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Arch. Min. Sci., Vol. 59 (2014), No 4, p. 869–886
Electronic version (in color) of this paper is available: http://mining.archives.pl
DOI 10.2478/amsc-2014-0060
GRZEGORZ KORTAS*, AGNIESZKA MAJ*
DEFORMATIONS OF THE PROTECTION SHELF IN THE “WAPNO” SALT MINE,
BASED ON MODEL STUDIES
ODKSZTAŁCENIA PÓŁKI OCHRONNEJ W KOPALNI SOLI W WAPNIE
NA PODSTAWIE BADAŃ MODELOWYCH
The catastrophic mine failure resulting from the inrush of water into the Wapno Salt Mine was pro-
bably caused by a fracture in the roof protection shelf. The purpose of the present study was to apply the
method of the homogenization of the multi-level room-and-pillar structure in the Wapno Salt Mine for
3D+t modelling of the elastic-viscous medium to determine the distribution of stress and strain, and, on
that basis, to estimate the geomechanical conditions existing in the roof shelf. This paper presents briefly
the spatial development of the salt mine’s structure and the results of the surveying measurements carried
out during the salt mine’s operation and after the mine was flooded. Those results constituted a basis for the
verification of the introduced homogenization parameters, i.e. the time-dependent changes of the elasticity
modulus and the susceptibility to creep at particular salt mine’s levels. A simulated process demonstrated
the development of positive values of principle stresses, increasing with time, and of omnidirectional
tensile strains. In such conditions, the cracking of the protection shelf body could proceed, also with
opening of water flow paths from the dome cap into the salt mine’s workings. This paper presents a new
research method, the results of its application, and the obtained distribution of stresses and strains that
can be useful for the assessment of water hazard in other salt mines.
Keywords: salt dome, model studies, homogenization, protection shelf
Katastrofa górnicza wywołana wdarciem wody do kopalni soli w Wapnie spowodowana była
prawdopodobnie pęknięciem ochronnej półki stropowej. Celem tej pracy było zastosowanie metody
homogenizacji struktury komorowo-filarowej wielopoziomowej kopalni Wapno do modelowania ośrodka
sprężysto-lepkiego 3D+t dla określenia rozkładu naprężeń i odkształceń oraz na tej podstawie oszacowania
warunków geomechanicznych w półce stropowej. W pracy przedstawiono krótko rozwój przestrzenny
struktury kopalni oraz wyniki przeprowadzonych pomiarów geodezyjnych w czasie działalności kopalni
i po jej zatopieniu. Wyniki te były podstawą do weryfikacji wprowadzanych parametrów homogeniza-
cji, tj. zmian w czasie modułu odkształceń i podatności na pełzanie poszczególnych poziomów kopani.
Symulowany proces wykazał wykształcanie się rosnących w czasie dodatnich naprężeń głównych oraz
* STRATA MECHANICS RESEARCH INSTITUTE OF THE POLISH ACADEMY OF SCIENCES, UL. REYMONTA 27, 30-059
KRAKÓW, POLAND
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wszechstronnych odkształceń rozciągających. W takich warunkach postępować mogło spękanie calizny
półki ochronnej, a także otwieranie dróg przepływu wód z zawodnionej czapy wysadu do wyrobisk.
W pracy przedstawiono nową metodę badań, jej wyniki i otrzymane rozkłady naprężeń i odkształceń,
która może być zastosowana w ocenie zagrożenia wodnego kopalń soli.
Słowa kluczowe: wysad solny, badania modelowe, homogenizacja, półka ochronna
1. Introduction
The protection of underground salt mines against waters found in the formations that surround
salt domes consists primarily in the maintenance of tight surroundings of the room-and-pillar
structure by leaving protective shelf and pillars close to the salt dome boundaries. The tightness
of pillars and protection shelves is also important for the purpose of underground liquid or gas
storage in salt caverns (Ślizowski & Urbańczyk, 2012). The salt bodies are subjected to deforma-
tions which increase with time under the influence of workings. Such deformations are difficult
to measure. Based on the symptoms of rock mass movements, a view was formulated, claiming
that catastrophic inrush of water into the underground Wapno Salt Mine in 1977 could have
been initiated by the tensile strain of the roof protection shelf (Kortas, 1979). Only the presently
available research methods, applied to determine the influence of the mining workings on rock
mass and land surface (e.g. Kortas, 2007; Tajduś, 2013), allow us to verify such hypotheses and
use research results for an analysis of hazards in the locations displaying similar geological and
mining conditions.
The purpose of this paper is to present a new method of determining deformations within
the roof protection shelf, based on 3D+t model studies of the elastic-viscous medium, with the
application of homogenization of the room-and-pillar structure in the Wapno Salt Mine, as well
as to demonstrate that the hypothesis of the connection between the deformations occurring in the
roof protection shelf with water inflow is also realistic in the case of the geological and mining
conditions that are similar to those of the Wapno Salt Mine.
In this work, we have used the results of own research conducted under the project designed for
the assessment of the safety status of post-mining areas in Wapno (Kortas & Maj, in: Rasała, 2014).
2. Symptoms of the Rock Mass Movement in the Wapno
Salt Mine
The horizontal cross-section of the Wapno salt dome is similar to oval, with 900 m and
350 m axes. The salt dome cap is located under the Quaternary formations. It extends from the
depth of ca. 160 m up to the central section of land surface. The exploitation Levels (III-X) were
established under a 200 m roof protection shelf, with 50 m protection boundary pillars. At Levels I
and II (within the roof protection shelf), and XI and XII, only main galleries were excavated, with
single rooms at Level X in 1977. The 15 m wide pillars correspond to 15 m high rooms. Smaller
10 m high pillars were left at Level IV. Larger 20 m high rooms were excavated at Level IX. The
distribution of rooms in the Salt Mine is presented in Fig. 1.
First, salt was extracted from Level IV in 1920-1939. Extraction started at Level III in
1943 and it was completed in 1968. In 1952-1968 salt was mined at Levels V and VI. Later, in
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1960-1972, extraction was continued in parallel at Levels VII, VIII and Level IX. In the 1970’s,
Levels XI and XII were made available and prepared for mining. However, protection pillars
and shelves suffered deformations which were increasing with time. The most degraded were
the pillars between rooms at Levels IV and V.
By the end of 1930’s, surveyors started to measure land surface subsidence, while the
measurements of vertical benchmark displacements in the salt mine’s galleries started in the
1950’s. Surveying observations inside the Salt Mine, initiated by S. Szpetkowski and carried
out by J. Czajkowski, T. Malara, and L. Wesołowski, indicated the propagation of subsidence
and uplifts, depending on the locations of underground workings at lower and upper levels, and
those were changing with time (Fig. 2).
During the mining operations, the volumes of the working were regularly increasing, with
limited increase of land subsidence rates (Fig. 3). The rate of maximum land subsidence at Level
III reached –30 mm/year in 1961-1976, and that of land surface Benchmark 127 above: –16.2
mm/year. From 1973 to 1976, surveyors observed a regular trough at that level, displaying the
maximum subsidence rate of –46 mm/year. Although the maximum land surface subsidence rate
increased twice in the 1970’s, up to –30 mm/year, it remained much slower than that at Level III.
Consequently, the space containing the salt protection shelf and the salt dome cap was expanding
in the vertical direction. Also, volumetric tensile strain of the rock mass were increasing, which
was indicated by the estimated drop of the proportion of the subsidence volume to the workings’
volume in the periods until 1945 and until 1977, by 0.090 and 0.037, respectively.
Fig. 1. The diagram of the distribution of rooms at Levels III-IX
Level III - 384 m
Level IV - 405 m
Level V - 430 m
Level VI - 454 m
Level VII - 479 m
Level VIII - 508 m
Level IX - 543 m
Shafts
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Fig. 2. Profiles of the vertical displacements of levels in the Wapno Salt Mine (Kortas, 2008)
900 m
(9) +102 mm
+128 mm
(8) +109 mm
+198 mm
+110 mm
III level, 1961 - 1976
V level, 1957 - 1967
VII level, 1962 - 1976
VIII, IX level, 1968 - 1976
-440 mm
In the coridor along
the longitudal axis of the salt dome
In the coridor a long
the longitudal axis of the salt dome
In the cori dor along
close to the edge of the salt dome
In the coridor along
close to the edge of the salt dome
Fig. 3. The volume of the Wapno Salt Mine and the land subsidence in 1937-1977 [mm]
1920 1940 1960 1980
5.5
5.0
4.5
4.0
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0
Time t
[year]
The Volume o
f
Salt Mine
[mln m
3
]
127
56
168 171
Water inrush 5.08.1977
1940 1950 1960 1970 1980
-600
-500
-400
-300
-200
-100
0
Land Surface Subsidance
[mm]
Time
[year]
56
124
127
168 171
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The boundaries of the formations that are different in respect of deformability constitute
special places in the rock mass undergoing deformation. That is where we can expect the oc-
currence of extreme stresses, followed by cracking and slides that develop during the deposit
formation and movements caused by the influence of workings. In the case of salt domes, the
places like that include vertically arranged formations of anhydrite and the adjacent K-Mg salt
layers which are more rigid than regular salt deposits. Owing to the water hazard, the most
dangerous is the occurrence of tensile strains in the direction which is normal in respect of layer
planes. The locations of the vertical layers containing anhydrite at Level III of the Wapno Salt
Mine are shown in Fig. 4.
Fig. 4. Subsidence at Level III of the Salt Mine in 1973-1976, with the locations of the vertical layers
of anhydrite and K-Mg salts (left), and land surface subsidence in 1937-1976 (right)
Close to anhydrite layers, brine leaks appeared, first at Level IV and later at Level III. The
presence of surface water markers was identified in such leaks. The leaks occurred first at the
SW and NE boundaries of the salt dome, and, in recent weeks before the inflow of water into
the mine, they were developing in the working zone, along the line of anhydrite and K-Mg salt
interlayers. The increase of inflow, with concurrent decrease of salt concentration, led to the
catastrophic inrush of water into the salt mine on 5 August 1977 (Ślizowski & Kortas, 1980).
Several small sink-holes, caused by dewatering of the salt dome cap, appeared already within the
first 24 hours, followed by a large land subsidence developing close to the NE salt dome wall,
within several months (Figs. 5 and 6). More than 0.3 million cubic metres of liquefied clay and
sand materials were transported from the salt dome surroundings into the mine workings and
forty buildings were destroyed or damaged.
Wapno 1
Wapno 2
Saltdome
Mineworkings
-600
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Fig. 5. Land surface subsidence in Wapno before and after water inrush into the Salt Mine in 1977
(Maj, in: Rasała, 2014)
Fig. 6. A sink-hole in Wapno
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Considering the above-mentioned geological and mining conditions, as well as the indica-
tions of the influence of salt extraction on rock mass and land surface, the question arises whether
the mine workings’ effects could have caused such significant horizontal tensile strain within
the protection shelf to allow for the contact of water from the salt dome cap with the mine’s
workings, leading to flooding.
2. Research Method
2.1. Modelling Simplifications
When the roof protection shelf and the boundary pillars are tight, deformations and cracks
occurring inside the salt dome do not cause any direct water hazard to the salt mine. It is claimed,
however, that the roof protection shelf cracking is the cause of numerous inflows of water into
the diapir salt mines (e.g. Spackeler, 1953). In order to determine the boundary of safe deforma-
tions in the roof protection shelf, A. Sałustowicz considered the dependence of the bending of
an elastic beam loaded with mass forces (Sałustowicz et al., 1962), however, omitting rheologi-
cal viscous properties of salt rocks. By the end of the 20th century, we obtained a possibility of
numerical determination of the time-dependent stresses, strains, and displacements in an elastic-
viscous medium (e.g. Filcek et al., 1994; Kortas, 2008; Munson, 1997; Munson & Dawson,
1984; Ślizowski, 2006; and Ślizowski & Urbańczyk, 2004). In such numerical calculations, the
transformation of the geological rock mass and the geometrical salt-mine complexity require
the construction of 3D models in which the number of elements is considerably larger than 106.
The consideration of the time of workings’ excavation in elastic-viscous medium models causes
the repetition of even several hundred-step cycles of calculations after each change of the salt
mine’s geometrical structure. Since the calculation time of a single step takes a dozen or several
dozens of minutes and time increases exponentially with the number of elements, the calcula-
tion time cycle takes many weeks for each single task. Consequently, it is necessary to introduce
simplifications in geometrical and physical assumptions. That is the case especially when we
look for the physical model parameters under multi-task model studies by comparing calculation
results with measurement results.
Considering the object of study concentrating on the condition of the protection rock salt
body, the accuracy of the geometrical model of the working zone is not a primary goal. Some
parts of the salt mine space, e.g. particular salt extraction levels, can be replaced by an equivalent
medium, with appropriately changed parameter values. What is the condition of such replacement,
however, is the geometrical and physical similarity of the repeating parts of the room-and-pillar
structure of the particular level and the assignment of continuity to the area of the structure being
homogenized, using appropriate equivalent properties. Proceeding in a similar way, we usually
apply homogenization to replace the lithological complexity of rock masses.
The homogenization method of the extraction area and the room-and-pillar structure in
a salt dome was introduced for the first time in 2011. A 2D+t elastic-viscous model was used to
determine the behaviour of the mining field’s surroundings in the Kłodawa Salt Mine (Kortas &
Maj, 2012). In the research project discussed in the present study, time-dependent homogenization
of the salt mine space in a 3D+t elastic-viscous model was applied for the purpose of simulation
and determining the deformations of the roof protection shelf in the Wapno Salt Mine.
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2.2. Physical Model
Current world literature uses Hooke’s constitutive model, with Norton-Bailey’s power creep
law (Bailey, 1929; Norton, 1929) to salt medium as a standard. Hooke’s law of linear elasticity
can be recorded in the form of two tensor equations, binding stress with strain, where the first
one describes the rule of shape change and the second one the rule of volume change:
(1 )/ ; (1 2 )/
DDA A
ij ij m m
EE
(1)
where:
Dεij = εij – Aεmδij (δij — Kronecker’s delta) is the strain deviator,
Dσij = σij – Aσmδij — the stress deviator,
Aεm = 1/3(ε1 + ε2 + ε3) — the mean strain,
Aσm = 1/3(σ1 + σ2 + σ3) — the mean stress,
E — Young’s modulus, and
ν — Poisson’s ratio.
We have applied Norton-Bailey’s power creep law for the purpose of simulation and viscous
medium behaviour study, as determined by the following equation:
11
3exp[ / ( )]
2
nm
ij ef ij
mA Q RT t
(2)
where:
Q — is the activation energy,
R — gas constant,
T — Kelvin temperature, and
A, n, m — material constants.
The function of A, Q and R material constants determines the compliance of material to
creep B, in particular temperature T, as expressed by the formula:
exp[ / ( )]BA QRT (3)
The Huber-Mises-Henky effective stress σef was determined by the formula:
222
11 22 22 33 33 11
1()()()
2
ef
(4)
The stress tensor components in the main directions of σ11, σ22, σ33 are recorded as p1 > p2 > p3
in the present study. In the hydrostatic state of stress which occurs in salt rocks before salt extrac-
tion: p1 = p2 = p3, or σef = 0.
2.3. Homogenization Parameters
In either natural or technical processes, elastic and viscous deformation properties of materi-
als can change under physical or chemical influences. Since in the case of a medium subjected
to the power creep law in constitutive equations multiplication, division, raising to a power or
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logarithming correspond to addition, subtraction, multiplication, and division, it is comfortable
to determine property changes with logarithmic functions. Let the value of β determine the power
change of the viscous properties from 1B to 2B:
21
log( / )BB
(5)
where B is the creep compliance and β is the increase of the creep compliance factor, 2B > 1B
and β > 0.
Similarly, we can define the value of η, as an power change of the bulk modulus K =
E/[3(1 – 2v)]. For the established value of Poisson’s ratio v, that would be limited to the change
of the Young’s modulus E:
21 21
log ( / ) log ( / ) for constKK EE
(6)
where η is the reduction of the bulk modulus, 2K < 1K and η < 0.
In such formulation, the values of η and β are the parameters of the medium sensitivity to
the factor that is responsible for the volumetric and shape changes of the medium. For example,
humidification or drying, cracking or perforation, and also mechanical degradation of pillars and
shelves or of their complexes can be such factors. The homogenization parameters of the Wapno
Salt Mine levels, resulting from perforation and degradation, were established by our model
studies, with the condition of their compliance with the observed displacements.
3. Course of Research
In our research, we applied a geometric model in the form of a cuboid, with the horizontal
dimensions of 1900 m × 1350 m and the height of 1000 m. In the X and Y axial directions, the
salt dome had the dimensions of 900 m × 350 m, and the dimensions of the salt mine’s structure
were 800 m × 250 m. The structure’s space included the levels, from Level III on the vertical level
ordinate of that roof, Z = –359 m, to the floor of Level IX, at the depth of 543 m. A protection
salt shelf was preserved over Level III, from the depth of 359 m to 160 m, with the salt dome
cap above it, to the depth of 10 m. Above the cap, Quaternary overburden was laid up to the land
surface (Z = 0 m). The surrounding formations were located outside the salt dome boundaries.
Four Areas were distinguished in the workings’ zone: (1) – from the floor of the roof protec-
tion shelf to the floor of Level III at the depth of 384 m, (2) – from the floor of Level III to the
floor of Level IV at Z = –405 m, (3) – Levels V and VI down to the depth of 454 m, and (4) –
Levels VII-IX down to the depth of 543 m. The properties of particular formations were assumed
to be those specified in the 2008 study (Kortas, 2008): for n = 2 and m = 1. The parameters β, η
of Areas 1-4 were different in each ten-year period.
Assuming a symmetry in vertical planes run along axes X and Y of the salt dome, the geo-
metrical model was reduced to 1/4 of the 3D space (Fig. 7, left). Displacement boundary conditions
were assumed (Fig. 7, left), and the hydrostatic state of initial stress (Fig. 7, right) was obtained
by simulation of the rock mass creep process, without consideration of workings, in the years
t = –5000 to 0. For salt rocks, the following were assumed: Young’s modulus E = 15 GPa, Pois-
son’s ratio: v = 0.3, and the creep compliance B = 5*10–25 Pa2s–1.
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A series of preliminary model studies was designed to determine the influence of the param-
eter η(E) [–0,25; –0,50; –1,00; –1,50; –2,00] on land surface subsidence, at the constant value
of the parameter b(B) = 0. In that series of studies, the parameters did not change in time, but
they were different in particular tasks. The simulation results are represented by the maximum
land subsidence in the function of time Pwmax(t,η) at the crossing point of symmetry planes. The
results obtained are approximated by a bunch of power functions shown on Fig. 8.
In the subsequent series of tasks, the influence of the concurrent h and b on the land sub-
sidence Pwmax (t) was tested. An example of results obtained is illustrated by the graph shown
in Fig. 9. After immediate subsidence as a result of elastic reaction, creep occurred, and that is
described by the power functions of time.
Fig. 7. A 1/4 model of the salt dome, with the location of the salt mine and the boundary conditions (left),
as well as the initial distribution of effective stresses (right)
Fig. 8. Correlations of w(t) at η(E) [–0,25; –0,50; –1,00; –1,50; –2,00]
0 1020304050
-3000
-2500
-2000
-1500
-1000
-500
0
Maximum Subsidance -
w
max
(t),
[mm]
T i m e
[year]
K
= -2.0:
-355
mm
*t
0.53
K
= -1.5:
-250
mm
*t
0.42
K
= -0.5:
-34
mm
*t
0.24
K
= -1.0:
-122
mm
*t
0.31
K
= -0.25:
-12
mm
*t
0.21
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Fig. 9. The influence of η and β parameters on the function wmax(t)
0481
2
16 20
-500
-400
-300
-200
-100
0
Maximum Subsidanece
w
max
(t),
[mm]
T i m e
[year]
K
= -1.08
K
= -0.85
E
= -1.00
E
= -1.00
K
= -1.08
E
=0.00
K
= -0.85
E
=0.00
After preliminary test series, the compliance between the model displacements Pwmax(t) and
those observed on the land surface above the Wapno Salt Mine was obtained. Subsequent test
series were designed to obtain compliance of a sequence of vertical displacements values at the
particular salt mine levels [Kwmax(t)] and on the land surface Pwmax(t). The tests are illustrated
by two graphs presented in Fig. 10.
Fig. 10. The dependence of maximum vertical displacements on depth, with η and β parameters
being constant (left) and changing in time (right)
-3000 -2000 -1000 0 1000 2000
-1000
-800
-600
-400
-200
0
Subsidence
Uplift
Exploitation area
D e p t h
[m]
t =10 years
t =20 years
t =40 yea rs
t =50 years
-3000 -2000 -1000 0 1000 2000
-1000
-800
-600
-400
-200
0
t =10 years
t =20 years
t =40 years
t =50 years
Vertical displacement
[mm]
Vertical displacement
[mm]
Subsidence
Uplift
Exploitation area
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The largest subsidence values occurred in the centre of Levels III and IV of the salt mine,
with the largest uplifts at lower Levels IX and VIII. The final result of that stage of studies in-
cluded proper diversification of the homogenization η and β parameters for particular salt mine
areas that are changeable in time. Fig. 11 presents the graphs of extreme model displacements
in the function of time, corresponding to the results of the measurements conducted in the salt
mine and on its land surface.
Fig. 11. Subsidence of land surface and of upper salt mine’s levels
10 20 30 40 50
-1600
-1400
-1200
-1000
-800
-600
-400
-200
0
1930 1940 1950 1960 1970
Vertical displacement w
(
z
,
t)
, [mm]
Landsurface,Z=0
Domecup,Z=-160
III
level
,Z=-384
IV
level
,Z=-405
Period of time
[year]
Floorofprotectiveshelf,Z=-359
IVlevel
T i m e
[year]
At the beginning, until year 30 (upper horizontal axis), the largest subsidence occurred at
the floor of Level III, followed by that at the floor of the protection shelf. In a later period, Level
III was converging and, consequently, the floor of the protection shelf was subsiding. Vertical
displacements of the horizon Z = –160 m (the roof of the protection shelf) were significantly lower.
The calculated difference between the shelf floor and roof increased with time, and it amounted
to +553 mm in year 50. For that reason, the average deformation of the protection shelves in the
vertical direction, equal to: 553 mm / 199 m = +2.8 mm/m, constituted expansion. Land surface
subsidence in year 50 reached the value of –872 mm (Fig. 11). At the lower Level IX, uplifts
occurred, reaching up to +1435 mm in year 50. In the next chapter, the results of the analysis of
stress and strain in the roof protection shelf are presented.
4. Results of the Model Studies Concerning the Roof
Protection Shelf Deformation
The analysis of the calculation results, obtained from the model studies, indicated that expan-
sion stresses appeared in three locations: the largest ones on the border of the boundary pillars
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and the salt dome surroundings and lower ones within the salt dome cap and the roof protection
shelf. The distribution of the maximum main stress p1 is presented in Fig. 12. After ten years,
the maximum stress p1 within the salt dome cap reached the value of +0.06 MPa, and increased
to +5.3 MPa after 30 years; however, the three main stress components reached the values of p1
= +7.8 MPa, p2 = +5.1 MPa, and p3 = +3.7 MPa in year 50. Similarly to the salt dome cap, the
three main stresses were expanding also in the roof shelf, and the maximum stress reached the
value of p1 = +5.1 MPa in year 50.
Fig. 12. The maximum stresses p1 [Pa] after 50 years, with salt mine workings locations
Stresses:
p1> 2 MPa
p1> 5 MPa
X
YZ
Cupofthesaltdome
Protectionshelf
Mineworkings
The maximum values of tensile strain occurred in the roof protection shelf. They were not
significant initially but they were increasing in proportion to the expansion stresses which were
increasing with time. The maximum values of the strain components in the horizontal plane of
the roof protection shelf occurred in the direction of the salt dome’s shorter axis Y. The strain
distribution is presented in vertical and horizontal cross-sections in Figs. 13-15 (the graphs contain
identification indices and colours in the deformation units, or 1 = 1000‰).
The maximum strain maxεy occurred in the central part of the roof protection shelf at the
depths from 220 to 260 m and at the distance of 100 m from the vertical axis Z. The maximum
deformation reached the value of +2.5‰ after ten years from the commencement of salt extrac-
tion, and it increased to +3.8‰ in year 30, and to +4.6‰ in year 50.
5. Rock Mass and Land Surface after Inrush of Water into
the Wapno Salt Mine
Opening of the water flow paths caused uncontrolled and increased leaching of salt in the
roof protection shelf. After the inflow of water into the salt mine, the protection pillars and shelves
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Fig. 13. Distribution of the horizontal strain εy in the roof protection shelf,in vertical cross-sections;
X [1000, 1050, 1100 m] after 10 (left) and 50 years (right)
Fig. 14. Distribution of the strain εy after 50 years in the roof shelf, in vertical cross-sections;
X [1000, 1050, 1100 m], maxεy [+4.6‰, +3.6‰, +2.9‰]
Tensile strains
Cupofthesaltdome
Protectiveshelf
X
Y
Z
were being leached, at first at the upper levels, next at the lower. After certain time, the filling of
workings with brine under hydrostatic pressure led to the relaxation of effective stresses and the
reduction of tensile strain in protection pillars and shelves between rooms. The results of survey
indicated the changing rates of land subsidence.
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Another series of model studies, with the variation of the homogenization parameters b and
h, was intended to obtain the compliance of the numerical calculation results with those of actual
land surface levelling measurements obtained after the salt mine had been flooded. Simulation
results are shown in Fig. 16.
Fig. 15. Locations of the maximum horizontal strain maxεy after 50 years, in horizontal cross-sections;
Z [–220, –260 and –300 m], Max[maxεy(H)] = +4.64‰
Tensile
strain
X
Y
Z
Fig. 16. Model vertical displacements of points within the salt dome
10 20 30 40 50 60 70 80 90 100
-1500
-1000
-500
0
1930 1940 1950 1960 1970 1980 1990 2000 2010 2020 2030
Landsurface
IIIlevel
Mine flooding
IVlevel
Domecup
V
ertical displacement
[mm]
T i m e
[year]
Floorofprotectiveshelf
During mining operations, from 0 to 50th year the results of the model calculations showed
the average rate of maximum land surface subsidence of –16.6 mm/year, while after the flooding
of workings in 1977-1978 (after 50 years), the rate was reduced primarily down to –7 mm/year,
to keep decreasing in the subsequent forty years down to –2 mm/year. The flooding of workings
caused initially a land surface uplift, changing into subsidence after several years, also observed
in measurement results (see Fig. 5).
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After the workings had been flooded, it was not possible to take any measurements inside the
salt mine. Flooding simulations indicated that the roof of protection shelf was raised by maximum
+65 mm, and the floor of protection shelf by +113 mm in year 50. We should mention that, after
a controlled filling of lower levels of the Solno Salt Mine in Inowrocław with brine, uplifting
of the highest level to the value of +81 mm (Kortas, 1997) was observed, and after the flooding
process completion, land surface uplifts by maximum +6 mm were identified. Land surface ob-
servations conducted after the Wapno Salt Mine flooding indicated that, after short-term several
millimetre uplifts found in 1978, land subsidence continued, with the largest one identified in
the discontinuous deformation zones outside the salt dome area (see Fig. 5).
6. Analysis of Results and Conclusions
Our model studies allowed us to appraise the tensile strains that were increasing under the
influence of salt extraction, within the roof protection shelf located above the workings of the
Wapno Salt Mine. The strain components in the horizontal and vertical directions were the tensile
strains, increasing with the spatial development of the salt mine.
The occurrence of omnidirectional tensile stresses in the protection rock salt body are the
signals of hazardous geomechanical conditions, owing to the possibility of deformation propa-
gation, allowing for the inflow of water into the salt mine. Laboratory studies indicated that
a uniaxial tensile strength of rock salt is close to 0.5 MPa (Dreyer, 1972), and the corresponding
critical strain for the Young’s modulus E ≥ 1 GPa complied with the conditions of the uniaxial
strain ε ≤ + 0.5‰. Therefore, the roof shelf deformations, obtained from our model and the ex-
traction process simulation, exceeded a safe critical strain already after ten years, and continued
to increase up to +5.1‰.
We should add that, during the halokinetic process of salt dome uplift, fractures were devel-
oping at the contact planes of salts that were susceptible to creep and the rigid formations, also
close to the salt dome boundary. Such fractures could be filled with syngenetic fluids. Excessive
deformation of the central part of the protection shelf was not the cause of water inflow into the
salt mine but rather the cause was the propagation of that deformation in the protection shelf
or, which is more probable, the opening of previously existing fractures during shelf expansion.
The opening of fractures within the shelf subjected to deformation, from the caprock into the
workings, allowed for water infiltration, followed by leaching out of migration paths, and that
led to final salt mine flooding.
We should also point out here the simulation results indicating the appearance of tensile stress
zone, within the salt dome cap and under-surface formations outside the salt dome’s contour in
the direction of the shorter axis Y.
In the case of opening of the flow paths across boreholes made in the boundary pillars, the
mining practice relies on plugging the boreholes and damming the leak area. However, no open
fractures in the roof shelves with water infiltration could have been controlled in any salt mine
yet. The appearance of a number of new leaks at Level III of Wapno Salt Mine, along WE direc-
tion, was an indication of the flow path propagation, observed by the author in July 1977. That
happened within several weeks before the water inrush into the salt mine. Initially, the humidi-
fication of the room roofs increased, followed by brine “rainfall” and rooms’ floors flooding.
A system of fractures, fissures, and leaching area was moving from the west to the east edge of
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the salt dome. Owing to faster solubility of the vertical K-Mg salt layers, existing at the east edge
of salt dome, favourable conditions existed for extensive leaching processes, followed by the
transport of liquefied sand and silt material from the salt dome surroundings into the workings,
and in consequence for the development of a large subsidence.
Omnidirectional tensile stresses in the roof protection shelf, found in the geomechanical
model, the identification of considerable tensile strains in the central part of the roof protection
shelf, and the occurrence of maximum values of strain in the direction being parallel to the shorter
salt dome axis confirm the opinion that the geomechanical conditions evoked by the workings’
effects constituted essential causes of the water hazard increase and, consequently, of the salt
mine’s catastrophic flooding. We should add that the exploitation commenced at Level X and
the preparation of Levels XI and XII for that purpose, was mining mistake. In the similar condi-
tions of other multi-level room-and-pillar salt mines, salt exploitation will lead to the occurrence
of positive values of stresses and tensile strains, favouring the opening of fractures within the
protection shelf. That was also demonstrated by the studies presented in the paper by Kortas and
Maj (2012).
The method of room-and-pillar structure homogenization was first introduced in a 2D+t
geometric model (Kortas & Maj, 2012). The present publication concerning a 3D+t model opens
new possibilities of applying physical elastic-viscous medium models to determine the changes
in time in the distribution of the displacements and strains inside the rock mass and on the land
surface.
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Received: 23 May 2014
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