Mining Block Life-Time Prediction Method by Roof-To-Floor Convergence
JYRI-RIVALDO PASTARUS
Tallinn Technical University, Estonia
This paper deals with long-term stability prediction methods of the room-and-pillar mining
system. Roof-to-floor convergence prediction method is preferred as it takes into
consideration all geological and mining features at the site of measuring station. It is
relatively simple, exact and suits for modeling on PC. It bases on the measurement of the
absolute deformation or deformation rate. Prediction method allows determining the
location, area and time of a collapse in a mining block. The uncertainty in time is less than
10 % at the 95 % confidence level. The applicability of the method is clearly demonstrated.
Keywords: room-and-pillar mining; roof-to-floor convergence; life-time prediction;
deformation rate method; absolute deformation method
1. Introduction
The mineral wealth of Estonia – oil shale - is located in a densely populated and rich
farming district. Underground oil shale production uses room-and-pillar method with
blasting. This method is cheap, highly productive, easily mechanize, and relatively simple
to design.
It has become apparent that the processes in overburden rocks and pillars have caused
unfavorable environmental side effects accompanied by significant subsidence of the
ground surface. They caused and will cause in the future a large number of technical,
economical, ecological and juridical problems. On the other hand, the collapse in a working
mining block stops the mining works. The first spontaneous collapse of the pillars and the
surface subsidence in an Estonian oil shale mine took place in 1964. Up to the present, 73
collapses on an area of 100 km2 have been recorded.
Working out the long-term stability prediction methods is the main aim of the present
work.
Methods of stability prediction by life-time of the pillars (Pastarus & Nikitin 2001),
statistical methods (Pastarus & Tomberg 2001) and by the rate of the current rock strength
(Pastarus & Toomik 2001) are relatively simple, but not applicable for long-term
prediction. For practical application the prediction method by roof-to-floor convergence is
suitable. Method bases on the phenomenological behavior of rock, linear rheological model
and failure deformation criterion. It is possible to perform the calculation by two following
methods: by deformation rate and absolute deformation methods. The uncertainty in time
does not exceed 10% at the 95 % confidence level.
Roof-to-floor convergence curve takes into consideration all the geological and mining
features at the site of the measuring station. On the other hand, the reference point
installation and roof-to-floor convergence measurement are expensive, cumbersome and
time-consuming. In a mining block there should be about 40…50 reference points. The
optimum quantity of reference points will be determined by conditional thickness method
(Pastarus 2004).
Prediction method by roof-to-floor convergence is applicable in different geological
conditions, where the room-and-pillar mining system is used. The surface subsidence
parameters will be determined according to conventional calculation schemes. The
applicability of the roof-to-floor convergence prediction method is clearly demonstrated in
theory and in in-situ conditions.
2. Geology and mining
Estonia oil shale deposit is located in the north-eastern part of the country. The
commercially important oil shale layer stretches for 200 km from west to east, and for 30
km from north to south. The oil shale bed has a form of a flat bed slightly inclined (2…3 m
per km) southward. The depth of the oil shale bed occurrence varies significantly: it lies
under the Quaternary sediments at the northern border of the field and reaches 100…150 m
at its southern rim. The oil shale reserves in Estonia are estimated to be approximately 4
thousand million tons.
The commercial oil shale bed and immediate roof consist of oil shale and limestone
seams. The main roof consists of carbonate rocks of varying thickness. Characteristics of
the individual oil shale and limestone seams are quite different. Oil shale compressive
strength is 20…40 MPa and that of limestone is 40…80 MPa. The strength of the rocks
increases southward and their volume density is 1.5…1.8 and 2.2…2.6 Mg/m3,
respectively. Dry oil shale calorific value varies within 7.5…18.8 MJ/kg depending on the
seam and deposit area.
In Estonian oil shale mines the room-and-pillar mining system with blasting is used. It
gives an extraction factor of 70…80 %. The field of the oil shale mine is divided into
panels, subdivided into mining block each approximately 300…350 m wide and 600…800
m long. A mining block consists usually of two semi-blocks. The oil shale bed is embedded
at the depth of 40…70 m. Its height corresponds to the thickness of the commercial oil
shale bed, approximately 2.8 m.
The width of the room is determined by the stability of the immediate roof. The latter is
very stable when it is 6…10 m wide. In this case bolting must still support the immediate
roof. The pillars are arranged in a singular grid. Actual mining practice has shown that
pillars with a square cross-section suit best. Intra-chamber pillars are left to secure the
solidity of the whole upper-laying rock mass and to eliminate surface subsidence. The
cross-sectional area of the pillars is 25…40 m2, depending on the depth of the oil shale bed.
Loading and transportation of blasted mined rock is carried out by powerful LHD machines
with diesel drive. A work cycle lasts for over a week.
3. Theoretical background
For the analysis, there are two basic approaches to study rheological behavior of the
materials: on the level of macrorheology or microrheology (Ranalli 1995). For practical
applications, the phenomenological approach (macrorheology) for stability calculations is
preferred. The analysis is based on the roof-to-floor convergence process of in-situ
conditions in a mining block. A typical roof-to-floor convergence curve (creep) is presented
in Figure 1.

u
e
ll
lll
lV
l
tt
ts
tu t
Figure 1 - Roof-To-Floor Convergence Curve
where εu is the ultimate deformation at fracture; tt is the transient creep limit; ts is the
steady-state creep limit; tu is the time at fracture; I is the elastic deformation εe; II is the
transient creep area έ<0; III is the steady-state creep area έ=const; IV is the transient creep
area before fracture έ>0; έ is the deformation rate.
Phenomenological behavior of rocks can be studied using conventional calculation
schemes: analog models, equations by L. Bolzmann and V. Volterra, G.S. Erzhanov
(Erzhanov et al. 1970, Bulychov 1989). These are cumbersome and time-consuming. For
practical applications the deformation criterion is suitable (Bulychov 1989). If the current
deformation ε(t) reaches the value of ultimate deformation at fracture εc for rock ε(t) > εc,
the fracture of the rocks takes place. The applicability of the deformation failure criterion
for rocks is demonstrated in microrheology (Rosenberg 1967). The deformation criterion is
valid for steady-state creep (Erzhanov et al. 1970, Bulychov 1989):
d
t p  const
dt
(1)
where d/dt is the deformation rate; tp is the collapse time at the fracture.
The analysis showed that the presented method is applicable only for linear rheological
model. Investigations in in-situ conditions and laboratory tests have shown that most of
rock mass is characterized by linear rheological behavior (Erzhanov et al. 1970). In the
practical application the regions of elastic deformation (I), transient creep (II) and transient
creep before the fracture (IV) are negligible (Figure1).
Investigation showed that for practical application the following equation is valid:
d
tp  u  0
dt
(2)
where εo is the ultimate deformation at stabilized strength; εu is the ultimate deformation at
fracture.
The roof-to-floor convergence can be measured in in-situ conditions by means of
extensometers in a mining block. The roof-to-floor convergence curve takes into
consideration all the geological and mining features at the site of the measuring station.
That is connected with the concept of critical width and critical area.
The critical width is the greatest width that the rock above the mine can span before its
failure, or, if there are pillars, the width we must mine before the pillars accept the full
weight of the overlying materials (Parker 1993). In the three-dimensional case, the critical
width becomes the critical area. The latter is the minimum area where the destruction of the
pillars and surface subsidence is possible.
On the other hand, the dimensions of the mining block determine the quantity of the
reference points (40…50). As the reference point installation and roof-to-floor convergence
measurement are expensive, cumbersome and time-consuming, their optimum quantity will
be determined by the conditional thickness method (Pastarus & Nikitin 2001, Pastarus &
Toomik 2001).
3.1. Mining block life-time prediction by deformation rate method
Method bases on the deformation rate of steady-state creep. The uncertainty in time is less
than 10 % at the 95 % confidence level. Pillar life-time prediction formula is derived from
the equation (2):
tp 
u  0

where έ = dε/dt is the deformation rate.
Graphical interpretation of the Formula (3) is represented in Figure 2.
(3)

u
έ
έ
έ
1
2
3
έ
4
o
t0
t1
t2
t3
t
Figure 2 - Time Dependent Deformation of a Pillar (deformation rate method)
where u is the ultimate deformation at fracture; o is the ultimate deformation at stabilized
strength; t<t0 is the elastic deformation and transient creep area; t>t0 is the steady-state
creep area; t1, t2 ... are the life-time of pillars; έ1, έ2 ... are the deformation rates
Advantage of this prediction method is visible: it is necessary only to know the
deformation rate of steady-state creep. Result does not depend on the absolute value of the
deformation. Prediction method is preferred for the calculations.
3.2. Mining block life-time prediction by absolute deformation method
Method uses the absolute value of the roof-to-floor convergence at fixed time. The definite
integral of equation (2)
t
t
0
tt
p
d   ( u   0 )dt ,
(4)
0
where εt is the absolute deformation at time tt, gives the formula for calculation the life-time
of the pillars and mining blocks:
tp 
u  o
tt .
t  0
Graphical interpretation of the Formula (5) is represented in Figure 3.
(5)

u
ε=f(t)
εc
o
to
tc
tp
t
Figure 3 - Time Dependent Deformation of a Pillar (absolute deformation method)
where u is the ultimate deformation at fracture; o is the ultimate deformation at stabilized
strength; t<t0 is the elastic deformation and transient creep area; t>t0 is the steady-state
creep area; tp is the life-time of a pillar; c is the deformation at time tc.
Investigation showed that this prediction method is very sensitive to installation moment
of reference point and quality of deformation measurement. The uncertainty of prediction
time depends on above mentioned parameters and does not exceed 15 % at the 95 %
confidence level.
4. Results
The data which have become available in the last 40…50 years concern experience
obtained at about 400 mining blocks on the area of 100 km2. They gave a good base for
working out the long-term stability prediction methods and adequacy determination of the
obtained results.
Investigation showed that critical width in the area of Estonian oil shale mines is
presented by following formula (Pastarus & Toomik 2001):
L  1.2H  10
where L is the critical width, m; H is the thickness of the overburden rocks, m.
(6)
Experiments showed that the duration of the elastic deformation and transient creep (area
I and II) is about 100 days and transient creep before fracture (area IV) does not exceed 14
days.
Following table represents the rock and room-and-pillar mining parameters in Estonian
oil shale mines.
Table 1. Characterization of Estonian oil shale mines and results of respective uncertainty
calculation at the 95% confidence level
Parameter
Thickness of overburden rocks H, m
Cross-sectional area of a pillar S, m2
Critical width of the roof L, m
Volume density of rock γ, KN/m3
Basic strength of rock σ0, MPa
Roof-to-floor convergence ε, mm
Ultimate deformation at stabilized strength ε0,
mm
Ultimate deformation at fracture by following
cross-sectional area of the pillars, εu, mm:
a) 16 - 20 m2
b) 20 - 25 m2
c) 33 -36 m2
Value
Absolute
uncertainty
40.0 -60.0
1.0
17.6-96.4
0.5-3.0
58.0-82.0
4.2-6.4
25.0
1.0
16.0
2.0
22.5-81.0
2.4
Relative
uncertainty
0.025-0.017
0.03
0.08
0.04
0.05-0.02
0.11-0.03
22.5
1.5
0.07
55.5
65.5
79.0
3.5
3.5
4.0
0.06
0.05
0.05
Roof-to-floor convergence method was used to analyze 5 mining blocks in the mines
Ahtme and Viru. The investigation results for the left semi-block No. 61L of the mine Viru
are presented below. The commercial oil shale bed of the thickness of 2.8 m is embedded at
the depth of 46 m. The mining block is bordered by barrier pillars. A spontaneous collapse
of the pillars in the left mining semi-block took place 4 years after the beginning of
exploitation. It reached the surface. The area of destruction was about 13,545 m2.
The age of the pillars in the collapse centre was 3.5 years. Investigation showed that the
ultimate deformation at stabilized strength εo is 22.5 mm, and ultimate deformation at
fracture by 25 m2 cross-section area of the pillars εu is 65.5 mm (Table 1). The critical
width is 65 m (Formula (6)) and critical area 3300 m2. Roof-to-floor convergence was
measured of in situ conditions by means of extensometer (tolerance 0.5 mm) between
anchor points in the roof and floor as function of time. The convergence curve is presented
in Figure 4.
70
Deformation, mm
60
50
40
30
20
10
0
0
200
400
600
800
1000
1200
1400
Time, days
Figure 4 – Roof-To-Floor Convergence Curve. Left Semi-block No. 61L, Viru Mine
The deformation rate of the roof-to-floor convergence was 12.6 mm per year. The
prediction time of the mining block collapse is 3.17 years (Formula (4)). The relative
uncertainty in time is 9.4 % at the 95 % confidence level.
Investigation results by absolute deformation method are presented in Table 2 (Formula
(5)).
Table 2. Results of mining block collapse prediction by absolute deformation method
Time, year
Deformation, mm
1
2
3
35.0
44.1
57.8
Prediction collapse
time, year
3.2
3.7
3.4
Relative uncertainty,
%
8.6
5.7
2.8
The results of theoretical and of in-situ investigations in Estonian oil shale mines showed
that they are close to the modeling results.
5. Conclusions and recommendations
1. The problem of the mining block stability is very important in a densely populated and
intensely farmed district like NE Estonia.
2. The applicability of the prediction method by roof-to-floor convergence is demonstrated
in theory and checked in in-situ conditions. The uncertainty in time is less than 10 % at
the 95% confidence level. This prediction method is of particular interest for practical
purposes.
3. Method allows determining the mining block collapse time, location, and area. The
surface subsidence parameters can be calculated by conventional calculation schemes.
4. Prediction method is applicable in different geological conditions, where the room-andpillar mining system is used. Presented method is suited for mining block stability
monitoring.
Estonian Science Foundation (Grant No. 5164, 2002-2005) supported the research.
6. Bibliography
1. Bulychov, N. Mechanics of underground constructions. Nedra. Moscow, 1989. (in
Russian)
2. Erzhanov, G.S., Saginov, A.S., Gumenyuk, G.N., Veksler, Y.A., Nesterov, G.A. Creep
of the sedimentary rocks. Nauka. Alma-Ata, 1970. (in Russian)
3. Parker, I. Mine pillar design in 1993: Computers have become the opiate of the mining
engineers. Mining Engineering, London, July and August 1993: 714-717 and 10471050, 1993.
4. Pastarus, J.-R. Mining block stability monitoring by roof-to-floor convergence. Proc. of
the 8th International Symposium on Environmental Issues and Waste Management in
Energy and Mineral Production – SWEMP 2004. (Pasamehmetoglu, A.G., Özgenoglu,
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Antalya, Turkey 17-20 May 2004, p.211-214, 2004.
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mines. Proc. of the International Symposium on Geotechnical Issues of Underground
Space Use for Environmentally Protected World. Dnipropetrovsk, Ukraine, 26-29 June
2001, NMUU/Dnipropetrivsk, p.121-125, 2001.
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by statistical methods. . Proc. of the 3nd International Conference "Environment.
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7. Pastarus, J.-R., Toomik, A. Roof and pillar stability prognosis in Estonian oil shale
mines. Rock Mechanics. Proc. of the ISRM Regional Symposium EUROCK 2001
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7. Biography
Jyri-Rivaldo Pastarus is an Associated Professor in the Department
of Mining at Tallinn Technical University. He obtained his
candidate of technical sciences (Ph.D.) degree in mining from
Leningrad Mining Institute and his Dr. Eng. degree from Tallinn
Technical University. Some years he works as Visiting Professor
in University of Oran. His research interest is in the area of mining
technology, rock mechanics, numerical modeling, stability
prediction of the underground mining systems, risk management,
environmental protection.