Dynamic events in hard rocks

Transcription

Autor: Christian Jakob & Prof. Dr. habil. Heinz Konietzky, (TU Bergakademie Freiberg,
Geotechnical Institute)
1
Introduction ................................................................................. 2
2
Introduction to seismology ............................................................... 4
3
4
5
2.1
Characteristics of elastic waves ..................................................... 4
2.1.1 Body waves ................................................................... 4
2.1.2 Surface waves ................................................................ 6
2.2
Localization of earthquakes .......................................................... 7
2.2.1 Absolute localization ......................................................... 7
2.2.2 Relative localization .......................................................... 9
2.3
Magnitudes and intensities ........................................................... 9
2.4
Seismotectonics ....................................................................... 12
2.5
Determination of source parameters ............................................... 13
2.5.1 Fault plane solution .......................................................... 13
2.5.2 Seismic moment, corner frequency and secondary source parameters15
2.6
Sensors for seismic waves ........................................................... 18
2.7
Station networks ....................................................................... 19
Engineering seismology .................................................................. 21
3.1
Engineering seismological parameters ............................................. 21
3.2
Estimation of maximal magnitude ................................................... 22
3.2.1 Determination from magnitude-frequency relation....................... 22
3.2.2 Determination from Benioff curve .......................................... 23
3.3
Estimation of peak ground velocities ............................................... 23
3.4
Legal standards........................................................................ 24
Induced seismicity ......................................................................... 28
4.1
Surface dam induced seismicity ..................................................... 28
4.2
Mining induced seismicity ............................................................ 28
4.3
Injection induced seismicity .......................................................... 30
Blast vibrations............................................................................. 33
Editor: Prof. Dr.-Ing. habil. Heinz Konietzky
Layout: Angela Griebsch
TU Bergakademie Freiberg, Institut für Geotechnik, Gustav-Zeuner-Strasse 1, 09599 Freiberg •[email protected]
Only for private and internal use!
1
Updated: August 16, 2014
Introduction
All geomechanical processes are time-dependent i.e. dynamic. Only process velocities
vary strongly. There are highly dynamic processes like explosions with propagation
speeds of several 1000 m/s and extremly slow elapsing processes like orogenesis or
creep processes with velocities in order of mm/year.
According to the length of the observation window processes can be treated as real
dynamic or quasi-static: Thus if change of physical quantities in the observation window
is insignificant low, a static view can be carried out.
In many cases processes interfere with each other, where velocities and magnitudes
can be very different (e.g. a blast event at digging in a creeping salt rock). That is why
it must be decided in every individual case how these coupled processes have to be
considered.
For practical reasons in geomechanic often just the “highly dynamic” ones are meant
by dynamic processes in contrast to the slowly elapsing ones, that usualy fall in the
definition “creeping”.
Page 2 of 35
Table 1 shows an overview over the significant geomechanical relevant dynamic processes.
Dynamic process
Duration
Occurances
Remarks
Earthquakes
Seconds to
minutes
Shocks, rifts,
cracks, faults
at plate
edges,
intra plate
seismicity
Blasts,
explosions
Seconds
Shocks,
fractures
because of
mining, tunnel
excavation
and military
Induced
seismicity
Seconds to
minutes
Shocks,
fractures
dam-,
mining-,
injection-,
reservoirinduced
and fracing
Recent
crust movements
Millions of
years
plate tectonics,
trench formation,
orogenesis
mm/year
Depression events
at earth
surface
Minutes
to years
Earth fall,
geosyncline
up to
several m
deep and
several km2
big
Mass movements
Minutes
Rockslide, mudflow
avalanches
into the
km3 range
Dynamic events
in rock and
tunnel construction
and mining
Seconds to
days
Rock burst,
fractures
triggers
microearthquakes
and earthquakes
up to M ≈ 5
Table 1: Dynamic processes in hard rocks
Page 3 of 35
2
Introduction to seismology
Dynamic events in the earth generate different kinds of elastic waves. The different
types of waves differ in propagation velocity, amplitude and frequency. Figure 1 shows
an seismological record, in which body waves (P and S) as well as surface waves
(Rayleigh and Love) are visible.
Fig. 1: Example seismological record (source: T. Meier, http://www.ifg.uni-kiel.de)
From the records of worldwide installed seismometers seismologists can characterize
the source (explosion, landslide, earthquake, mine collapse, meteor impact and so on)
and determine source parameters (hypocenter, source time, magnitudes, source mechanism and so on).
2.1
Characteristics of elastic waves
During propagation in a media elastic waves dissipate energy. The dissipation differentiates between geometrical spreading, damping and scattering. Surface waves
propagate only at the surface of a media, accordingly in two dimensions. Body waves
propagate in three dimensions in the media. Consequently the energy dissipation from
geometrical spreading of surface waves is smaller and the range of influence is bigger
than that of body waves.
The damping of elastic waves is frequency dependent. High frequencies are damped
stronger than low frequencies. This is the reason for the frequency spectra change of
the wave depending on traveled distance in a media.
2.1.1
Body waves
The P-Wave (primary wave or also called pressure wave or longitudinal wave) is characterized by high frequencies and high propagation velocities. Because of the stronger
damping of this high frequency waves they mostly have smaller amplitudes than other
waves. The oscillation of particles in the media take place in the direction of propagation
(see Fig. 2).
Page 4 of 35
Fig. 2: P-wave
P-waves propagate in all media (solids, liquids and gases). Depending on the density
of a media the propagation velocity varies between 343 m/s (acoustic waves in air) and
∼ 13700 m/s in the lower mantle of the earth. More propagation velocities for rocks and
sediments are shown in table 2
Die propagation velocity for P-waves is given by the elasticity parameters (elasticity
modulus E and Poisson’s ratio ν) and the density ρ. With the Lamé parameters
λ=
νE
(1 + ν)(1 − 2ν)
and
µ=
E
2(1 + ν)
(1)
the P-wave velocity is resulting in
s
vp =
λ + 2µ
.
ρ
(2)
The S-Wave (secondary wave or also called transverse wave or shear wave) has lower
frequencies and lower propagation velocities than the P-wave. Normally the S-wave
has a higher amplitude than the P-wave. The oscillation of particles in the media take
place orthogonally to the direction of propagation (see Fig. 3).
Fig. 3: S-wave
S-waves propagate only in media which have a shear modulus G = µ > 0 and hence
have a shear resistance. For that reason shear waves can not propagate in liquids and
gases. The S-Wave velocity is determined by µ and ρ as follows.
r
µ
vs =
(3)
ρ
√
As an approximation the S-wave velocity can determined by the ratio vp /vs ≈ 3.
Page 5 of 35
material
air
clay
loam
marl
sand∗
sand∗∗
gravel∗
sandstone
limestone
claystone
vp in km/s
vs in km/s
0.3
sediments
1.2 - 2.8
0.11 - 1.5
0.5 - 1.9 0.44 - 1.08
1.2 - 4.7
0.4 - 2.6
0.1 - 0.6
0.1 - 0.5
0.2 - 2.0
0.1 - 0.5
0.6 - 1.4
0.32 - 0.7
0.8 - 4.5
2.0 - 6.2
2.2 - 4.2
0.32 - 2.7
1.8 - 3.8
0.42 - 0.8
material
vp in km/s vs in km/s
water
1.5
metamorphic
gneiss
6.6 - 7.0
amphibolite 6.9 - 7.0
peridotite
7.9 - 8.1
eclogite
7.8 - 8.1
magmatic
granite
5.6 - 6.3
gabbro
6.5 - 6.8
basalt
5.5 - 6.3
∗
(dry)
∗∗
3.4 - 4.0
3.8 - 4.6
4.2 - 4.7
4.5 - 5.0
2.5 - 3.8
3.8 - 3.9
n. a.
(wet)
Table 2: Typical propagation velocities for P- and S-waves in rocks and sediments
2.1.2
Surface waves
Surface waves are generated by refraction of P- and S-waves at all free surfaces (huge
impedance contrast). Rayleigh-waves, named by the british physicist John William
Rayleigh (1842-1919), are characterized by low frequencies (around 0.05 Hz) and high
amplitudes. The oscillation of particles in the media is elliptically on a vertical plain (see
Fig. 4).
Fig. 4: Rayleigh-wave
The propagation velocity is with 2 - 4 km/s a bit smaller than the S-wave velocity. Water
waves at the surface of a sea or an ocean are typical Rayleigh-waves. Rayleigh-waves
triggered from earthquakes felt most strongly and cause the most damage.
Love-waves, named by the british mathematician Augustus Edward Hough Love (1863
- 1940), are also characterized by low frequencies and high amplitudes. The oscillation
of particles in the media is horizontal, perpendicular to the direction of movement (see
Fig. 5).
They are with 2 - 4.4 km/s the fastest surface waves, but still slower than S-Waves.
Love-waves generated from earthquakes can cause damage by horizontal shearing of
the soil.
Page 6 of 35
Fig. 5: Love-wave
2.2
Localization of earthquakes
The localization of an earthquake consists of the determination of the source parameters geographic location, depth and source time of the earthquake. To determine this
parameters the arrival times (tp and ts ) from P-waves and S-waves are used.
2.2.1
Absolute localization
The analysis of the differences in the waves runtime is denominated absolute localization. This method for local earthquakes presumes a homogeneous and isotropic half
space. The model concept supposes a punctate rupture (hypocenter with coordinates
x0 , y0 , z0 ) in the rock at the time t0 . The source emits seismic waves spherical with the
velocities vp respectively vs and hit the seismic stations (seismometers or geophones) i
at the times ti . With the coordinates (xi , yi , zi ) the station locations are termed. If the
arrival time of P-wave and S-wave tp,i und ts,i can be determined, then the source time
t0 and the hypocenter distance Di to the station can also by determined.
vp =
Di
tp,i − t0
and
vs =
Di
ts,i − t0
(4)
Equations in (4) result in the relation between runtime difference ts,i − tp,i and source
time.
vp
− 1 (tp,i − t0 )
(5)
ts,i − tp,i =
vs
From equations (4) and (5) the source time can be determined by
t0 = tp,i −
ts,i − tp,i
vp
−1
vs
(6)
and the hypocenter distance Di to the station i by
Di = vp (tp,i − t0 ).
(7)
In general P-onsets are allocable more exactly than S-onsets from the seismograms.
For this reason most locating algorithms use P-onsets preferential. The theoretical onset time result from geometric considerations as follows.
p
(xi − x0 )2 + (yi − y0 )2 + (zi − z0 )2
Di
=
(8)
ttheo. =
v
v
Page 7 of 35
Thereby is v the propagation velocity of the P-wave or the S-wave. The measured
runtime
tmeas. = ti − t0
(9)
differs in normally from the theoretical value ttheo. . Hence is the difference
∆t = tmeas. − ttheo. 6= 0,
(10)
because the propagation velocity distribution is not homogeneous in the ground and the
onsets are not exactly allocable. Using equations (8) and (9) in equation (10) results in
the Geiger-equation (named by the swiss geophysicist Ludwig Carl Geiger).
p
(xi − x0 )2 + (yi − y0 )2 + (zi − z0 )2
(11)
∆t = ti − t0 −
v
For solving the equation system the least square method is used, that means it becomes
a minimization problem (Künzel 2013).
#2
"
p
N
(xi − x0 )2 + (yi − y0 )2 + (zi − z0 )2
1 X
⇒ M in
(12)
ti − t0 −
N i=1
v
This minimization problem is solved by giving a start value and find the minimum iteratively (Schulte-Theis 1995). Equation (11) contains four unknowns (x0 , y0 , z0 und t0 ).
For this reason at least four onsets of P- and S-waves from at least three stations
are necessary for localization. Figure 6 shows the overlap of three hemispheres with
the radius Di .
Fig. 6: Localization of an earthquake with three stations (source:
http://www.geophysik.uni-muenchen.de/)
Page 8 of 35
2.2.2
Relative localization
A relative localization can be used to improve the distribution resolution from nearby
events. In the process a relocation with the results of the absolute localization is performed. Thereby the runtime of different earthquakes is compared to get more accurate
results. For the relative localization an absolute reference point is necessary. For the
Master-Event-Technique a well localized earthquake or a performed blast is used for
that. For the Joint Hypocenter Determination (JHD) the focal point of all hypocenters
is used instead. Both methods can be combined with a waveform correlation (Waldhauser). The relative localization error can be reduced significantly with this methods
(see Fig. 7).
Fig. 7: Comparison of localization accuracy of absolute (left) and relative localization (right)
(source: Fischer and Horálek 2000)
2.3
Magnitudes and intensities
Magnitudes are normally related to maximum amplitudes of the seismograms and therefore they are related to the released energy of an earthquake. A well known magnitude
is the local magnitude ML also called Richter-magnitude. Charles Richter (1900 1985) realized the correlation between measured amplitude A and the epicenter distance ∆ and found the following relation.
A(∆)
= constant
A0 (∆)
(13)
A0 denotes the amplitude of a reference earthquake. In doing so the reference earthquake in a distance of ∆ = 100 km and a amplitude of A0 = 1 mm in California is defined
by Richter as magnitude ML = 3. The local magnitude is given by equation (13).
ML = log A(∆) − log A0 (∆)
(14)
Equation (14) is valid for epicenter distances ∆ < 600 km only. The local magnitude has
an upper limit of ML = 6.5 which is caused by measurement devices. Larger magnitudes
are determined by moment magnitudes.
Page 9 of 35
The moment magnitude Mw is based on the concept of the seismic moment M0 and
is calculated as follows.
Mw =
2
(log M0 − 9.1)
3
(for M0 in Joule)
(15)
The seismic moment is a measure for the strength of the earthquake and is composed
of rocks shear modulus G, the rupture area F and the displacement u along F .
M0 = GF u (scalar)
(16)
To determine the surface wave magnitude Ms the peak ground velocity (A/T )max is
used.
Ms = log (A/T )max + 1.66 log ∆ + 3.3
(17)
The Moscow-Prague-equation (17) is valid for epicentral distances between 2° and 160°
and hypocenter depths up to 50 km. The surface wave magnitude scale is limited at
Ms = 8.5.
For the body wave magnitude Mb (also mb or mB ) the peak ground velocity (A/T )max
of P- and S-waves is used.
(18)
Mb = log (A/T )max + Q(∆, h)
Where Q is the correcting term which depends on epicentre distance, depth h and the
used instrument. The body wave magnitude scale is valid up to Mb = 6.5. Table 3 gives
an overview about the Richter scale (respectively other scales at M > 6.5) including the
released energies and the frequency of occurrence per year.
Magnitude
Description
0,1 - 1,9
2,0 - 2,9
3,0 - 3,9
4,0 - 4,9
5,0 - 5,9
6,0 - 6,9
7,0 - 7,9
8,0 - 8,9
9,0 - 9,9
10,0 - ∞
Micro
Minor
Minor
Light
Moderate
Strong
Very strong
Disastrous
Catastrophic
Ruinous
Released energy
0,006 to 1 t
1 to 32 t
32 to 1.000 t
1 to 32 kt
32 to 1.000 kt
1 to 50 Mt
50 to 1.000 Mt
1 to 5,6 Gt
5,6 to 1.000 Gt
> 1.000 Gt
0,002 to 4,2 GJ
4,2 to 135 GJ
135 to 4.200 GJ
4,2 to 135 TJ
135 to 4.200 TJ
4,2 to 210 PJ
210 to 4.200 PJ
4,2 to 23,5 EJ
23,5 to 4.200 EJ
> 4.200 EJ
Occurrence
> 2.500.000
350.000
49.000
6.200
800
120
18
1
0,05
0,01
Table 3: Magnitude scale with description, released energy (TNT-equivalent in [t] and in [J]) and
the average frequency of occurrence per year
Page 10 of 35
Fig. 8: Comparison of moment magnitude with other magnitudes (source: Studer and Koller
1997)
The intensity is a measure for the strength of an earthquake. It describes the observed
effects of an earthquake without measurement devices (Studer and Koller 1997). These
effects are damages at buildings and human feelings (macro seismics). In contrast to a
magnitude multiple intensity values exist for one earthquake depending on the epicentral distance.
There are different scales of intensity. Most of them are divided in twelve steps an usually numbered by roman digits. The most common scales are the European Macroseismic Scale (EMS-98), the Modified Mercalli Scale (MMS) and the Rossi-Forel-Scale.
Figure 9 shows the EMS-98 in short form.
Page 11 of 35
Fig. 9: Short form of EMS-98
2.4
Seismotectonics
Seismotectonics describes the earthquake origin with focus on movements and deformations of the earth’s crust. The american geophysicist Harry Fielding Reid (1859 1944) developed the elastic rebound theory that implies that stresses in the earth’s
crust are discharging jerkily in form of earthquakes along preexisting faults.
The conceptional model is a shear fracture like shown in Fig. 10. With the growing
stress the strength of the rock is exceeded at a certain point and it comes to a fracture
along the shear surface.
A black dot (see Fig. 11) tags the hypocenter of the earthquake. The movement of
the rupture front around the hypocenter is pointed by the time steps t1 and t2 . The
displacement field is indicated by the small arrows.
Page 12 of 35
initial state
preexisting fault
stress is growing
rupture
Fig. 10: Elastic rebound theory
Hypocenter
t2
Rupture area
t0
t1
Displacement field
Rupture front
Fig. 11: Rupture area in a volume
2.5
2.5.1
Determination of source parameters
Fault plane solution
P-wave polarities of the vertical component (z) are picked from seismometer recordings.
This happens already during picking the onsets. Imagine a hypothetic sphere around
the earthquake focus (s. Fig. 12). The pentration points of ray paths to the stations are
marked on the spheres surface.
A peak upwards means a compressive onset and is denoted by C. In contrast a movement downwards is a dilatative onset and is denoted by D. The penetration points are
marked by C or D respectively their onset (s. Fig. 13 left). In doing so quadrants with
same polarities develop, which are seperated by big circular curves (s. Fig. 13, middle).
After convention of Aki & Richards compressive onsets are colored in black or any other
(dark) color and dilatative onsets in white or any other (light) color (Fig. 13 right). If
many points are located in the transition zones of C to D, both areas can be exactly
Page 13 of 35
dilatative onsets
compressive onsets
Epicenter
2
1
North
4
3
East
Station
Depth
Pentration point
Ray paths
Hypocenter
Fig. 12: Earthquake focus with hypothetic sphere and penetration points of the ray paths (red:
compressive, black: dilatative) to the stations
seperated and a very accurate faul plane solution can be achieved. That is why many
station recordings are needed for this method.
C
C
C
D
D
C
C
C
C
D
D
C
D
(a) mark onsets
(b) plot circles
(c) color quadrants
Fig. 13: Evolution of a fault plane solution by the onset method
With this method good results can just be obtained, when a sufficient amount of polarities are available and when they are well distributed over the sphere surface. This
means that this method can be used for earthquakes with big magnitudes. To determine
fault plane solutions of smaller earthquakes with less polarities, additional informations
like amplitude ratios are neccessary.
Page 14 of 35
A fault plane solution is usually illustrated by a azimuthal equal-area projection (also
called Lambert azimuthal projection or Schmidt net) of the lower hemisphere.
Fig. 14: Different fault types with corrensponding fault plane solutions (source: Berckhemer
1990)
2.5.2
Seismic moment, corner frequency and secondary source parameters
log(amplitude)
From the amplitude spectrum of P- and S-wave the long-period amplitude level A0 and
the corner frequency f0 can be determined (s. Fig. 15).
A0
log(f requency)
f0
Fig. 15: P-wave amplitude spectrum of an earthquake (source: Chair for rock mechanics, TU
Bergakademie Freiberg)
The seismic moment M0 is (like magnitude) a measure for the strength of the source
Page 15 of 35
process. From amplitude level the seismic moment is derived as follows.
M0 = 4πρDi vp3 A0 /Φ
(19)
Φ represents the directivity factor from directional characteristic1 of the earthquake. The
hypocentral distance to station i is denoted by Di . The corner frequency f0 characterizes the dimension of the seismic source. Assuming a circular source plane the source
radius R is calculated from corner frequency after Madariaga 1976.
R=
2vp
(2πf0 )2
(20)
For the calculation of displacement D with shear modulus µ it applies:
D=
M0
µπR2
(21)
f0 , R, M0 und Mw are closely linked. Figure 16 demonstrates these correlations graphically with the help of some global earthquakes.
The difference between source stress σ0 before and source stress σ1 after the earth-
Fig. 16: Correlations between corner frequency, source radius, moment and magnitude of
induced earthquakes (source: G.Kwiatek from presentation FKPE-Workshop 2010)
1
In case of a shear failure Φ can be obtained from fault plane solution.
Page 16 of 35
quake is called stress drop.
∆σ = σ0 − σ1
(22)
Assuming a circular source plane stress drop can be derived from displacement and
source radius.
7 πµD
·
(23)
∆σ =
16
R
Stress drop is closely linked with the seismic moment Mij . The seismic moment (tensor)
is obtained by volume integration over moment tensor volume density mij .
ZZZ
mij dV
(24)
Mij =
V
The moment tensor volume density is a fictitious stress tensor, which is derived from
the product of inelastic deformation tensor Eijkl and the inelastic deformations εTij .
mkl = Eijkl · εTij
(25)
σij
mij
∆σij
εTij
εij
Fig. 17: Visualization of seismic moment und stress drop
Page 17 of 35
2.6
Sensors for seismic waves
We distinguish between deformation sensors, velocity-proportional sensors and acceleration sensors. In seismology mainly geophones and seismometer (technical advancement of seismograph) are established. These sensors convert mechanical vibrations acting at measuring point into a velocity-proportional electrical voltage. The
voltage signal is amplified and digitized afterwards.
An inertia seismometer consists of a mass M ,
that is connected in parallel with a spring and a
damper (s. Fig. 18).
Assuming that all movements are restricted in zz(t)
direction, then u(t) is the movement of the earth
and z(t) is the relative movement of the mass M .
In idle state the spring has a length of z0 . Two
z0
M
forces are acting on mass M in this system. The
spring bears a force proportional to deflection z −
z0 . With the stiffness of the spring k the force
z
is obtained by −k(z − z0 ). The damper bears a
force proportional to its relative velocity ż(t) beEarth
tween mass and earth. With damping constant C
Fig. 18: Inertia seismometer
damping force is defined as −C ż(t). With accelerations ü(t) and z̈(t) following relationship is given.
M (z̈(t) + ü(t)) = −C ż(t) − k(z(t) − z0 )
(26)
By setting z0 = 0 the equation becomes
z̈ + 2hω0 ż + ω02 z = −ü,
(27)
where 2hω0 = C/M and ω02 = k/M . Hence, acceleration ü can be described from a
linear combination of z(t) and its time derivations.
Seismographs are no longer used today. They were used before digital age and
recorded soil movement by a needle on paper strips (s. Fig. 19 left).
Geophones (s. Fig. 19 middle) work the same way as inertia seismometers. They are
used in seismic exploration, to gather informations about the ground. There, usually artificial sources are used (hammer stroke, drop weight, vibratory plate or blast) to create
seismic waves.
In modern seismometers (s. Fig. 19 right) a magnet induces a voltage in a surrounding
inductor. The measured voltage is amplified, digitized and either saved on site (offline
station) or sent via internet conection to a data-collection center (online station).
Page 18 of 35
Fig. 19: Different seismic sensors: seismograph (left), geophone (middle) and inner life of a
seismometer (right)
Both geophones and seismometers are available as 1-component variant (just vertical)
and 3-component variant (1 vertical and 2 horizontal). They differ furthermore in their
frequency sensitivity. For long-range seismic applications low-frequency sensors (0.01
- 10 Hz) and for microseismic applications high-frequency sensors (1 - 200 Hz) come to
use.
2.7
Station networks
A requirement for a good source parameter determination is a good azimuthal coverage
with stations around the epicenter region. In the ideal case stations are distributed with
equal distance on a circle around the epicenter. For local earthquakes with magnitudes
< 4 distances of several 100 meters to several kilometers are favorable. In this case
the sensors should be desinged to record higher frequencies (seismometers with 1sor 5s-pendular). For global events it is better to choose stations with higher distances.
Here broadband seismometers (with 20s- or 100s-pendular) are favored.
Page 19 of 35
Fig. 20: Distribution of seismological stations in central Germany and Czech Republic (source: Jakob 2009)
Page 20 of 35
3
Engineering seismology
Engineering seismology is understood as a branch of seismology, that provides required physical data about potentially destructive ground movements of earthquakes
to the engineer who is responsible for earthquake-resistant constructions. In contrast
earthquake engineering is an engineering discipline, that deals with design and construction of earthquake-resistant structures and thereto uses seismological output parameters provided by engineering seismology (Hurtig 1984).
3.1
Engineering seismological parameters
Every building represents a vibratory system, that responds different depending on its
resonance on dynamic load caused by waves with corresponding frequencies. To translate the effect of an earthquake into engineering technically feasible parameter, spectral
composition and polarization of seismic wave must be considered (Hurtig 1984).
Sensors (s. section 2.6) can detect engineering seismological parameters ground acceleration a, ground velocity v and ground displacement s. But regardless of which
physical parameters are recorded by the sensor, representation of adequate information of ground motion as acceleration, velocity or displacement is also possible, because
it is:
Z
ZZ
d2 s
dv
= 2
(28)
s = v dt =
a dt2 resp. a =
dt
dt
Figure 21 shows values for a, as well as calculated values for v and s for a typical
earthquake.
Fig. 21: Acceleration recording of an earthquake plus calculated velocities and displacements
(source: Chair for rock mechanics, TU Bergakademie Freiberg)
Respective maximum values are denoted by amax = P GA (Peak Ground Acceleration),
vmax = P GV (Peak Ground Velocity) and smax = P GD (Peak Ground Displacement).
Additional dynamic stresses can be determined from velocities.
p
σdyn
= ρ · vp · vc
and
s
σdyn
= ρ · vs · vt
There vc and vt are velocities in compression and translation (shearing).
Page 21 of 35
(29)
When a seismic wave propagates through the earth, its frequency and amplitude changes
(s. section 2.1). Figure 22 shows averaged response spectra2 for an earthquake with 8
and 32 km source distance.
Fig. 22: Response spectra of horizontal accelerations of an earthquake with magnitude 6,5 in 8
(left) and 32 km (right) source distance (after Seed et al. 1974, source: Hurtig 1984)
The curves in figure 22 show, that big amplitudes with higher frequencies (T = 1/f <
0, 5 s) occur in small distance (8 km). With increasing source distance the influence of
damping becomes apparent. At soft underground damping effect is compensated due
to soil reinforcement within certain period range, so that a relative delay of amplitudes
is observed compared to amplitudes on rocky underground. In a period range of 0,5
to 1,5 s and source distance 32 km it becomes apparent, that amplitudes are higher at
soft underground (Hurtig 1984).
3.2
Estimation of maximal magnitude
For every region a maximal magnitude Mmax and intensity Imax exists. Their determination is of extremely importance for assessment of earthquake hazard. However
there are only few reliable approximate approaches (Hurtig 1984). Two of them will be
presented in the following sections.
3.2.1
Determination from magnitude-frequency relation
The Gutenberg-Richter law describes the relation between magnitude and frequency
of earthquakes in an area.
log10 N = a − bM
(30)
There N is the number of earthquakes, that have a magnitude of ≥ M . a and b are
constants, whereupon b generally3 is near 1. Figure 23 shows the Gutenberg-Richter
relation for micro-earthquakes in the area Aue-Schneeberg (Germany). In the space of
time from 1998 to 2013 approx. 1650 events were registered in this area.
Smaller events are harder to detect by seismic sensors, because their amplitudes are
near noise level. For this reason the maximum number of events is at a magnitude of
2
Response spectrum is achieved by fourier transformation of time series (e.g. accelerations) in frequency domain.
3
The b-value describes the ratio of small to big earthquakes. For example if many small and few big
earthquakes occur, b-value is > 1.
Page 22 of 35
Fig. 23: Gutenberg-Richter relation for the area Aue-Schneeberg (source: Chair for rock
mechanics, TU Bergakademie Freiberg)
−1, 5 (see Fig. 23). At highest magnitudes the relation usually bends down because
space of time for observation is too small for statistical analysis of big earthquakes. By
installing a straight line at the linear part of the relation (red line in Fig. 23) maximal
magnitude can be estimated (here: Mmax ≈ 2, 5). Hurtig 1984 proposes for estimation
of Mmax and Imax :
Mmax = Mmax,beobachtet + 0, 5 resp. Imax = Imax,beobachtet + 1
3.2.2
(31)
Determination from Benioff curve
With Benioff curve is understood to the representation of cumulative release of energy
within an area with time t (Hurtig 1984).
Xp
Ei = f (t)
(32)
There Ei is the release of energy for a single earthquake. Figure 24 shows the Benioff
curve of eastern Germany since year 1500. The curve shows clearly periods of weak
and strong activity (Grünthal 1981).
From this curve some conclusions can be derived: Assuming that total activity of the
region of interest is limited by an upper and a lower strain state (dashed lines in Fig. 24),
a possible maximal earthquake can be defined as abrupt release of energy from lowest
to highest peak state. This would give a maximal magnitude of 5,7 for the investigated
territory (Grünthal 1981).
3.3
Estimation of peak ground velocities
From the empirical relation
P GV0 = k1 · Mmax + k2
(33)
hypocenter peak ground velocity P GV0 can be estimated. k1 and k2 are empirical coefficients, that have to be determined from a given data set for the respective investigation
Page 23 of 35
Fig. 24: Benioff curve for the territory of the GDR since 1500 with energy E in Joule (source:
Grünthal 1981)
area. Peak ground velocity P GV (x) changes with distance x according to the following
relationship.
P GV (x) = P GV0 · e−αt x
(34)
Here αt is a theoretical damping parameter that contains energy dissipation from diffusion and damping. αt is obtained by the seismic quality factor Q, that depends on
frequency f and phase velocity c of the seismic wave.
Q=
πf
αt c
(35)
Near the source geometrical spreading dominates. This can be considered in equation
(34) by multiplication by factor 1/x. Figure 25 shows the decrease of peak ground
velocities with distance x at different magnitudes for the region Aue-Schneeberg.
3.4
Legal standards
In the construction of buildings in seismic areas special regulations apply. The aim is to
save human life, to limit damage and to ensure, that important constructions for public
safety and infrastructure stay operable in the case of an earthquake. Following standards are specified from legislator:
The european standard Eurocode 8 (EN 1998) “Design of structures for earthquake
resistance” applies for design and construction of buildings and structures in seismic
Page 24 of 35
Fig. 25: Peak ground velocities at different magnitudes (source: Chair for rock mechanics, TU
Bergakademie Freiberg)
areas. It contains ordinary as well as special constructions e.g. nuclear facilities, big
dams or offshore-constructions.
The DIN 4149 (2005-04) “Bauten in deutschen Erdbebengebieten” applies for conceptual and structural design and construction of usual buildings.
Essentially the force F acting on a building or part of the building is calculated. Newton’s
second law says, that the force F is given by multiplication of mass m (here: building
mass) and the acting acceleration a (here: rated ground acceleration ag ). Different factors affect applied force F . Hence the law is extended by a function f to consider these
factors.
F = m · ag · f (f actors)
(36)
Seismic areas in Germany affected by DIN 4149 are classified in earthquake zones 1
to 3 (s. Fig. 26). Seismic risk outside of zones 1 to 3 is regarded as so low, that the
standard does not have to be applied there.
In DIN 4149 it applies the rated ground acceleration ag as zone specific parameter.
earthquake zone
1
2
3
intensity range
6, 5 ≤ I < 7
7 ≤ I < 7, 5
7, 5 ≤ I
ag in m/s2
0,4
0,6
0,8
Table 4: Rated ground acceleration relating to earthquake zones and intensity range
Page 25 of 35
Fig. 26: Maps: Earthquake intensity (left) and earthquake zones (right) in Germany (source:
Grünthal 2004 and DIN 4149)
F actors are:
• Regularity of the construction ⇒ behavior factor
• Geological bedrock ⇒ control periods of response spectrum and bedrock parameters
• Importance of the construction ⇒ importance factor
• Construction damping ⇒ damping correction factor
• Correction factor for multi-story buildings
A method for determination and assessment of impact on buildings caused by vibrations
is defined in DIN 4150-3 (1999-02) “Erschütterungen im Bauwesen”. The assessment
is based on guide values for velocities of short-time and long-lasting vibrations (s. Table
5 and 6).
Page 26 of 35
Type of building
Guide values for velocities vi in mm/s
Base frequencies
1 Hz to 10 Hz 10 Hz to 50 Hz 50 Hz to 100 Hz
Commercially used buildings,
industrial and similar
structured buildings
20
20 to 40
40 to 50
Residential buildings and in
construction and/or use
similar buildings
5
5 to 15
15 to 20
3
3 to 8
8 to 10
Buildings with special
shock sensitivity that do not
match with the above ones
and especially worth preserving
Table 5: Guide values for velocities for assessment of impact of short-time vibrations on
buildings (source: DIN 4150-3)
Type of building
Guide values for velocities vi in mm/s
Uppest ceiling, horizontal, all frequenzies
Commercially used buildings,
industrial and similar
structured buildings
10
Residential buildings and in
construction and/or use
similar buildings
5
Buildings with special
shock sensitivity that do not
match with the above ones
and especially worth preserving
2,5
Table 6: Guide values for velocities for assessment of impact of long-lasting vibrations on
buildings (source: DIN 4150-3)
The estimation of peak ground velocities is described in section 3.3. The recieved
values for P GV are compared with the guide values.
Page 27 of 35
4
Induced seismicity
Engineering activity of humans can strongly influence the stress state near the surface,
so that earthquake-like events called induced seismicity were generated. Even in
mainly aseismic areas strong earthquakes can be caused in this way (Hurtig 1984).
4.1
Surface dam induced seismicity
Earthquakes are denoted by dam induced, when significant space and time relationships with dam parameters and storage regime are observable. The occurance of seismic events at construction and operation of surface dams may constitute a serious danger for the dam itself and also for residential areas downriver of the dam. Generally
seismicity increases at filling the dam, but there are also references on decreasing seismicity especially in seismic active areas (Hurtig 1984).
The maximal observed magnitude of a dam induced event was approx. 6,3 at 10. December 1967 in India (Koyna dam). Because of this event around 200 humans lost their
life, over 1500 were hurt and thousands got homeless. The dam got damaged, but resists.
Significant dam induced changes in seismicity were detected at over seventy sites
worldwide. Among all the factors storage regime most likely correlates with the observed induced seismicity (Gupta 1992). It suggests itself, that dam induced events
occur just in areas, where the earths crust is heterogenous near the surface and under significant latent tectonic stress state. Fault plane solutions obtained so far show
nearly exclusively either normal slip or horizontal displacements. It is noteworthy, that
movement process and fracture direction, which were obtained by fault plane solutions,
correlates with the tectonic deformation regime and the orientation of main stress axes.
Thus the mechanism of induced seismic events can be explained with given tectonic
frame (Hurtig 1984).
According to Hurtig 1984 there are two interpretation models for explanation of dam
induced seismicity. The load model sees additional stresses, that were generated by
load of the accumulated water interfering with the present tectonic stress, as cause of
the events. Thus stress increase can reach (at water filling of 100 m) maximal 10 bar.
The pore fluid model assumes a reduction of effective stresses by presence of a pore
filling medium. The effect of an increased pore pressure expresses itself in a displacement of MOHRs circle at constant radius to the left (s. Fig. 27). While reaching the limit
stress curve MOHRs failure criterion can be achieved. Simulatously water infiltration
can also lead to a decrease of the inner friction coefficient (Hurtig 1984).
4.2
Mining induced seismicity
In numberous mining areas in the world seismic events are detected, whose occurance
is related to underground mining. Especially often mining induced seismic events are
observed in coal mining. Strong seismic activity is also known from ore and salt mining
areas (Hurtig 1984).
Because of the variety of complex relationships (geomechanical causes, prerequisits
and promotive factors) a typification mining induced events is still not clearly possible.
Page 28 of 35
Fig. 27: Influence of load (a) and changes in pore pressure (P) on stress field (according to
Simpson 1976, source: Hurtig 1984)
Hurtig 1984 speaks therefore in general of “seismic events in mining areas” and divides
into these three types:
indirect Earthquakes in mining areas1 cause damage at constructions on and below
the surface or trigger seismic events in the extraction area.
Type I The local mining induced stress field triggers seismic events in the extraction
area. This type corrensponds largely hitherto existing conception of rock bursts.
Hurtig 1984 denotes this type as extraction induced seismicity.
Type II Underground cavities causes long-range stress rearrangement in a long-term,
that can cause earthquakes. Hurtig 1984 denotes this type as digging indued
seismicity. Thereby the events are in no relationship with the current extraction
operation.
However above typification contains just the failure of mine workings. Further events,
covered by the term mining induced seismicity, are:
• Seismicity in opencasts (mass rearrangements with and without soil liquefaction)
• Events triggered by drilling (specifically at natural gas/raw oil extraction)
1
Mostly a natural earthquake is assumed as cause. But it usually can not be excluded, that these
earthquakes were triggerd itself by mining activities!
Page 29 of 35
• Injection induced seismicity (geothermal energy, fracking, s. section 4.3)
• Fluid extraction induced seismicity (geothermal energy, natural gas/raw oil)
• Blast induced seismicity
• Events triggered by influx (dissolution in salt or karst)
In Germany the strongest events occured in salt mining (see table 7).
Year
Date
Month
Day
1888
1936
1940
1943
1953
1958
1961
1971
1975
1981
1989
1991
1996
2003
3
11
5
3
2
7
6
4
6
7
3
5
9
1
18
3
24
5
22
8
29
4
23
13
13
16
11
6
Localization
ML
I0
Ruhrgebiet NW
Ruhrgebiet NW
Krügershall, Saale-Revier
Schierstedt, Nord-Harz
Heringen, Werra-Revier
Merkers, Werra-Revier
Merkers, Werra-Revier
Aschersleben, Nord-Harz
Sünna, Werra-Revier
Ibbenbüren
Völkershausen, Werra-Revier
Ibbenbüren
Teuschenthal, Saale-Revier
Ibbenbüren
3,6
3,9
4,9
3,9
5
4,7
3,6
3,9
5,2
4,1
5,6
4,3
4,9
4,2
VI
V I − V II
V II
V I − V II
V II − V III
V II
VI
V I − V II
V III
VI
V III − IX
VI
V II
VI
Table 7: Induced seismic events in german mining areas with ML > 4, 0 or I > 6 (source:
Grünthal and Minkley 2005)
4.3
Injection induced seismicity
By grout injecting of liquids in deep boreholes earthquakes are induced. At hydraulic
fracturing this is even desired, because you want to generate cracks in the rock to
create or extend flow paths. In particular this procedure is used at extraction of raw oil
and natural gas as well as at hydraulic salt production and in deep geothermal systems.
Thereby pre-existing fault zones can be reactivated (s. Fig. 28) or unfractured rock will
be stimulated by crack formation (Hot-Dry-Rock-Method).
Similar to surface dam induced events (s. section 4.1) the increasing pore pressure
reduces the effective stress. The effect expresses itself in a displacement of MOHRs
circle at constant radius to the left (s. Fig. 27).
Some examples of injection induced events in europe are shown in the following table.
Interestingly no relationship between maximal magnitude and peak ground acceleration
(PGA) results from the table.
Page 30 of 35
Fig. 28: Schematic illustration of a reactivated fault zone at fracking (source: Dusseault et al.
2001)
Location/Country
Depth
[km]
Rock
PGA
[% g]
Date
Type
pmax
w
[MPa]
Vinj.
[m3 ]
max
ML
Soultz/FR
Soultz/FR
Bad Urach/DE
KTB/DE
Landau/DE
Hellisheidi/IS
Monte Amiata/IT
Basel/CH
3.5
5.0
4.3
9.0
3.0
2.5
3.0
5.0
Granite
Granite
Gneiss
Gneiss
complex
Basalt
Metam.
Granite
8
8
9
6
8
49
19
15
1993
2003
2002
1994
2007
2003
1969
2006
Stimulation
Stimulation
Stimulation
Inject. test
Circulation
Drill&Stim.
Circulation
Stimulation
10
18
34
55
6.0
1.7
20 · 103
37 · 103
5.6 · 103
200
Balanced
30
12 · 103
1.9
2.9
1.8
1.2
2.7
2.4
3.5
3.4
Unterhaching/DE
Larderello/IT
Latera/IT
Torre Alfina/IT
Cesano/IT
3.6/3.35
2.0
1.0
2.0
2.0
Carb.
Carb.
Carb.
Carb.
Carb.
5
16
19
20
14
2007
1977
1984
1977
1978
Circulation
Circulation
Injection
Injection
Injection
2.5
Balanced
1.2
7.5
Balanced
4.2 · 103
2 · 103
2.4
3.0
2.9
3.0
2.0
Table 8: Selected events of injection induced seismicity with maximal magnitudes (source:
Evans et al. 2012)
Based on the example Basel the processes during a stimulation should be explained
in more detail. The Basel1 borehole was put down between may and october 2006
to a depth of 5 km. In this depth granitic rocks of this region reach a temperature of
200°C, which makes a geothermal use economical interesting. The stimulation (Fracking), performed in December 2006, induced a notable seismic activity. In consequence
the project had to be aborted and a complete seismic risc analysis took place (Delacou
and Sartori 2009).
As part of the stimulation 11500 m3 water were injected under high pressures. The injection rate reaches temporary 3300 l/min, which lead to a maximum wellhead pressure
of nearly 300 bar (s. Fig. 29). A network of seismometers installed around the borehole
detected 10500 seismic events during the stimulation. The seismic activity reached its
maximum as expected at maximal injection rate. Although the pressure after closing
the bore hole (shut-in) already dropped sharply, the biggest detected event reached a
magnitude ML = 3.4 and intensities of IV to V (EMS-98). Further three aftershocks
Page 31 of 35
with ML > 3 occured in january and february 2007 (Delacou and Sartori 2009).
Fig. 29: Injection rate, injection phases, wellhead pressure and quake number during Basel1
stimulation (source: Delacou and Sartori 2009)
Page 32 of 35
5
Blast vibrations
Blasts are used in many geotechnical applications like
• in hard rock open-cast mining (basalt, granite, diabase etc.),
• in underground mining (coal, salt, ores etc.),
• at traffic route engineering,
• at tunnel construction and
• in seismic exploration methods.
During detonation explosion gases are generated. Due to the high explosion pressure
the gas is compressed and increases the gas pressure. The pressure change is approximately
K
p1
V2
.
(37)
∆p =
=
p2
V1
Thereby K is the gas rigidity factor and is usually around K ≈ 3. The detonation velocity
vdet can be estimated as follows.
p
vdet = 2(K 2 − 1)U · g
(38)
g denotes the gravity acceleration and U the specific explosion energy. The detonation
velocity reaches several km/s depending on the blasting force. The detonation pressure
pdet can be assessed with the explosive density ρ as follows.
pdet = 2(K − 1)ρ · U · g
(39)
The order of pdet lies in the range of GPa.
At squibbing (here ejecting masses) the cavity radius R can be estimated empirical with
the explosive charge quantity q (in kg).
m
√
3
RK = 0, 1 · · · 0, 4 · q · √
(40)
3
kg
The size of the corresponding pressure destruction zone is nearly RD ≈ 2RK and the
size of the fractured zone RR ≈ 4RK .
The fracture patterns for homogeneous full and half space are illustrated in figure 30.
Page 33 of 35
Fig. 30: Fracture patterns for homogeneous full and half space (source: Jendersie et al. 1981)
1. bore hole
2. pressure destruction
3. radial cracks
4. extention of radial cracks and (at half space:) tangential cracks from decompression wave
5. tangential cracks from reflected tension wave
6. radial cracks near surface from compression and tension waves
Page 34 of 35
References
Berckhemer, Hans (1990). Grundlagen der Geophysik. Darmstadt: Wissenschaftliche
Buchgessellschaft, 201 S. ISBN: 3-534-03974-2.
Delacou, Bastien and Mario Sartori (Nov. 2009). AP2000 Report - Structural model of
potential seismogenic faults. Bureau d’Etudes Géologiques SA.
Dusseault, Maurice B., Michael S. Bruno, and John Barrera (2001). “Casing Shear:
Causes, Cases, Cures”. In: SPE Drilling & Completion 16.2, pp. 98–107.
Evans, Keith F., Alba Zappone, Toni Kraft, Nicolas Deichmann, and Fabio Moia (2012).
“A survey of the induced seismic responses to fluid injection in geothermal and CO2
reservoirs in Europe”. In: Geothermics 41, pp. 30–54.
Fischer, T. and J. Horálek (2000). “Refined locations of the swarm earthquakes in the
Novy Kostel focal zone and spatial distribution of the January 1997 swarm in Western
Bohemia, Czech Republic”. In: Studia Geophysica et Geodætica 44.2, pp. 210–226.
Grünthal, G. (1981). “Zur Seismizität des Territoriums der DDR”. In: Gerlands Beiträge
zur Geophysik 90.3, pp. 202–212.
— (2004). “Erdbeben und Erdbebengefährdung in Deutschland sowie im europäischen
Kontext”. In: Geographie und Schule 151, pp. 14–23.
Grünthal, G. and W. Minkley (2005). “Bergbauinduzierte seismische Aktivitäten als
Quelle seismischer Belastungen - Zur Notwendigkeit der Ergänzung der Karte der
Erdbebenzonen der DIN 4149:2005-04”. In: Bautechnik 82.8, pp. 508–513.
Gupta, Harsh K. (1992). Reservoir-Induced Earthquakes. Elsevier.
Hurtig, Eckart (1984). Erdbeben und Erdbebengefährdung. Berlin: Akademie-Verlag,
328 S.
Jakob, Christian (2009). Herdparameterbestimmung von Erdbeben zur seismotektonischen Analyse in der Schwarmbebenregion Vogtland/NW-Böhmen. Diplomarbeit. TU
Bergakademie Freiberg.
Jendersie, Hans, Dietmar Hartz, and Rainer Dietze, eds. (1981). Sprengtechnik im
Bergbau. Leipzig: Deutscher Verlag für Grundstoffindustrie, 232 S.
Künzel, Ulrich (2013). Seismizität im Umfeld der Uranerzlagerstätte Schlema-Alberoda
und modifizierte Auswertemethoden für eine präzise Lage- und Stärkeermittlung der
im Nahfeld instrumentell registrierten Mikrobeben. Ed. by Heinz Konietzky. Freiberg:
Institut für Geotechnik der TU Bergakademie Freiberg.
Madariaga, Raul (1976). “Dynamics of an expanding circular fault”. In: Bulletin of the
Seismological Society of America 66.3, pp. 639–666.
Schulte-Theis, H. (1995). Automatische Lokalisierung und Clusteranalyse regionaler
Erdbeben. Dissertation. Ruhr-Universität Bochum.
Seed, H. B., C. Ugas, and J. Lysmer (Dec. 1974). Site-dependent spectra for
earthquake-resistant design. Tech. rep. EERC-Rep.
Simpson, D. W. (1976). “Seismicity changes associated with reservoir loading”. In: Engineering Geology 10, pp. 123–150.
Studer, Jost A. and Martin G. Koller (1997). “Geotechnisches Erdbebeningenieurwesen”. German. In: Bodendynamik. Springer Berlin Heidelberg, pp. 224–322. ISBN:
978-3-662-06124-4. DOI: 10.1007/978-3-662-06123-7_7. URL: http://dx.doi.
org/10.1007/978-3-662-06123-7_7.
Waldhauser, Felix. hypoDD – A Program to Compute Double-Difference Hypocentre
Locations. Manual.
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Dynamic events in hard rocks

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