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Fracture interaction in the Gregory Rift, East Africa
Tectonophysics,
47
104 (1984) 47-65
Elsevier Science Publishers
FRACTURE
B.V., Amsterdam
INTERACTION
- Printed
in The Netherlands
IN THE GREGORY RIFT, EAST AFRICA
DOV BAHAT Department (Received
of Geology and Mineralogy, February
The Ben Gurion Unioersity of the Negev, Beersheoa (Israel)
2, 1982; revised version accepted
August
24, 1983)
ABSTRACT
Bahat,
D., 1984. Fracture
Vertical
fracture
Crack-branching fatilts.
interaction
is important,
and fracture
and non-coplanar
These two manifestations
reasonably fracture,
in the Gregory
well. Mantle
crack follow
diapirism
Rift, East Africa.
interaction
interactions theoretical
is quite intensive
and experimental
resulting
in fault dips deviating
104: 47-65
in the Central
in the rift are characterized
seems to have been responsible
and block tilting, ultimately
Tectonophysics,
angular
Gregory
for major relationships
for both tensile (probably
Rift.
and minor of fracture unstable)
from the vertical.
INTRODUCTION
The present study is based on continued investigations into various aspects of fracture interaction in the earth’s crusts. In a previous paper (Bahat, 1982), evidence and arguments were presented that, in southern California, extension fractures associated with an earthquake occurred in a strike-slip regime. The present study concerns an extension rift typified by abundant fracture interactions. Certain interactions are characterized in reference to experimental investigations, distinctions
between
regarding
near
and
the rift tectonics
far field
stress
conditions
are made,
An unconventional analysis of normal faulting is presented According to a conventional theory (Anderson, 1951) normal fractures under conditions of vertical maximum pressure pressure
(or greatest
shears.
The intermediate
and
implications
are discussed.
tension)
perpendicular
principal
in the present study. faults result as shear and horizontal least
to the intersection
stress is horizontal
and parallel
of the conjugate to this intersec-
tion. The consequent fault planes should dip at angles more than 45” (the angle 60” is considered typical to normal faulting by various investigators, e.g., Golombek, 1981). Following this theory such a normal fault would be characterized as mode III (tearing) operation in fracture mechanic terms, because shearing close to the tip of the fault occurs parallel to the fracture front (see Lawn and Wilshaw, 1975; Petrovic and Mendiratta, 1976; and Bahat, 1982; for the characterization of the conventional three modes of fracture). 0040-1951/84/$03.00
0 1984 Elsevier Science Publishers
B.V.
48
In the present initial
vertical
sub-vertical
investigation
tensile
normal
fracture
displacements
faulting
that propagates
occur. The initial
is viewed as a development horizontally. fracture
process
since separation
interaction
study below is related to this initial fracture process. It is understood
an evolution
expected
of a normal
fault a transition
and
I (opening)
is mode
operation, during
of the crack walls is perpendicular
from an
Later. block tilting
to stress. The fracture that
from mode I to mode III can be
to occur.
THEORETICAL
The stress intensity factor K is a basic parameter in fracture mechanic (Irwin, 1960). and has been applied most usefully to fracture analyses in the crust (e.g., Lachenbruch, 1961; Delaney and Pollard, 1981). The stress intensity factor for the opening mode K, is a key parameter in discussing fracture velocities. The elastic stress a at a point near the tip of a flat crack, defined 8, is given by (Irwin, 1960): CJ= K,(2ar)
by its polar coordinates
r and
“‘f(e)
(1)
where r is the distance
between
the crack tip and the point in question
and f( 8) is a
trigonometric
of the polar angle. For a crack in an infinitely
wide plate of
infinite
function
thickness:
K, = ~<~(m)
”
(2)
where Us is the far field applied Definitions
of fracture
Slow fracture rapid
propagation
tensile stress. and a is half crack length.
velocities
propagation
is identified
is an unstable
here with stable crack growth.
growth.
The transition
between
whereas
a
the two is de-
termined by the critical stress intensity factor K,, taken as that value of K, needed to drive the crack at a velocity of >, IO-’ m/s (Wiederhorn et al.. 1974) through the material.
This transition
may be gradual
or abrupt
(Bahat et al.. 1982) as a function
of the material properties (Rabinovitch and Bahat, 1979). Lower velocity values than 2 10-l m/s were also proposed for the K, at the transition (Kerkhof, 1973: Freiman et al., 1974). According to Carlsson et al. (1973) on the other hand, the transition from slow to fast propagation is between 7 and 8 m/s. Cruck interaction and bifurcation
When crack bifurcation occurs a single fracture is divided into two branches that move separately, under combined loading of tension (mode 1) and longitudinal shear (mode II). Kalthoff (1972) has shown that in Araldite B (polymeric glass) these
49
branches original
interact direction
Erdogan K,,/K,
with one another, following
and each crack deviates
bifurcation
by an angle y from its
(Fig. 1). This angle can be determined
from
and Sih (1963): = sin y/3 cos y - 1
(3)
where K, and K,, are the stress intensity
factors
for modes
I and II, respectively.
Kalthoff has also shown that for forks with small branch angles cr < (Y, where (Y, is approximately 14”, the propagation of the branches tends to enlarge the angle. For of the branches tends to forks with larger branch angles (Y> LY,the propagation diminish
the angle. Forks with the critical
direction. Experimental
crack branching
angle (Y, will propagate
has been mostly observed
in their original
close to or at maximum
fracture velocities (Yoffe, 1951; Schardin, 1959; Kerkhof, 1973; Payne 1976). However, crack branching has also been observed at lower velocities
and Ball, including
0.39 maximum velocity (Anthony et al., 1970) and 0.41 shear wave velocity (Carlsson et al., 1973). Hackles were also observed at low fracture velocity (at K, < K*,, Michalske, velocity
1979). There is not yet an established
at which critical
The abundance however suggests
conditions
for bifurcation
theory
on the minimum
of fracture branching phenomena commonly observed in rocks that bifurcation in the crust may occur at low fracture velocities
(Bahat, 1980). On the other hand, fracture propagation associated (and often with volcanic activities) can generally be considered
KI ,/KI=O
KI QKI’O
y
Y>O
paths of a branch
crack in a symmetric
axis (thin line) are shown (between
field stresses. The branch
angles a is shown between
path (after Kalthoff,
with earthquakes rapid. Repeated
KI I/KI
Y=O propagation
line) and the symmetric the initial propagation
fracture
may be created.
curved arrows).
two curved arrows,
1972, fig. 4).
fork. Only one branch Straight
arrows indicate
and y is the deviation
(thick near
angle from
50
earthquake Allen
determinations
and Nordquist,
induced
by earthquakes
relationships 4
a
v’
observed
x-
in the crust by Kalthoff
velocities
(1982) showed in southern
of 3 km/s that
rapid
California
(Bollinger. branching
followed
1970: ruptures
the angular
(1972).
y
x’
(a)
---XV
Fig. 2. A. Schematic of both cracks proceeds
illustration
of propagation
from X and X’ is shown. At (c) overlap
from Y and Y’. Stage (d) represents
specimen,
behaviors
interaction
from Z and 2’ proceeds
B. Parallel
two cracks caused by indentation
simulation
induces
fracture
propagation
other leads to bifurcations. (after Swain and Hagan, C. High magnification
Distance
is attained,
parallel cracks
propagation
cracks.
Inner tips
before overlapping.
stops at X and X’ and
a finite body. After the arrival of Y and Y’ at the edges of (after Yokobori
et al., 1971, fig. 26).
(at two large black spots) are simulated by stress wave. This (at = 300 m/s). At the centre prior to overlap the cracks deviate
away from each other, then they grow towards
Y are shown.
of two non-coplanar
are X and X’. and outer tips are Y and Y’. Stage (a) describes
At (b) propagation
slightly
fracture
/
‘!A
b
showed
1972). Bahat
separating
each other and join. Propagation
the cracks 10 Frn. Distance
away from each
between indentations
210 pm
1978, fig. 1).
of the region of crack overlap (after Swain and Hagan,
1978, fig. 2). Cracks
X and
51
Interaction between non-coplanar opposing cracks A different parallel two
non-coplanar
theoretical
is one which occurs about parallel
factors
papers.
at points
opposing
et al. (1971) investigated elastic
was in good agreement
on cellophane
intensity
intensity
opposing
analysis
experiments stress
crack interaction
cracks (Fig. 2A). Yokobori
cracks
X and
under
tensile
with experimental
They observed
or overlapping
the interaction loading.
results
Their
derived
from
that when K, and K, are tensile
Y, respectively
(Fig. 2A), K is the stress
tensile crack, and T is the ratio between
factor of an isolated
between
the parallel
distance between the two non-coplanar cracks and the length of each crack (which is equal for both), K, has a maximum at 2T = 0 and a minimum at 2T = - 1.5. K, has a maximum at 2T = 0 and a minimum at 2T = - 2. In general K, is smaller than both iy, and 1y when overlap is present due to relatively high stress relaxation. K, is greater than K except when overlap is large. They also found that the stress intensity factors of shear stress produced by the interaction are considerably smaller than those of tensile stress. The former are nearly zero when T is large. During the interaction
between
the cracks, when small overlap is present,
the crack tips at X and
X’ deviate away from each other. When large overlap is present these tips approach each other. Swain and Hagan (1978) observed similar interactions between such cracks in soda-lime glass (Fig, 2B). They established that the angular deviation from straight line growth for these cracks may also be determined by eq. 3. Kranz (1979) observed such crack interactions which he calls “en passant” tinguish it from “en echelon” interaction) in stressed granite. APPLICATION
OF FRACTURE
MECHANICS
TO FRACTURE
interaction
INTERACTION
(to dis-
IN THE CRUST
Assumptions A recent study has shown that crustal fractures and bifurcated in a similar manner to experimental Araldite
B. These two sets of fractures
behave also numerically ruptures
in southern
which are four orders of magnitude
the same. Hence, extensional California
can
of about 1 km long propagated fractures of about 10 cm long in aspects of earthquake
be characterized
by
an analysis
different induced of crack
interaction and bifurcation according to fracture mechanics principles (Bahat, 1982). Similar assumptions that were made in the study on South California can be made in the present
analysis
of faults
in the Gregory
Rift (East
Africa).
Basically,
these
assumptions claim that unstable fracture in the crust can be modeled by elastic theories and simulated by brittle materials, The fracture interactions investigated in the present study can be simulated by static numerical methods (Yokobori et al., 1971; Kalthoff, 1972) although they basically represent dynamic processes (Kalthoff, 1972). The significance of this duality is still not clear (Kalthoff, 1972; Bahat, 1982). The opposing non-coplanar
52
interaction
shown in Fig. 2B took place at mean crack velocity
Swain and Hagan dynamic
effects.
present
definition.
by earthquakes assumed
that
(1978) assume This
fracture
that this velocity
propagation,
Also, supported follow predicted
similar
study are of unstable
analogous nature
of about
was sufficientty
however.
by the observation
was rapid
300 m/s.
low to neglect according
that rapid ruptures
patterns
of crack interaction
fracture
interactions
(Bahat,
investigated
to the induced
19X2), it is
in the present
as well.
The inhomogeneity of the crust in the Gregory Rift is important. but it has no significant effects on fracture behaviour as far as the Kalthoff’s theory is concerned, especially when dynamic conditions are considered (Bahat, stress anisotropy on fracture interaction is quite significant,
1982). The influence of and is being evaluated
below.
The Gregory
Rift in Kenya
structural characteristics: (a) This rift is an extensile only little stretching,
possibly
km of rift width (King,
was selected rift (Sengor
for this study
and Burke,
1978). It probably
not more than 8 km of crustal extension
1978) or even considerably
1978). It is highly fractured
due to a number
of
suffered
over about X0
less than that (Chapman
et al..
into swarms of closely spaced faults (Baker et al.. 1972).
$7’
A
Fig. 3. A. The Gregory Rift (after Griffiths, 1980, fig. 1). Location of Fig. 3B is between equator and 0°30’N, and covers parts of the Kamasia and Aberdare ranges. B. Fault pattern in central Gregory Rift, after P.S. Griffiths (King, 1978, fig. 3.9A; Griffiths, 1980. fig. 3). Numbers I - I2 in map relate to forks characterized in Table I. Letters A-I
relate to non-coplanar
opposing cracks characterized in Table II. Thickness of fault lines proportional to accumulated downthrow.
Black and white lines are inferred
faults.
In this rift the faults are strike-slip component is only (b) There are numerous faults in the Gregory Rift. It of faulting
all essentially of normal dip-slip type. An assumed minor (King, 1978). well defined observations of vertical or near vertical is generally accepted that there were four main episodes
in the rift (Baker,
1958; McCall,
1967). The two first episodes
were
responsible for great displacements and build-up of the major escarpments. The third phase of faulting was of much lesser magnitude. The patterns produced in this phase are characterized by the intensive fracture interaction. Finally, there was a late minor faulting involving renewals of older fault lines. According to McCall (1967) “the Tertiary-Quaternary faulting is entirely of one type, normal faulting characterized by steep hades, most commonly near vertical but occasionally as low as 60
degrees”.
This is especially
emphasized
in the third faulting
episode,
where faulting
is more vertical and fault scarps are more pronounced and more closely Near vertical dips in this region were also reported by Mason and Gibson Baker (1958), Walsh (1969) Truckle
et al. (1978, figs. 5 and 6) and Williams
(1980, fig. 3, after King, 1978 and Golden,
(c) The East African uplift
Chapman
Plateau
since the Jurassic,
spaced. (1957).
has been formed
but the Kenya
Dome
and
1978). during
several stages of regional
is a consequence
of a particularly
great uplift (Searle, 1970). (d) There is a positive
Bouguer
anomaly
associated
with the great uplift, which is
40-80 km wide. It occurs over the rift floor and is flanked by negative anomalies on the shoulders. The positive anomaly follows the trend of the swarms of the closely spaced Pleistocene faults (called also grid faults). This trend also coincides with a line of greatest crustal thinning (Searle, 1970). (e) Repeated microseismic, tectonic and volcanic activities have been abundantly connected in the rift. Faulting has developed by a succession 1978) associated with earthquakes (Tiercelin et al., 1980).
of movements
(King,
(f) According to Fairhead and Girdler (1971) the lack of large magnitude events and the presence of microseismic activity along the rift suggests that stress release is at a lower level than elsewhere in Africa with the possible exception of the Ethiopian rift. One possible explanation is that the tensile strength of the lithosphere may be low due to the presence of igneous material at very shallow depths (perhaps reaching to within 2 km of the surface in places (Searle, 1970)). (g) Detailed
fault mapping
(King,
a remarkable fracture interaction Hence, in the Gregory Rift
1978, fig. 3a; Griffiths.
1980, fig. 2) has shown
in the central part of the Gregory Rift. there is a unique combination of detailed
fault
mapping of clearly defined young fractures characteristically vertical or close to vertical. These fractures appear in abundance and are mostly oriented sub-parallel to the rift-axis. Faulting appears to have been mostly associated with volcanism and earthquakes,
and may have resulted
from specific fracture
and consequent
intensive
part of Gregory
Rift (Fig.
crack interaction. CHARACTERIZATION
Crack branching
OF FRACTURE
INTERACTION
in the Gregory Rift
There is an intensive
fracture
interaction
in the central
3B). Two types of fracture interaction are analyzed. These are crack branching (Kalthoff, 1972; Bahat, 1982) and interacting non-coplanar opposing cracks (Yokobori et al., 1971; Swain and Hagan, 1978). There is an abundance of crack branching in major faults (faults with downthrows greater than 200 m) and in minor faults (faults with downthrows lower than 200 m). Branching is bilateral, being oriented sub-parallel to the rift axis both northward and southward. Branching
55
angles for well defined
forks related to both major and minor faults are summarized
in Table I. Major faults 2 and 3 represent south
along
transitional
the Kamasia between
are complex, (the
initial
generally
branch angle
(Y> 14O change initial
minor
and major faults. Evidently,
angles (Fig. 1) increase
changes
followed
more
than
by the branching
to sub-parallel
(Y is reduced
a series of forks that bifurcate
Hills (W side of Fig. 3B). Faults
below
once).
Kalthoffs
cracks (Table
opening
(branch
sub-parallelism.
most branching
and decrease
alternately angular
interactions are
forks with initial
angle is reduced). branching
the to be
several times
relationships
I). Typically,
Initial
towards
7 and 8 appear
In forks 2 and 8
angle
LYcommonly
increases at second angular change from sub-parallelism. Few forks also have a third angular change. There are only few forks with initial small branch angles (a < 14”) that enlarge on further propagation.
A series of faults with complex branching
Gregory Rift is shown in Fig. 4a. In contrast, in the Coyote Creek fault, California (Bahat, 1982) most forks are simple (not complex) and initial
in the South small
branch angles are nearly as common as initial large branch angles (ratio of 3 : 5, respectively). In general the forks in the Coyote Creek fault seem to reflect relatively low crack interaction. The complexity of the forks in the Gregory Rift, on the other hand, suggests high interaction between closely distributed cracks. An exceptional complex branching from the Coyote Creek fault is also interpreted to be the result of local interferring stresses. The local stresses of the latter are approximately N-S compressional,
as indicated
by the folding
of the adjacent
and Clark, 1972). Three forks with one complex fault are shown in Fig. 4b. TABLE Crack Fork No.
Ocotillo
branching
Badlands
I branching
in the central
Branching type
Gregory
Rift *
Fault
Initial
First
Second
Third
We
a*l”
afl”
afl”
a+1°
change
change
change
complex
major
35
II
14
complex
major
22
(-PO
10
21
complex
major
19
II
simple
minor
15
II
14 _
II
4 5
complex
minor
16
II
12
-
6
complex
minor
19
II
10
-
complex
transitional
32
II
8
complex
transitional
22
9
complex
minor
32
II
2
(Sharp
along the Coyote Creek
C-J 5
c--)6
-
f-)9 32
_
10
complex
minor
20
II
14
II
complex
major
19
II
26
I2
simple
major
20
II
* Fork numbers the two branches
are identical
with those in Fig. 3B. II indicates
of the fork become
sub-parallel.
(-) indicates
that branch
_
II
angle a is diminished
that a is reduced
so that
below sub-parallelism.
(4 1Okm
lkm
Fig. 4. Crustal
fracture
interactions.
(a) complex
branching
3B). (b) complex
branching
South California
(after Allen et al., 1972; and Bahat,
E-W
folding
Direction
which
(No. 5) and additional
implies
of compression
approximate
and location
from the Gregory
Rift (forks
7 and 8. Fig.
two forks (Nos. 6 and 7) from the Koyote Creek fault.
local N-S
of branching
1982. fig. 4). Dashed compression “deformation”
which
line designates affected
approximate
branching
is shown by arrow.
of No. S.
Note differences
in scale.
Fourty-four initial 2a: branching angles (Fig. 1) were measured in Fig. 3B. These are plotted in Fig. 5~. This figure is a histogram which represents the combination of Figs. 5b and c. There is a wide scattering of results in Fig. 5~. However, there is a tendency of high concentration within the 2a range 42”-48”. This is especially observed in the minor faults (Fig. 5b). The major faults do not show this tendency, in these faults high concentration appears to be within the 2a range 29”-38” (Fig. 5. c). The data
Fig. 5. Histogram 3B). Abscissa determinations,
in Figs.
5u-(,
was statistically
of initial 2a branching shows b-minor
2a f2”
A Kolmogorov-Smirnov
angles in 44 minor and major faults in central
in degrees,
faults, c-major
evaluated.
and faults.
ordinate
shows
number
Gregory
of determinations.
Rift (Fig. a -total
5-l
2-sample
test (Siegel,
hypothesis
1956) has resulted
which claims different
support
to a possible
different
sets of conditions,
suggest specific angular
distributions
suggestion
that
although,
maxima
in a 60% probability
of an error
in Figs. 5b and c. Here, there is no
the two fault
due to limited
groups
represent
data this test cannot
for these groups. A Kolmogorov-Smirnov
of test (Siegel, 1956) has determined
to a
only 0.5% probability
two quite positively goodness
of an error to a claim that
Fig. 5a is not a uniform distribution. Namely, the maximum observed in the Latter histogram is statistically significant. In the approximate 29”-48” 2tu range the median is 42” only 3” lower than 45’ which shows the highest number of determinations. The test suggests that within this range the angular significance. Preston
(1935) showed
fractured rapidly of the horizontal
experimentally
maximum
that the branching
is of mechanical
angle of a glass lath
by tensile-bending can be correlated with the relative magnitudes principal stresses. Apparently, forking values of 2a = 45” were
obtained when the horizontal tensionfx was normal to the direction of fracture, and the horizontal direction parallel to fracture fv was zero. The vertical stress was not considered in this experiment. Quite possible that initial fracture in the minor faults (third episode) was considerably controlled by such stress conditions (tension normal to fracture), and deviations from 2a = 42”-48” represent local deviations from this stress. The high concentration of 2a at lower angles (29”-38’) in the major faults (mostly
first and second episodes)
seems to indicate
relative increase
of shear
influence. Preston found that at this angular rangefy is compressional, and at about 2a = 33” fy/fx = - $. Possibly, the deviations of 2n from 45” in the major faults reflect the important influence of mode III displacements mode I fracture (as suggested in the introduction). Non-coplanar
that followed
the earlier
cracks in the Gregory Rift
Interacting non-coplanar cracks are also common. It appears to be more associated with the minor faults. Idealized experimental results of non-coplanar crack interaction after Swain and Hagan (1978) are shown in Fig. 6A. Measured angles for the two interacting cracks (X and Y) from Fig. procedure crack X propagated a short distance two cracks seem to behave quite similarly. The of Yokobori, et al.), for an idealized case of
2C are plotted. Due to experimental before crack Y. Apart from that, the calculated Ku/K, (from the analysis identical deviations of both cracks
(assuming they propagate in straight lines) is given. Detailed behavior of interacting non-coplanar opposing cracks in the crust, A and C (Fig. 3B) is presented in Fig. 6B. The measured angles for the interacting cracks for A and C are shown with the respective curves of K,,/Ki calculated by eq. 3. There is a considerable difference between the curves derived from idealized conditions (Fig. 6A) and interacting cracks A (Fig. 6B). Crack X in the latter figure does not show the theoretical expected initial deviation away from crack Y (and therefore there is no negative y).
length
Crock
A
(pm)
I
I
3
x
0
2
4
6
8
IO
0
Fig. 6. A. Experimental of overlapping
ratio of Ku/K,
4
6
6
IO
12
-1 14
B
CRKCKL~NClH(~~l40)
CRllEK LCHGlK~R~l46~
relationship
2
results
of non-coplanar
cracks as a function
crack
interaction
from
with crack length is shown in b (after Swain and Hagan,
B. Left side, a plot similar similar to 6A showing
to 6A showing
the behavior
crack by dots (circles in 6A).
Fig. 2C. Measured
of crack length is shown in a. Variation
the behavior
angular
of the calculated
1978).
of fault A (Fig. 38, Table II). Right side. a plot
of fault C (Fig. 3B. Table II). X crack is represented
by crosses and Y
59
A much closer approach interacting crustal
cracks
fractures
to idealized
C (Fig.
conditions
are shown,
6B). The deviations
may be attributed
from
on the other hand,
idealized
interaction
to the fact that these fractures
are close in space, so that deviation
from idealized
interactions
in
in the
are abundant
between
and
them should
have significant effects. A comparison of the map shown in Fig. 3B to other fault maps of the Gregory Rift, like Baker et al. (1972, figs. 11 and 12) Crossley
(1980, fig. 2) and Tiercelin
et
al. (1980, fig. 3) indicates that in all these maps crack branching and opposing crack interaction can be observed. However, due to a more detailed mapping (lower scale) and strong emphasis on ground work, Fig. 3B demonstrates more clearly the various aspects of fracture interaction, particularly in minor faults within the rift. contrast, fault map of the same area which defined fault trends and lineaments shown by ERTS imagery (King, 1978, fig. 3: 16) does not interaction, and commensurately points out different implications fracture systems. An interesting
structural
Rift
in the Scottish
is observed
network
of normal
resemblance
to the fracture
Central
Coalfield.
faults and dykes commonly
faults are not straight,
“but
regarded
more or less sinuous”
show this fracture related to regional
interaction
Anderson
In as
in the Gregory
(1951)
describes
as being due to tension.
and crack interaction
a
The
is common
(words like “trailing” and “heaved” are being used). Fault branching appears to be fairly common (Anderson, 1951, fig. 12). Anderson observes that “individual faults may be vertical; others are inclined as little as 45”, or in some cases 25”-30”. Some, but not the whole of these exceptional instances, may be accounted for by tilting, which is subsequent
to the formation
fractures responded to perpendicular fault development is complementary ing normal
of the fracture”. horizontal tension, to the more popular
Assuming
that these vertical
this explanation of normal Anderson’s model attribut-
faults to a shear process.
Crack interaction
of the nature
investigated
here is not typical to all other normal
fault systems. In contrast, fractures along the rift in Iceland (Saemundsson, 1977) are typically straight and sub-parallel to each other, and do not show the intensive crack curving
which characterizes
the Gregory
Rift. This suggests different
mecha-
nisms of fracture (at least at the surface) along these two rift systems. Freund and Merzer (1976) analyzed the curved “zigzag” fault patterns in the Gregory Rift. They reached the conclusion that within the rift these fault patterns were initiated by strike-slip fractures. This opinion is shared by Crossley (1980). The curved fault lines within the rift appear to be primarily the consequence of fracture interaction (Fig. 3B). Results for nine interacting opposing cracks (minor faults) within the rift are summarized in Table II. The results indicate that in most crack interactions the tensile mode is higher than the shear mode (Ku/K, < 0.5). It follows from bifurcation analysis (Kalthoff, 1972) that local shear (mode II) can be developed at crack branching even under conditions of far field normal tension (Bahat,
1982). Hence,
local
shear
stresses
may
not necessarily
indicate
far field
60
TABLE
1I
Interacting
non-coplanar
opposing
cracks
A
R
c
y,,,,, for x * 2”
40
25
23
y,,,,,
35
29
19
Interacting
in central Gregory ~_______~ II
Klft * __
_____
E
F
33
36
29
?6
17
31
34
37
13
41
20
42
<;
IL
I
cracks
for
Y Ifi 2”
“lax K,,,‘K, for x+2”
0.50
0.25
0.22
0.36
0.41
0.30
0.41
0.16
0.36
max K,,/K, for Y + 2”
0.39
0.30
0.18
0.38
0.43
0.12
U.70
0.19
0.54
* Letters
representing
interacting
Values for y and K,,/K, Y (equivalent
maxima
cracks
are identical and calculated
with those in Fig. 3B. note also Fig. 6B. at terminations
of interacting
cracks X and
to ends of stage d in Fig. 2A).
stress. Although
in few crack interactions
2 0.5), it must be emphasized towards
(A-I)
are measmed
K,,/K,
values are relatively
that these are maximum
the ends of the crack interaction.
K,,/K,
and are only confined
high (K,,/K,
values which develop to small areas of the
crack interaction (Fig. 2A). The K,,/K, values rapidly subside with distance from these areas. Strike-slip fault initiation in the rift would require far field shear, which is not demonstrated
by the present
analysis.
DISCUSSION
Muntle diupirism
The results
presented
above point
to crustal
extension.
There is evidence
which
implies that this extension is a consequence of mantle diapirism. This includes observations by McCall (1967) that the early (Miocene) Samburu basalts are arched up with increasing intensity as one moves towards the median line of the rift. and this is attributed to up-warpings. Baker and Wohlenberg (1971) concluded that there were three periodic up-archings in the central Kenya, and the location of the main rift is on the crest and major axis of the uplift. They suggest that “the first extensive rift faults developed early in the Pliocene at the culmination of the Miocene uplift phase”. Furthermore, the fault patterns in central Gregory Rift (Fig. 3B, and related maps), show many interior horsts distributed along the rift. Burke (1976) made similar observations to the latter in other East African Rifts. Horsts in an extensional rift can result only from a vertical upward pressure where positive evidence for lateral compression is not available. According to McConnell (1967) and others no significant lateral displacements are known from the East African Rift. Baker and Wohlenberg (1971. fig. 7) suggest that there is crustal thinning and a zone of hot low density upper mantle beneath the rift. These two features are equated with mantle diapirism in the Rhine Graben (Fuchs et al., 1981). Also, it
61
corresponds
well with numerical
results
“lend support to the idea that the mechanism upwarping of the crust”
with
the theory
that
(Neugebauer,
from the Rhine Graben which
obtained
of rifting
1978). Hence,
in the Gregory
Rift
mantle
is caused by epeirogenetic
the above arguments diapirism
coincide
was responsible
for
extensile fracture,
and support the interpretation by Chapman et al. (1978) that “the majority of the faults developed as vertical fractures in horizontal rock sequences and were then rotated tilted fault-block
by continued
extension
and up-arching
to produce
complex
system”.
Fracture oelocities in the crust There seem to be close relationships of faults with volcanic and seismic activities in the Gregory Rift. This appliesespecially to the so-called grid faults within the rift itself (Tobin Gregory
et al., 1969). Association
Rift (Molnar
of recent faulting
and Aggarwal,
1971), and generally
(Fairhead and Girdler, 1971) have been suggested. recent faulting, volcanism, geothermal, microseismic maximum crustal thinning of crack growth associated
with earthqu~es
within
the
in the East African
A remarkable activity and
Rift
correlation axial zone
of of
was noted by Searle (1970). A recent historical evidence with an earthquake (Tiercelin et al., 1980) suggests that
most probably many more such associations have occurred in the past. The close correlation of faulting with earthquakes in the Gregory Rift implies that fracture in this rift was rapid. This fits the observation common, it follows quite well the angular
that crack interaction relationship observed
in the rift is very by Kalthoff, and
resembles crack interactions that can be simulated by unstable fracture in soda-lime glass (Swain and Hagan, 1978). Furthermore, it may suggest the applicability of eq. 3 to tectonic problems in rifts. determined by future work. Perhaps planar each
the most pronounced
parallel other
locations
The extent
settings.
for considerable
(for instance,
feature
In contrast, Engelder
of all the faults
vertical
distances
of this will have,
planar
characterize
extensile
of course,
studied
two groups of extensile fractures most probably circumstances. If extensile joints of the type
here is lack of
fractures
systematic
that parallel
joints
and Geiser, 1980). The dissimilarities
to be
in various
between
these
reflect different initial mechanical mentioned above are mostly the
consequence of slow processes of fracture propagation (Bahat, 1979), and the far&s associated with the Gregory Rift reflect unstable fracture propagation, rate of crustal fracture propagation evidently is a parameter of great importance. Fracture branching in low strength terrains It was pointed out by Tchalenko and Berberian (1975) and Bahat (1982) that branching associated with earthquakes seems to prefer association with faulting through alluvium with properties of low strength (abundance of mechanical discontinuities and low fracture toughness). Fairhead and Girdler (1971) suggested that in the Gregory Rift the tensile strength of the lithosphere may be low due to the
62
presence
of igneous
material
rift floor to a significant pyroclastics
interbedded
contributed
to low strength
crack branching
at very shallow depths. extent
with
consisted local
lake-sediments.
succession
This
(1981) recently
that the
of lavas and
succession
could
of the rift floor, which made it amenable
and other facets of fracture
King and Vita-Finzi
Searle (1970) observed
of a complex
have
to intensive
interaction.
addressed
the problem
of the elastic-brittle-
ductile response of the crust to earthquake at shallow depths. They suggested that the rapid deformation at the time of an earthquake is elastic-brittle in nature, and in the process of ductile relaxation the elastic deformation may be “freezed in”. My own observations of elastic fracture propagation in (probably alluvium rich formations appears to support this suggestion. behavior in such formations seems to obey elastic theory.
ductile) low strength Apparently. fracture
CONCLUSIONS
Vertical fracture
is important
and fracture
interaction
is quite intensive
in Central
Gregory Rift. This interaction is commonly bilateral. Crack branching occurs in major and minor faults and it is mostly complex. Interacting opposing non-coplanar cracks
are more common
fracture
interaction
angular
relationships
in the younger
types
follow
reasonably
minor
theoretical
faults
and
within
experimental
well. As such they support
the rift. These fracture
previous
two
mechanic
observations
(Bahat, 1982) of a similar behavior of two fracture sets which are four orders of magnitude different in size and follow eq. 3. The vertical fracture and these relationships indicate a predominance of extension fracture, probably with local incrases of shear limited to small areas in minor faults and in association with late displacements in major faults. The implication is that in the rift curved and angular faults were not initiated
as strike-slip
patterns
and
of the
earthquakes monly
faults
suggest
observed
fracture. In the Gregory
their
that fracture
planar,
parallel,
Rift mantle
fractures close occurred
systematic
diapirism
(as previously
association unstably joints
with
proposed). volcanic
(rapidly) which
was responsible
The angular activities
in contrast
result from stable for both extensile
and
to com(slow) fracture
and block tilting, ultimately resulting in fault dips deviating from the vertical. A previous suggestion that crack branching is more easily facilitated in crustal formation of low strength (low fracture toughness) receives some support in the present study. It is pointed out that the characteristic crack interactions observed along the Gregory Rift do not appear along the rift in Iceland. This suggests that fracture (at least at the surface) of these two rifts was controlled by different mechanisms. ACKNOWLEDGEMENTS
I would like to thank Paul S. Griffiths who has granted me the permission to use his structural maps of the Gregory Rift and made useful comments, and Christopher
63
H. Scholz who read the first draft and made important suggestions that helped to improve the manuscript. I received assistance in the statistical analysis from members of the computation centre of the Ben Gurion University of the Negev. This paper was partly written while I was on Sabbatical leave at Lamont-Doherty Geological Observatory. The courtesies extended to me by Terry Engelder and other members of this institute are very much appreciated.
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47
104 (1984) 47-65
Elsevier Science Publishers
FRACTURE
B.V., Amsterdam
INTERACTION
- Printed
in The Netherlands
IN THE GREGORY RIFT, EAST AFRICA
DOV BAHAT Department (Received
of Geology and Mineralogy, February
The Ben Gurion Unioersity of the Negev, Beersheoa (Israel)
2, 1982; revised version accepted
August
24, 1983)
ABSTRACT
Bahat,
D., 1984. Fracture
Vertical
fracture
Crack-branching fatilts.
interaction
is important,
and fracture
and non-coplanar
These two manifestations
reasonably fracture,
in the Gregory
well. Mantle
crack follow
diapirism
Rift, East Africa.
interaction
interactions theoretical
is quite intensive
and experimental
resulting
in fault dips deviating
104: 47-65
in the Central
in the rift are characterized
seems to have been responsible
and block tilting, ultimately
Tectonophysics,
angular
Gregory
for major relationships
for both tensile (probably
Rift.
and minor of fracture unstable)
from the vertical.
INTRODUCTION
The present study is based on continued investigations into various aspects of fracture interaction in the earth’s crusts. In a previous paper (Bahat, 1982), evidence and arguments were presented that, in southern California, extension fractures associated with an earthquake occurred in a strike-slip regime. The present study concerns an extension rift typified by abundant fracture interactions. Certain interactions are characterized in reference to experimental investigations, distinctions
between
regarding
near
and
the rift tectonics
far field
stress
conditions
are made,
An unconventional analysis of normal faulting is presented According to a conventional theory (Anderson, 1951) normal fractures under conditions of vertical maximum pressure pressure
(or greatest
shears.
The intermediate
and
implications
are discussed.
tension)
perpendicular
principal
in the present study. faults result as shear and horizontal least
to the intersection
stress is horizontal
and parallel
of the conjugate to this intersec-
tion. The consequent fault planes should dip at angles more than 45” (the angle 60” is considered typical to normal faulting by various investigators, e.g., Golombek, 1981). Following this theory such a normal fault would be characterized as mode III (tearing) operation in fracture mechanic terms, because shearing close to the tip of the fault occurs parallel to the fracture front (see Lawn and Wilshaw, 1975; Petrovic and Mendiratta, 1976; and Bahat, 1982; for the characterization of the conventional three modes of fracture). 0040-1951/84/$03.00
0 1984 Elsevier Science Publishers
B.V.
48
In the present initial
vertical
sub-vertical
investigation
tensile
normal
fracture
displacements
faulting
that propagates
occur. The initial
is viewed as a development horizontally. fracture
process
since separation
interaction
study below is related to this initial fracture process. It is understood
an evolution
expected
of a normal
fault a transition
and
I (opening)
is mode
operation, during
of the crack walls is perpendicular
from an
Later. block tilting
to stress. The fracture that
from mode I to mode III can be
to occur.
THEORETICAL
The stress intensity factor K is a basic parameter in fracture mechanic (Irwin, 1960). and has been applied most usefully to fracture analyses in the crust (e.g., Lachenbruch, 1961; Delaney and Pollard, 1981). The stress intensity factor for the opening mode K, is a key parameter in discussing fracture velocities. The elastic stress a at a point near the tip of a flat crack, defined 8, is given by (Irwin, 1960): CJ= K,(2ar)
by its polar coordinates
r and
“‘f(e)
(1)
where r is the distance
between
the crack tip and the point in question
and f( 8) is a
trigonometric
of the polar angle. For a crack in an infinitely
wide plate of
infinite
function
thickness:
K, = ~<~(m)
”
(2)
where Us is the far field applied Definitions
of fracture
Slow fracture rapid
propagation
tensile stress. and a is half crack length.
velocities
propagation
is identified
is an unstable
here with stable crack growth.
growth.
The transition
between
whereas
a
the two is de-
termined by the critical stress intensity factor K,, taken as that value of K, needed to drive the crack at a velocity of >, IO-’ m/s (Wiederhorn et al.. 1974) through the material.
This transition
may be gradual
or abrupt
(Bahat et al.. 1982) as a function
of the material properties (Rabinovitch and Bahat, 1979). Lower velocity values than 2 10-l m/s were also proposed for the K, at the transition (Kerkhof, 1973: Freiman et al., 1974). According to Carlsson et al. (1973) on the other hand, the transition from slow to fast propagation is between 7 and 8 m/s. Cruck interaction and bifurcation
When crack bifurcation occurs a single fracture is divided into two branches that move separately, under combined loading of tension (mode 1) and longitudinal shear (mode II). Kalthoff (1972) has shown that in Araldite B (polymeric glass) these
49
branches original
interact direction
Erdogan K,,/K,
with one another, following
and each crack deviates
bifurcation
by an angle y from its
(Fig. 1). This angle can be determined
from
and Sih (1963): = sin y/3 cos y - 1
(3)
where K, and K,, are the stress intensity
factors
for modes
I and II, respectively.
Kalthoff has also shown that for forks with small branch angles cr < (Y, where (Y, is approximately 14”, the propagation of the branches tends to enlarge the angle. For of the branches tends to forks with larger branch angles (Y> LY,the propagation diminish
the angle. Forks with the critical
direction. Experimental
crack branching
angle (Y, will propagate
has been mostly observed
in their original
close to or at maximum
fracture velocities (Yoffe, 1951; Schardin, 1959; Kerkhof, 1973; Payne 1976). However, crack branching has also been observed at lower velocities
and Ball, including
0.39 maximum velocity (Anthony et al., 1970) and 0.41 shear wave velocity (Carlsson et al., 1973). Hackles were also observed at low fracture velocity (at K, < K*,, Michalske, velocity
1979). There is not yet an established
at which critical
The abundance however suggests
conditions
for bifurcation
theory
on the minimum
of fracture branching phenomena commonly observed in rocks that bifurcation in the crust may occur at low fracture velocities
(Bahat, 1980). On the other hand, fracture propagation associated (and often with volcanic activities) can generally be considered
KI ,/KI=O
KI QKI’O
y
Y>O
paths of a branch
crack in a symmetric
axis (thin line) are shown (between
field stresses. The branch
angles a is shown between
path (after Kalthoff,
with earthquakes rapid. Repeated
KI I/KI
Y=O propagation
line) and the symmetric the initial propagation
fracture
may be created.
curved arrows).
two curved arrows,
1972, fig. 4).
fork. Only one branch Straight
arrows indicate
and y is the deviation
(thick near
angle from
50
earthquake Allen
determinations
and Nordquist,
induced
by earthquakes
relationships 4
a
v’
observed
x-
in the crust by Kalthoff
velocities
(1982) showed in southern
of 3 km/s that
rapid
California
(Bollinger. branching
followed
1970: ruptures
the angular
(1972).
y
x’
(a)
---XV
Fig. 2. A. Schematic of both cracks proceeds
illustration
of propagation
from X and X’ is shown. At (c) overlap
from Y and Y’. Stage (d) represents
specimen,
behaviors
interaction
from Z and 2’ proceeds
B. Parallel
two cracks caused by indentation
simulation
induces
fracture
propagation
other leads to bifurcations. (after Swain and Hagan, C. High magnification
Distance
is attained,
parallel cracks
propagation
cracks.
Inner tips
before overlapping.
stops at X and X’ and
a finite body. After the arrival of Y and Y’ at the edges of (after Yokobori
et al., 1971, fig. 26).
(at two large black spots) are simulated by stress wave. This (at = 300 m/s). At the centre prior to overlap the cracks deviate
away from each other, then they grow towards
Y are shown.
of two non-coplanar
are X and X’. and outer tips are Y and Y’. Stage (a) describes
At (b) propagation
slightly
fracture
/
‘!A
b
showed
1972). Bahat
separating
each other and join. Propagation
the cracks 10 Frn. Distance
away from each
between indentations
210 pm
1978, fig. 1).
of the region of crack overlap (after Swain and Hagan,
1978, fig. 2). Cracks
X and
51
Interaction between non-coplanar opposing cracks A different parallel two
non-coplanar
theoretical
is one which occurs about parallel
factors
papers.
at points
opposing
et al. (1971) investigated elastic
was in good agreement
on cellophane
intensity
intensity
opposing
analysis
experiments stress
crack interaction
cracks (Fig. 2A). Yokobori
cracks
X and
under
tensile
with experimental
They observed
or overlapping
the interaction loading.
results
Their
derived
from
that when K, and K, are tensile
Y, respectively
(Fig. 2A), K is the stress
tensile crack, and T is the ratio between
factor of an isolated
between
the parallel
distance between the two non-coplanar cracks and the length of each crack (which is equal for both), K, has a maximum at 2T = 0 and a minimum at 2T = - 1.5. K, has a maximum at 2T = 0 and a minimum at 2T = - 2. In general K, is smaller than both iy, and 1y when overlap is present due to relatively high stress relaxation. K, is greater than K except when overlap is large. They also found that the stress intensity factors of shear stress produced by the interaction are considerably smaller than those of tensile stress. The former are nearly zero when T is large. During the interaction
between
the cracks, when small overlap is present,
the crack tips at X and
X’ deviate away from each other. When large overlap is present these tips approach each other. Swain and Hagan (1978) observed similar interactions between such cracks in soda-lime glass (Fig, 2B). They established that the angular deviation from straight line growth for these cracks may also be determined by eq. 3. Kranz (1979) observed such crack interactions which he calls “en passant” tinguish it from “en echelon” interaction) in stressed granite. APPLICATION
OF FRACTURE
MECHANICS
TO FRACTURE
interaction
INTERACTION
(to dis-
IN THE CRUST
Assumptions A recent study has shown that crustal fractures and bifurcated in a similar manner to experimental Araldite
B. These two sets of fractures
behave also numerically ruptures
in southern
which are four orders of magnitude
the same. Hence, extensional California
can
of about 1 km long propagated fractures of about 10 cm long in aspects of earthquake
be characterized
by
an analysis
different induced of crack
interaction and bifurcation according to fracture mechanics principles (Bahat, 1982). Similar assumptions that were made in the study on South California can be made in the present
analysis
of faults
in the Gregory
Rift (East
Africa).
Basically,
these
assumptions claim that unstable fracture in the crust can be modeled by elastic theories and simulated by brittle materials, The fracture interactions investigated in the present study can be simulated by static numerical methods (Yokobori et al., 1971; Kalthoff, 1972) although they basically represent dynamic processes (Kalthoff, 1972). The significance of this duality is still not clear (Kalthoff, 1972; Bahat, 1982). The opposing non-coplanar
52
interaction
shown in Fig. 2B took place at mean crack velocity
Swain and Hagan dynamic
effects.
present
definition.
by earthquakes assumed
that
(1978) assume This
fracture
that this velocity
propagation,
Also, supported follow predicted
similar
study are of unstable
analogous nature
of about
was sufficientty
however.
by the observation
was rapid
300 m/s.
low to neglect according
that rapid ruptures
patterns
of crack interaction
fracture
interactions
(Bahat,
investigated
to the induced
19X2), it is
in the present
as well.
The inhomogeneity of the crust in the Gregory Rift is important. but it has no significant effects on fracture behaviour as far as the Kalthoff’s theory is concerned, especially when dynamic conditions are considered (Bahat, stress anisotropy on fracture interaction is quite significant,
1982). The influence of and is being evaluated
below.
The Gregory
Rift in Kenya
structural characteristics: (a) This rift is an extensile only little stretching,
possibly
km of rift width (King,
was selected rift (Sengor
for this study
and Burke,
1978). It probably
not more than 8 km of crustal extension
1978) or even considerably
1978). It is highly fractured
due to a number
of
suffered
over about X0
less than that (Chapman
et al..
into swarms of closely spaced faults (Baker et al.. 1972).
$7’
A
Fig. 3. A. The Gregory Rift (after Griffiths, 1980, fig. 1). Location of Fig. 3B is between equator and 0°30’N, and covers parts of the Kamasia and Aberdare ranges. B. Fault pattern in central Gregory Rift, after P.S. Griffiths (King, 1978, fig. 3.9A; Griffiths, 1980. fig. 3). Numbers I - I2 in map relate to forks characterized in Table I. Letters A-I
relate to non-coplanar
opposing cracks characterized in Table II. Thickness of fault lines proportional to accumulated downthrow.
Black and white lines are inferred
faults.
In this rift the faults are strike-slip component is only (b) There are numerous faults in the Gregory Rift. It of faulting
all essentially of normal dip-slip type. An assumed minor (King, 1978). well defined observations of vertical or near vertical is generally accepted that there were four main episodes
in the rift (Baker,
1958; McCall,
1967). The two first episodes
were
responsible for great displacements and build-up of the major escarpments. The third phase of faulting was of much lesser magnitude. The patterns produced in this phase are characterized by the intensive fracture interaction. Finally, there was a late minor faulting involving renewals of older fault lines. According to McCall (1967) “the Tertiary-Quaternary faulting is entirely of one type, normal faulting characterized by steep hades, most commonly near vertical but occasionally as low as 60
degrees”.
This is especially
emphasized
in the third faulting
episode,
where faulting
is more vertical and fault scarps are more pronounced and more closely Near vertical dips in this region were also reported by Mason and Gibson Baker (1958), Walsh (1969) Truckle
et al. (1978, figs. 5 and 6) and Williams
(1980, fig. 3, after King, 1978 and Golden,
(c) The East African uplift
Chapman
Plateau
since the Jurassic,
spaced. (1957).
has been formed
but the Kenya
Dome
and
1978). during
several stages of regional
is a consequence
of a particularly
great uplift (Searle, 1970). (d) There is a positive
Bouguer
anomaly
associated
with the great uplift, which is
40-80 km wide. It occurs over the rift floor and is flanked by negative anomalies on the shoulders. The positive anomaly follows the trend of the swarms of the closely spaced Pleistocene faults (called also grid faults). This trend also coincides with a line of greatest crustal thinning (Searle, 1970). (e) Repeated microseismic, tectonic and volcanic activities have been abundantly connected in the rift. Faulting has developed by a succession 1978) associated with earthquakes (Tiercelin et al., 1980).
of movements
(King,
(f) According to Fairhead and Girdler (1971) the lack of large magnitude events and the presence of microseismic activity along the rift suggests that stress release is at a lower level than elsewhere in Africa with the possible exception of the Ethiopian rift. One possible explanation is that the tensile strength of the lithosphere may be low due to the presence of igneous material at very shallow depths (perhaps reaching to within 2 km of the surface in places (Searle, 1970)). (g) Detailed
fault mapping
(King,
a remarkable fracture interaction Hence, in the Gregory Rift
1978, fig. 3a; Griffiths.
1980, fig. 2) has shown
in the central part of the Gregory Rift. there is a unique combination of detailed
fault
mapping of clearly defined young fractures characteristically vertical or close to vertical. These fractures appear in abundance and are mostly oriented sub-parallel to the rift-axis. Faulting appears to have been mostly associated with volcanism and earthquakes,
and may have resulted
from specific fracture
and consequent
intensive
part of Gregory
Rift (Fig.
crack interaction. CHARACTERIZATION
Crack branching
OF FRACTURE
INTERACTION
in the Gregory Rift
There is an intensive
fracture
interaction
in the central
3B). Two types of fracture interaction are analyzed. These are crack branching (Kalthoff, 1972; Bahat, 1982) and interacting non-coplanar opposing cracks (Yokobori et al., 1971; Swain and Hagan, 1978). There is an abundance of crack branching in major faults (faults with downthrows greater than 200 m) and in minor faults (faults with downthrows lower than 200 m). Branching is bilateral, being oriented sub-parallel to the rift axis both northward and southward. Branching
55
angles for well defined
forks related to both major and minor faults are summarized
in Table I. Major faults 2 and 3 represent south
along
transitional
the Kamasia between
are complex, (the
initial
generally
branch angle
(Y> 14O change initial
minor
and major faults. Evidently,
angles (Fig. 1) increase
changes
followed
more
than
by the branching
to sub-parallel
(Y is reduced
a series of forks that bifurcate
Hills (W side of Fig. 3B). Faults
below
once).
Kalthoffs
cracks (Table
opening
(branch
sub-parallelism.
most branching
and decrease
alternately angular
interactions are
forks with initial
angle is reduced). branching
the to be
several times
relationships
I). Typically,
Initial
towards
7 and 8 appear
In forks 2 and 8
angle
LYcommonly
increases at second angular change from sub-parallelism. Few forks also have a third angular change. There are only few forks with initial small branch angles (a < 14”) that enlarge on further propagation.
A series of faults with complex branching
Gregory Rift is shown in Fig. 4a. In contrast, in the Coyote Creek fault, California (Bahat, 1982) most forks are simple (not complex) and initial
in the South small
branch angles are nearly as common as initial large branch angles (ratio of 3 : 5, respectively). In general the forks in the Coyote Creek fault seem to reflect relatively low crack interaction. The complexity of the forks in the Gregory Rift, on the other hand, suggests high interaction between closely distributed cracks. An exceptional complex branching from the Coyote Creek fault is also interpreted to be the result of local interferring stresses. The local stresses of the latter are approximately N-S compressional,
as indicated
by the folding
of the adjacent
and Clark, 1972). Three forks with one complex fault are shown in Fig. 4b. TABLE Crack Fork No.
Ocotillo
branching
Badlands
I branching
in the central
Branching type
Gregory
Rift *
Fault
Initial
First
Second
Third
We
a*l”
afl”
afl”
a+1°
change
change
change
complex
major
35
II
14
complex
major
22
(-PO
10
21
complex
major
19
II
simple
minor
15
II
14 _
II
4 5
complex
minor
16
II
12
-
6
complex
minor
19
II
10
-
complex
transitional
32
II
8
complex
transitional
22
9
complex
minor
32
II
2
(Sharp
along the Coyote Creek
C-J 5
c--)6
-
f-)9 32
_
10
complex
minor
20
II
14
II
complex
major
19
II
26
I2
simple
major
20
II
* Fork numbers the two branches
are identical
with those in Fig. 3B. II indicates
of the fork become
sub-parallel.
(-) indicates
that branch
_
II
angle a is diminished
that a is reduced
so that
below sub-parallelism.
(4 1Okm
lkm
Fig. 4. Crustal
fracture
interactions.
(a) complex
branching
3B). (b) complex
branching
South California
(after Allen et al., 1972; and Bahat,
E-W
folding
Direction
which
(No. 5) and additional
implies
of compression
approximate
and location
from the Gregory
Rift (forks
7 and 8. Fig.
two forks (Nos. 6 and 7) from the Koyote Creek fault.
local N-S
of branching
1982. fig. 4). Dashed compression “deformation”
which
line designates affected
approximate
branching
is shown by arrow.
of No. S.
Note differences
in scale.
Fourty-four initial 2a: branching angles (Fig. 1) were measured in Fig. 3B. These are plotted in Fig. 5~. This figure is a histogram which represents the combination of Figs. 5b and c. There is a wide scattering of results in Fig. 5~. However, there is a tendency of high concentration within the 2a range 42”-48”. This is especially observed in the minor faults (Fig. 5b). The major faults do not show this tendency, in these faults high concentration appears to be within the 2a range 29”-38” (Fig. 5. c). The data
Fig. 5. Histogram 3B). Abscissa determinations,
in Figs.
5u-(,
was statistically
of initial 2a branching shows b-minor
2a f2”
A Kolmogorov-Smirnov
angles in 44 minor and major faults in central
in degrees,
faults, c-major
evaluated.
and faults.
ordinate
shows
number
Gregory
of determinations.
Rift (Fig. a -total
5-l
2-sample
test (Siegel,
hypothesis
1956) has resulted
which claims different
support
to a possible
different
sets of conditions,
suggest specific angular
distributions
suggestion
that
although,
maxima
in a 60% probability
of an error
in Figs. 5b and c. Here, there is no
the two fault
due to limited
groups
represent
data this test cannot
for these groups. A Kolmogorov-Smirnov
of test (Siegel, 1956) has determined
to a
only 0.5% probability
two quite positively goodness
of an error to a claim that
Fig. 5a is not a uniform distribution. Namely, the maximum observed in the Latter histogram is statistically significant. In the approximate 29”-48” 2tu range the median is 42” only 3” lower than 45’ which shows the highest number of determinations. The test suggests that within this range the angular significance. Preston
(1935) showed
fractured rapidly of the horizontal
experimentally
maximum
that the branching
is of mechanical
angle of a glass lath
by tensile-bending can be correlated with the relative magnitudes principal stresses. Apparently, forking values of 2a = 45” were
obtained when the horizontal tensionfx was normal to the direction of fracture, and the horizontal direction parallel to fracture fv was zero. The vertical stress was not considered in this experiment. Quite possible that initial fracture in the minor faults (third episode) was considerably controlled by such stress conditions (tension normal to fracture), and deviations from 2a = 42”-48” represent local deviations from this stress. The high concentration of 2a at lower angles (29”-38’) in the major faults (mostly
first and second episodes)
seems to indicate
relative increase
of shear
influence. Preston found that at this angular rangefy is compressional, and at about 2a = 33” fy/fx = - $. Possibly, the deviations of 2n from 45” in the major faults reflect the important influence of mode III displacements mode I fracture (as suggested in the introduction). Non-coplanar
that followed
the earlier
cracks in the Gregory Rift
Interacting non-coplanar cracks are also common. It appears to be more associated with the minor faults. Idealized experimental results of non-coplanar crack interaction after Swain and Hagan (1978) are shown in Fig. 6A. Measured angles for the two interacting cracks (X and Y) from Fig. procedure crack X propagated a short distance two cracks seem to behave quite similarly. The of Yokobori, et al.), for an idealized case of
2C are plotted. Due to experimental before crack Y. Apart from that, the calculated Ku/K, (from the analysis identical deviations of both cracks
(assuming they propagate in straight lines) is given. Detailed behavior of interacting non-coplanar opposing cracks in the crust, A and C (Fig. 3B) is presented in Fig. 6B. The measured angles for the interacting cracks for A and C are shown with the respective curves of K,,/Ki calculated by eq. 3. There is a considerable difference between the curves derived from idealized conditions (Fig. 6A) and interacting cracks A (Fig. 6B). Crack X in the latter figure does not show the theoretical expected initial deviation away from crack Y (and therefore there is no negative y).
length
Crock
A
(pm)
I
I
3
x
0
2
4
6
8
IO
0
Fig. 6. A. Experimental of overlapping
ratio of Ku/K,
4
6
6
IO
12
-1 14
B
CRKCKL~NClH(~~l40)
CRllEK LCHGlK~R~l46~
relationship
2
results
of non-coplanar
cracks as a function
crack
interaction
from
with crack length is shown in b (after Swain and Hagan,
B. Left side, a plot similar similar to 6A showing
to 6A showing
the behavior
crack by dots (circles in 6A).
Fig. 2C. Measured
of crack length is shown in a. Variation
the behavior
angular
of the calculated
1978).
of fault A (Fig. 38, Table II). Right side. a plot
of fault C (Fig. 3B. Table II). X crack is represented
by crosses and Y
59
A much closer approach interacting crustal
cracks
fractures
to idealized
C (Fig.
conditions
are shown,
6B). The deviations
may be attributed
from
on the other hand,
idealized
interaction
to the fact that these fractures
are close in space, so that deviation
from idealized
interactions
in
in the
are abundant
between
and
them should
have significant effects. A comparison of the map shown in Fig. 3B to other fault maps of the Gregory Rift, like Baker et al. (1972, figs. 11 and 12) Crossley
(1980, fig. 2) and Tiercelin
et
al. (1980, fig. 3) indicates that in all these maps crack branching and opposing crack interaction can be observed. However, due to a more detailed mapping (lower scale) and strong emphasis on ground work, Fig. 3B demonstrates more clearly the various aspects of fracture interaction, particularly in minor faults within the rift. contrast, fault map of the same area which defined fault trends and lineaments shown by ERTS imagery (King, 1978, fig. 3: 16) does not interaction, and commensurately points out different implications fracture systems. An interesting
structural
Rift
in the Scottish
is observed
network
of normal
resemblance
to the fracture
Central
Coalfield.
faults and dykes commonly
faults are not straight,
“but
regarded
more or less sinuous”
show this fracture related to regional
interaction
Anderson
In as
in the Gregory
(1951)
describes
as being due to tension.
and crack interaction
a
The
is common
(words like “trailing” and “heaved” are being used). Fault branching appears to be fairly common (Anderson, 1951, fig. 12). Anderson observes that “individual faults may be vertical; others are inclined as little as 45”, or in some cases 25”-30”. Some, but not the whole of these exceptional instances, may be accounted for by tilting, which is subsequent
to the formation
fractures responded to perpendicular fault development is complementary ing normal
of the fracture”. horizontal tension, to the more popular
Assuming
that these vertical
this explanation of normal Anderson’s model attribut-
faults to a shear process.
Crack interaction
of the nature
investigated
here is not typical to all other normal
fault systems. In contrast, fractures along the rift in Iceland (Saemundsson, 1977) are typically straight and sub-parallel to each other, and do not show the intensive crack curving
which characterizes
the Gregory
Rift. This suggests different
mecha-
nisms of fracture (at least at the surface) along these two rift systems. Freund and Merzer (1976) analyzed the curved “zigzag” fault patterns in the Gregory Rift. They reached the conclusion that within the rift these fault patterns were initiated by strike-slip fractures. This opinion is shared by Crossley (1980). The curved fault lines within the rift appear to be primarily the consequence of fracture interaction (Fig. 3B). Results for nine interacting opposing cracks (minor faults) within the rift are summarized in Table II. The results indicate that in most crack interactions the tensile mode is higher than the shear mode (Ku/K, < 0.5). It follows from bifurcation analysis (Kalthoff, 1972) that local shear (mode II) can be developed at crack branching even under conditions of far field normal tension (Bahat,
1982). Hence,
local
shear
stresses
may
not necessarily
indicate
far field
60
TABLE
1I
Interacting
non-coplanar
opposing
cracks
A
R
c
y,,,,, for x * 2”
40
25
23
y,,,,,
35
29
19
Interacting
in central Gregory ~_______~ II
Klft * __
_____
E
F
33
36
29
?6
17
31
34
37
13
41
20
42
<;
IL
I
cracks
for
Y Ifi 2”
“lax K,,,‘K, for x+2”
0.50
0.25
0.22
0.36
0.41
0.30
0.41
0.16
0.36
max K,,/K, for Y + 2”
0.39
0.30
0.18
0.38
0.43
0.12
U.70
0.19
0.54
* Letters
representing
interacting
Values for y and K,,/K, Y (equivalent
maxima
cracks
are identical and calculated
with those in Fig. 3B. note also Fig. 6B. at terminations
of interacting
cracks X and
to ends of stage d in Fig. 2A).
stress. Although
in few crack interactions
2 0.5), it must be emphasized towards
(A-I)
are measmed
K,,/K,
values are relatively
that these are maximum
the ends of the crack interaction.
K,,/K,
and are only confined
high (K,,/K,
values which develop to small areas of the
crack interaction (Fig. 2A). The K,,/K, values rapidly subside with distance from these areas. Strike-slip fault initiation in the rift would require far field shear, which is not demonstrated
by the present
analysis.
DISCUSSION
Muntle diupirism
The results
presented
above point
to crustal
extension.
There is evidence
which
implies that this extension is a consequence of mantle diapirism. This includes observations by McCall (1967) that the early (Miocene) Samburu basalts are arched up with increasing intensity as one moves towards the median line of the rift. and this is attributed to up-warpings. Baker and Wohlenberg (1971) concluded that there were three periodic up-archings in the central Kenya, and the location of the main rift is on the crest and major axis of the uplift. They suggest that “the first extensive rift faults developed early in the Pliocene at the culmination of the Miocene uplift phase”. Furthermore, the fault patterns in central Gregory Rift (Fig. 3B, and related maps), show many interior horsts distributed along the rift. Burke (1976) made similar observations to the latter in other East African Rifts. Horsts in an extensional rift can result only from a vertical upward pressure where positive evidence for lateral compression is not available. According to McConnell (1967) and others no significant lateral displacements are known from the East African Rift. Baker and Wohlenberg (1971. fig. 7) suggest that there is crustal thinning and a zone of hot low density upper mantle beneath the rift. These two features are equated with mantle diapirism in the Rhine Graben (Fuchs et al., 1981). Also, it
61
corresponds
well with numerical
results
“lend support to the idea that the mechanism upwarping of the crust”
with
the theory
that
(Neugebauer,
from the Rhine Graben which
obtained
of rifting
1978). Hence,
in the Gregory
Rift
mantle
is caused by epeirogenetic
the above arguments diapirism
coincide
was responsible
for
extensile fracture,
and support the interpretation by Chapman et al. (1978) that “the majority of the faults developed as vertical fractures in horizontal rock sequences and were then rotated tilted fault-block
by continued
extension
and up-arching
to produce
complex
system”.
Fracture oelocities in the crust There seem to be close relationships of faults with volcanic and seismic activities in the Gregory Rift. This appliesespecially to the so-called grid faults within the rift itself (Tobin Gregory
et al., 1969). Association
Rift (Molnar
of recent faulting
and Aggarwal,
1971), and generally
(Fairhead and Girdler, 1971) have been suggested. recent faulting, volcanism, geothermal, microseismic maximum crustal thinning of crack growth associated
with earthqu~es
within
the
in the East African
A remarkable activity and
Rift
correlation axial zone
of of
was noted by Searle (1970). A recent historical evidence with an earthquake (Tiercelin et al., 1980) suggests that
most probably many more such associations have occurred in the past. The close correlation of faulting with earthquakes in the Gregory Rift implies that fracture in this rift was rapid. This fits the observation common, it follows quite well the angular
that crack interaction relationship observed
in the rift is very by Kalthoff, and
resembles crack interactions that can be simulated by unstable fracture in soda-lime glass (Swain and Hagan, 1978). Furthermore, it may suggest the applicability of eq. 3 to tectonic problems in rifts. determined by future work. Perhaps planar each
the most pronounced
parallel other
locations
The extent
settings.
for considerable
(for instance,
feature
In contrast, Engelder
of all the faults
vertical
distances
of this will have,
planar
characterize
extensile
of course,
studied
two groups of extensile fractures most probably circumstances. If extensile joints of the type
here is lack of
fractures
systematic
that parallel
joints
and Geiser, 1980). The dissimilarities
to be
in various
between
these
reflect different initial mechanical mentioned above are mostly the
consequence of slow processes of fracture propagation (Bahat, 1979), and the far&s associated with the Gregory Rift reflect unstable fracture propagation, rate of crustal fracture propagation evidently is a parameter of great importance. Fracture branching in low strength terrains It was pointed out by Tchalenko and Berberian (1975) and Bahat (1982) that branching associated with earthquakes seems to prefer association with faulting through alluvium with properties of low strength (abundance of mechanical discontinuities and low fracture toughness). Fairhead and Girdler (1971) suggested that in the Gregory Rift the tensile strength of the lithosphere may be low due to the
62
presence
of igneous
material
rift floor to a significant pyroclastics
interbedded
contributed
to low strength
crack branching
at very shallow depths. extent
with
consisted local
lake-sediments.
succession
This
(1981) recently
that the
of lavas and
succession
could
of the rift floor, which made it amenable
and other facets of fracture
King and Vita-Finzi
Searle (1970) observed
of a complex
have
to intensive
interaction.
addressed
the problem
of the elastic-brittle-
ductile response of the crust to earthquake at shallow depths. They suggested that the rapid deformation at the time of an earthquake is elastic-brittle in nature, and in the process of ductile relaxation the elastic deformation may be “freezed in”. My own observations of elastic fracture propagation in (probably alluvium rich formations appears to support this suggestion. behavior in such formations seems to obey elastic theory.
ductile) low strength Apparently. fracture
CONCLUSIONS
Vertical fracture
is important
and fracture
interaction
is quite intensive
in Central
Gregory Rift. This interaction is commonly bilateral. Crack branching occurs in major and minor faults and it is mostly complex. Interacting opposing non-coplanar cracks
are more common
fracture
interaction
angular
relationships
in the younger
types
follow
reasonably
minor
theoretical
faults
and
within
experimental
well. As such they support
the rift. These fracture
previous
two
mechanic
observations
(Bahat, 1982) of a similar behavior of two fracture sets which are four orders of magnitude different in size and follow eq. 3. The vertical fracture and these relationships indicate a predominance of extension fracture, probably with local incrases of shear limited to small areas in minor faults and in association with late displacements in major faults. The implication is that in the rift curved and angular faults were not initiated
as strike-slip
patterns
and
of the
earthquakes monly
faults
suggest
observed
fracture. In the Gregory
their
that fracture
planar,
parallel,
Rift mantle
fractures close occurred
systematic
diapirism
(as previously
association unstably joints
with
proposed). volcanic
(rapidly) which
was responsible
The angular activities
in contrast
result from stable for both extensile
and
to com(slow) fracture
and block tilting, ultimately resulting in fault dips deviating from the vertical. A previous suggestion that crack branching is more easily facilitated in crustal formation of low strength (low fracture toughness) receives some support in the present study. It is pointed out that the characteristic crack interactions observed along the Gregory Rift do not appear along the rift in Iceland. This suggests that fracture (at least at the surface) of these two rifts was controlled by different mechanisms. ACKNOWLEDGEMENTS
I would like to thank Paul S. Griffiths who has granted me the permission to use his structural maps of the Gregory Rift and made useful comments, and Christopher
63
H. Scholz who read the first draft and made important suggestions that helped to improve the manuscript. I received assistance in the statistical analysis from members of the computation centre of the Ben Gurion University of the Negev. This paper was partly written while I was on Sabbatical leave at Lamont-Doherty Geological Observatory. The courtesies extended to me by Terry Engelder and other members of this institute are very much appreciated.
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