566
southwest part, it reaches a value of 52˚ and eventually
reaches its minimum value, 38˚, in the southern zone.
4. The distance of inuence is inversely proportional to
the boundary angle trend; therefore, it has the smallest
value in the northern part with 240 m, the southwestern
part has a value of 624 m, and the maximum value is
988 m in the southern area.
In addition, the presented methodology allows using the
least squares method to approximate the subsidence curve
to the Gaussian function successfully. Moreover, the charac-
teristic parameters, such as the key parameters “i”,” x”, and
“θ/l”, were identied following the same methodology. The
subsidence process algorithm has also been accurately cal-
culated, allowing for a precise approximation of deformation
at any given point in the area of interest. This enhancement
signicantly improves the forecasting and prediction of the
subsidence basin, resulting in increased safety levels in the
mining area and its surroundings.
Conclusions
The research introduces a novel approach to characterise
and predict subsidence basins in the area of interest. This
new methodology allows for eciently handling large data-
sets to determine key parameters of any subsidence basin,
with potential applications in other subsidence basin case
studies. The analysis of 74 subsidence proles has been
done based on the methodology presented. Thus, the main
ndings of the case study are the following:
1. The area of interest has been divided into four zones
according to cardinal directions: North, South, East, and
Southwest.
2. The eastern zone is considered under a process of resid-
ual subsidence, while the other three belong to an active
subsidence process. In that case, it has been possible to
calculate their boundary angle and distance of inuence.
3. The highest boundary angle value is 71˚ in the north-
ern zone, decreasing towards the south. Thus, in the
Fig. 16 Relationship between
strain and θ/l meters
Fig. 15 Interpretation of measurements by an empirical Gaussian curve. (a) Section 1_1’_2016_2017 (b) Section 1_1’_2017_2018
1 3
Page 13 of 16 566
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Environmental Earth Sciences (2024) 83:566
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Finally, the presented method can constitute an appropri-
ate complement to upgrading the management of land sub-
sidence in mining companies, not only for its adaptability
and simplicity but also due to its eective, accurate, and
functional approach.
Author contributions All authors contributed to the study conception
and design. Material preparation, data collection and analysis were
performed by N. Sidki-Rius, T. Yubero, Ll. Sanmiquel. The rst draft
of the manuscript was written by N. Sidki-Rius, T. Yubero and M.
Bascompte. All authors commented on previous versions of the manu-
script. All authors read and approved the nal manuscript.
Funding Open Access funding provided thanks to the CRUE-CSIC
agreement with Springer Nature. The authors declare that no funds,
grants, or other support were received during the preparation of this
manuscript.
Open Access funding provided thanks to the CRUE-CSIC agreement
with Springer Nature.
Data availability No datasets were generated or analysed during the
current study.
Declarations
Competing interests The authors declare no competing interests.
Open Access This article is licensed under a Creative Commons
Attribution 4.0 International License, which permits use, sharing,
adaptation, distribution and reproduction in any medium or format,
as long as you give appropriate credit to the original author(s) and the
source, provide a link to the Creative Commons licence, and indicate
if changes were made. The images or other third party material in this
article are included in the article’s Creative Commons licence, unless
indicated otherwise in a credit line to the material. If material is not
included in the article’s Creative Commons licence and your intended
use is not permitted by statutory regulation or exceeds the permitted
use, you will need to obtain permission directly from the copyright
holder. To view a copy of this licence, visit http://creativecommons.
org/licenses/by/4.0/.
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