Arch. Min. Sci., Vol. 55 (2010), No 4, p. 723–731

Arch. Min. Sci., Vol. 55 (2010), No 4, p. 723–731
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Electronic version (in color) of this paper is available: http://mining.archives.pl
PIOTR BAŃKA*, ANDRZEJ JAWORSKI*
POSSIBILITY OF MORE PRECISE ANALYTICAL PREDICTION OF ROCK MASS ENERGY CHANGES
WITH THE USE OF PASSIVE SEISMIC TOMOGRAPHY READINGS
MOŻLIWOŚĆ ZWIĘKSZENIA DOKŁADNOŚCI ANALITYCZNYCH PROGNOZ ZMIAN
ENERGETYCZNYCH W GÓROTWORZE POPRZEZ WYKORZYSTANIE WSKAZAŃ
PASYWNEJ TOMOGRAFII SEJSMICZNEJ
Selection of rock layers, which deformation is linked to changes of tremors and rock burst hazard
status, becomes a common problem during the application of analytical prediction methods. The article
presents a possibility of more precise analytical prediction of potential tremor hazard formation during
mining exploitation, based on passive seismic tomography results. With a use of exploitation area model,
utilization possibility of longitudinal wave’s velocity field was presented, which is determined based on
tremors recording used for rock stratum selection, in which occuring energy processes may have fundamental influence on the observed seismic and rock burst hazard level.
Keywords: analytical prediction, induced seismic activity, passive seismic tomography
W trakcie stosowania analitycznych metod prognozowania często problemem staje się wytypowanie
warstw skalnych, z deformowaniem których należy wiązać zmiany stanu zagrożenia wstrząsami i tąpaniami. W artykule zasygnalizowano możliwość zwiększenia dokładności analitycznych prognoz kształtowania się poziomu potencjalnego zagrożenia wstrząsami robót górniczych w oparciu o wyniki pasywnej
tomografii sejsmicznej. Dla przykładowego rejonu eksploatacji pokazano możliwość wykorzystania
pola prędkości fali podłużnej określanego na podstawie rejestracji wstrząsów do wytypowania warstw
skalnych, w których zachodzące procesy energetyczne mogą mieć zasadniczy wpływ na obserwowany
poziom zagrożenia sejsmicznego i tąpaniami.
Do wyznaczania zmian energetycznych zachodzących we wstrząsogennych warstwach skalnych
zastosowano funkcję określającą potencjał sprężystości w ogólnym przypadku stanu naprężenia i odkształcenia. Taki ilościowy analityczny opis zmian energetycznych dotyczy jedynie energii sprężystej
akumulowanej w górotworze w następstwie naruszania go dowolnie wykształtowaną eksploatacją,
nic nie mówi o jej dyssypacji i przemianach, a w konsekwencji nie określa ilości energii wyzwalanej
w procesie niszczenia określonej objętości skał. W procesie niszczenia ośrodka skalnego ta potencjalna
energia sprężysta przechodzi między innymi w kinetyczną energię fal sprężystych utożsamianą z energią
*
INSTITUTE OF MINING, FACULTY OF MINING & GEOLOGY, TECHNICAL UNIVERSITY OF SILESIA, 44-100 GLIWICE,
UL. AKADEMICKA 2, POLAND
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sejsmiczną rejestrowanych wstrząsów. Tak więc, chociaż rozpatrujemy jedynie zależne od parametrów
eksploatacji zmiany energii potencjalnej (energii odkształcenia sprężystego), to przekładają się one choć
w nieznanym nam ilościowym stopniu na poziom zagrożenia sejsmicznego (tąpaniami). Liczne obliczenia
testowe pozwoliły stwierdzić istnienie jakościowych związków pomiędzy obliczanymi zmianami energii
właściwej a obserwowanym w typowych sytuacjach przebiegiem sejsmiczności indukowanej.
O poziomie sejsmiczności indukowanej najczęściej decydują procesy zachodzące nie w jednej,
a w szeregu warstwach wstrząsogennych. Obiektywne przeszkody w praktyce uniemożliwiają najczęściej
określenie z wystarczającą dokładnością współrzędnej głębokościowej wstrząsów, co pozwoliłoby je
przypisać do określonej warstwy skalnej. W zależności od przestrzennej konfiguracji zaszłości eksploatacyjnych, zmiany potencjalnej energii sprężystej mogą mieć bardzo różnorodny charakter, zależny od
głębokości zalegania warstwy, w której są one obliczane. Na rys. 2 pokazano przykładowo zmiany wartości
właściwej energii sprężystej (unormowane do 1), wzdłuż linii równoległych do wyrobiska przyścianowego
analizowanej śc. 3, obliczone w przedziale głębokości 400÷800 m z krokiem 100 m. Szacunki wykonano
dla 1200 m odcinka dotychczasowego biegu ściany. Dla analogicznego odcinka wybiegu ściany 3 wykonano
obliczenia metodą tomografii pasywnej. Prędkości rozchodzenia się fali podłużnej określono dla kolejnych
miesięcznych (dwumiesięcznych – w przypadku małej ilości indukowanych wstrząsów) okresów biegu
ściany, uzyskując różne obrazy pola prędkości. Na rys. 3 zaprezentowano syntetyczną mapę, powstałą
w wyniku wybrania w każdym z jej punktów maksymalnej wartości oszacowanej prędkości. Wartości,
podobnie jak na rys. 2, zostały następnie unormowane do 1.
Wyniki zaprezentowanej analizy wskazują, że największy udział w obserwowanym poziomie zagrożenia sejsmicznego i tąpaniami mają warstwy położone około 200 m nad i 100 m pod eksploatowanym
pokładem. Zgodnie z wynikami regresji krokowej, udział pozostałych warstw jest pomijalnie mały.
Opracowany sposób może być wykorzystywany do sporządzenia jakościowych, uwzględniających
zmiany energetyczne zachodzące w wytypowanych warstwach skalnych, prognoz zagrożenia sejsmicznego i tąpaniami na wybiegach prowadzonych i projektowanych wyrobisk ścianowych. Wykorzystanie
równania regresji (8) umożliwia również sporządzanie ilościowych oszacowań zmian poziomu zagrożenia
(w częściach złoża, w obrębie których można założyć niezmienność własności wytrzymałościowych
warstw skalnych).
Słowa kluczowe: prognozy analityczne, sejsmiczność indukowana, pasywna tomografia sejsmiczna
1. Introduction
One of the most significant virtues of analytical methods using the solution of the displacement boundary-value problem of linear elasticity theory provided by H. Gil (1991), determining
distribution of stress and deformations in half-space surrounding a rectangle shaped void, is its
perfect numerical effectiveness. Fast calculation enables series of multivariate predictions even
for the big rock mass areas (Bańka & Jaworski, 2004; Drzęźla et al., 1988). Using this simple
model for the description purpose of movements and stresses around longwall is a far-fetched
idealization of rock mass mechanic characteristics (homogeneous isotropic elastic medium). Also,
the established displacement boundary conditions describe the situation near the roof seam in
somewhat approximate way. In order to receive realistic solutions, this strong idealization requires
the use of comparable way of calculating variable values of stress and deformation tensor, in which
equivalent constants characterizing the rock mass are specified, e.g geomechanic parameters for
which the results of compared predictions concur with the previously obtained results of in-situ
observation and measurements. Performed numeric tests demonstrated that even in relatively small
horizontal and vertical distances from extraction edge, singularity that comes from discontinuity
of boundary condition declines, and distributions of stresses and displacements are close to the
ones described with the use of continuous boundary condition formula. It is of high importance,
because tensor constants are determined on higher deposited rock layers.
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State of stress caused in rock mass by rectangle shaped extraction, according to H. Gil’s
solution is described by following dependences:
¶f 1
¶ 2 f 3ù
G é ¶f 3
+ 2(1 - n )
-z 2 ú
ê2n
(1 - n) ëê ¶ z
¶x
¶ x ûú
sx =
sz =
¶2 f3 ù
G é¶f 3
z
ê
ú
¶x¶z ûú
(1 - n ) ëê ¶z
s zx =
s xy =
G
¶2 f3
z
(1 - n ) ¶x¶z
sy =
¶f 2
¶ 2 f 3ù
G é ¶f 3
+ 2(1 -n )
-z 2 ú
ê2
(1 - n ) ëê ¶ z
¶y
¶ y ûú
æ ¶f 1 ¶ f 2 æ
¶2 f 3ù
G é
ç
ç
+
z
(
1
n
)
ê
ú
ç ¶y
¶ x çè
¶x¶y ûú
(1 - n ) ëê
è
s zy =
(1)
-G
¶2 f3
z
(1 - n ) ¶y¶z
where:
G
v
f1, f2, f3
σx, σy, σz, σxy, σzx, σzy
—
—
—
—
coefficient of transverse elasticity,
Poisson variance,
functions dependent on elementary selection geometry and v,
stress state components.
Similar solution was obtained by F. Dymek (1969), who applied different boundary condition.
Performed tests proved that in terms of vertical displacements and stresses H. Gil and F. Dymek’s
solutions have very similar results.
In order to determine energy changes taking place in seismogenic layers, a function was
used that describes elasticity potential in general state of stress and deformation:
φ = 0.5Tσ Tε
(2)
where:
φ — absolute energy of the elastic strain [J/m3],
Tσ — stress-state tensor,
Tε — strain-state tensor.
This quantitative analytical description of energy changes refers only to stress energy accumulated in rock mass in the wake of its disturbance with a freely generated exploitation. It does
not mention its dissipation or changes, and consequently does not describe the energy amount
triggered during selected rock damaged. In the process of rock mass damage, this potential elastic
energy changes into kinetic energy of elastic waves, that are identified with seismic energy of
the recorded tremors. Even though, we are only taking into consideration changes of potential
energy (elastic strain energy) dependant on exploitation parameters, they are somewhat reflected,
though at unknown quantitative level, in the level of seismic hazard (rock burst). Numerous test
calculations allowed us to find out about the qualitative relations between the calculated changes
of absolute energy and the observed course of induced seismicity.
The article suggests the use of passive seismic tomography method for the purpose of analytical method readings verification. Presented solutions were limited to flat condition.
Data coming from observation networks functioning in Polish mines, due to a small depth
variety of seismometer placement, does not allow the use of the spacious model of passive seismic
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tomography. The problem of passive tomography belongs to reverse problems. These are usually
ill-conditioned, ambiguous problems, what brings possibility of many solutions for a specific
set of measurements. Many examples from literature (Bańka, 2009; Dębski, 2006; Dubiński at
al., 1997) indicate that difficulties with finding the “real” solution, considering current level of
method development, are possible to overcome. Passive tomography then becomes a valuable
source of information about seismic waves velocity distribution in considerable areas of rock
mass. The analysis of seismic waves velocity changes may allow evaluation of seismic and rock
burst hazard level changes (Luxbacher at al., 2008).
The basic relation used in seismic tomography takes the following form:
t=
R
dr
v ( x, y , z )
(3)
where:
t — time of particular seismic wave propagation from a source to a receiver,
v — velocity of the particular seismic wave,
R — wave radius.
For the effective solution of the problem it is necessary to assume some simplifications.
The first one, widely recognized, is based on division of the considered area into cells or
nodes, in which fixed velocity value of wave dispersion is established. The next one, also widely
recognized, is the assumption of rectilinear wave propagation from the source to the receiver.
The experiences of many authors suggest that rectilinear tomography might be applied with
a satisfactory result, when wave’s velocity at particular cells does not diverge from the average
by more than 10÷15% (Gibowicz & Kijko, 1994; Kasina, 2001).
The use of above simplifications allows replacement of contour integral (3) with a finite
sum:
t=
n
rj
å vj
(4)
j =1
where:
rj
vj
n
t
—
—
—
—
radius length in j-changes cell,
wave velocity in j-changes cell,
number of cells of the divided area of calculation,
time of seismic wave propagation from the source to the receiver.
Taking into consideration:
t = tobs – t0
where:
tobs — time of the particular seismic wave occurrence at seismometer,
t0 — time of tremor occurrence.
(5)
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The formula (4) takes the following form:
tobs =
n
rj
å vj
j =1
+ t0
(6)
The problem of finding a solution to the formula of passive tomography, might be presented
as the solution of the formula that focuses on finding the minimum norm L1 or L2 of the vector
margin of the calculated and measured times of seismic waves entry into seismometers:
F (h, m) =
ne ns
åå æè tobsij - toblij æè
P
(7)
i =1 j =1
where:
for P = 1 – norm L1,
for P = 2 – norm L2,
tobs — measured times of entries,
tobl — calculated times of entries,
hi = (x0i, y0i, z0i)T — focus coordinates of “i-changes” tremor,
m — nm dimensional vector with seismic wave velocity at particular cells, into
which the analyzed area of the mass rock was divided.
For the minimum functional search (7) differential evolution algorithm was used (Price &
Storn, 2010). It is a stochastic algorithm that uses converted population of base vectors in the
process of optimization. The basic idea, which found its reflection in the name of the algorithm,
is that of converting vectors population differences between randomly chosen vectors of that
population.
Conducted calculations (Bańka, 2009) show high usability of these algorithms in solving
passive tomography equations.
2. Rock burst hazard, rock mass seismicity
in the research area
Presented simulations refer to exploitation conducted in the area of the deposit considered
the III level of rock burst hazard, where mining is accompanied by high seismic activity of the
rock mass. In the researched area, at a different range, extraction of higher situated seams 501,
419 and 418 (in the respective distance of 30 m, 60 m and 80 m) and lower situated seams 507,
509 and 510 (70 m, 90 m and 100 m) took place. Seam 503 with an average thickness of 2,8 is
the subject of currently conducted exploitation, at the depth of 700 m. For the wall 3, the results
of velocity field calculations were presented, as well as potential elastic energy distribution of
the undermined and overmined rock formations.
Among the main factors causing high seismicity level in this part of the deposit, is the presence of sand rock layers, created edges and remnants, but also nonuniformity in the thickness of
its extraction. Potentially seismogenic formations occur within both big and small distances of
the extracted seam, thus (taking into consideration rock burst hazard of the roof) the character
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K1
K3
Sc.3
K8
K7
K39
K10
419, 418
501
507
509
510
10^4 J
10^5 J
10^5 J
10^6 J
10^7 J
Fig. 1. Exploitation outline of seam 503 with highlighted tremors focii, recorded during the mining wall 3
construction and edges of the conducted exploitation
of their involvement in tremor energy is crucial. Works in the researched area, conducted thus
far near the wall 3, generated close to 2 thousand tremors, including 114 high-energy tremors:
98 with energy of 105 J, 13 with energy of 106 J, 2 with energy of 107 J and one tremor with
energy of 8×108 J.
3. Energy changes formation in rock mass, changes
of longitudinal wave velocity
The level of induced seismicity is usually determined by processes taking place in more
than one seismogenic layers. In practice, the objective obstacles make it impossible to calculate
depth coordinates of the tremors with satisfactory accuracy, what would allow their allocation
to particular strata. In respect to spacious configuration of exploitation correlations, changes of
potential elastic energy may have various character, depending on the stratum’s depth in which
they are calculated. Figure 2 shows an example of absolute value changes of elastic energy
(standardized to 1), along the lines parallel to raise gallery 4 (the head of wall no. 3), calculated
at depth ranging between 400÷800 m with 100 m step. The estimates were computed for 1200 m
sector of the panel length.
For the analogical panel length of the longwall 3, calculations were performed with the
use of passive tomography method. Velocity of longitudinal wave dispersion was determined
for successive monthly (two-month – in case of small amount of the induced tremors) periods
of the longwall mining course, obtaining different pictures of velocity field. Figure 3 presents
a synthetic map that was created as a result of estimated velocity maximum value selection at
each point. The values, as on Figure 2, were standardized to 1.
Absolute elastic energy (standardized to 1)
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1
0.8
Fi400
Fi500
Fi600
0.6
Fi700
Fi800
0.4
0.2
0
0
100
200
300
400
500
600
700
800
900 1000 1100 1200
Raise gallery 4 [m]
Fig. 2. Absolute elastic energy changes calculated for layers of different depth – contour along
the raise gallery no. 4
Sc.3
Fig. 3. Maximum velocity changes of the longitudinal wave – standardized to 1
4. Discussion
Accuracy of the seismic hazard prediction depends on proper selection of rock layers, in
which occurring energy changes decide about the observed hazard level (Fig. 2). During the first
evaluation, prognostic calculations can be performed that take into consideration energy processes
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taking place in all layers, assuming for each of them the same balance equal 1. Using additional
information – the results of velocity field estimates, it becomes possible to select the layers, in
which occurring energy changes have important influence on the observed hazard level changes,
and variety of balances assumed for particular strata during the hazard status estimate.
The simple model of regression was established:
jS =
where:
ai, a0
φi
lw
ε
—
—
—
—
lw
å ai j i + a 0 + e
(8)
i =1
regression model parameters,
elastic energy values calculated for i-changes layer,
number of layers,
random parameter.
In order to determine, which of the considered rock layers have influence on the observed
seismicity and rock burst hazard level (quantified with a use of maximum estimated values of longitudinal wave velocity), in the process of model building the procedure of step-by-step regression
was used. Each time after variable entry into the model, F distribution values (Fischer-Snedecor)
were calculated for each independent regression variable and compared with fixed critical value.
That provided information about participation of each independent variable in the regression.
Performed calculations let us assume that in both cases of raise gallery 3 data analysis, and
data describing energy changes in the contour along the raise gallery 4 (Fig. 2), the observed
hazard changes, expressed by changes of maximum wave velocity P (Fig. 3) can be described
taking into consideration processes occurring in two seismogenic layers – located at depth of
500 m and 800 m, both above and under the exploited seam 503. Conducted research of model
accuracy did not indicate errors requiring its modification. Significantly better match was obtained
for the data coming from the contour of raise gallery no. 4. It is crucial because most of highenergy tremors that occurred during longwall mining 3 (Fig. 1) were located in the surroundings
of that area. Figure 4 shows the results of regression equation. Diagram of analyzed parameters
changes was prepared for cross section of both wall headings. Correlation coefficient between
φS values and maximum wave velocity changes P, equals respectively 0,3 and 0,5.
The results of the presented analysis show that the layers situated about 200 m above and
100 m under the exploited deposit is of biggest influence in relation to the observed seismic
and rock burst hazard. According to the results of step-by-step regression, the influence of other
layers is insignificant.
Developed method might be used in preparation of qualitative predictions of seismic and
rock burst hazard at the active and constructed panels of longwall mining, which take into consideration energy changes occurring in selected rock strata.
The application of regression equation (8) enables as well preparation of quantitative estimates of hazard level changes (in the parts of deposit, in which the constancy of rock layers
mechanical properties can be assumed).
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1
Calculated value changes j,
changes of max. wave velocity P
0.98
0.96
0.94
0.92
0.9
0.88
0.86
0.84
0.82
0
200
Obs. Dow. 3
400
600
Raise gallery [m]
Pred. Dow. 3
800
Obs. Dow. 4
1000
1200
Pred. Dow. 4
Fig. 4. Value changes φS calculated with use of regression equation and standardized to 1 changes of maximum
wave velocity P – cross section of raise gallery 3 and 4
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Received: 02 July 2010