Journal of Applied Mechanics Vol.3, pp.585-594 Viscous-Plastic
Analysis
(August 2000)
of Crustal
JSCE
Deformation
of Fault-bend
Folds
摺曲 断層 を有 す る地殻変形 の粘塑性解析 に関す る研 究
Yun
GAO*
高昀
Zhishen
呉
WU**
Yutaka
智深 村上
*Student Member of JSCE,Dr.Cand.,Dept.of
MURAKAMI
***
裕
Urban & Civil Eng.Ibaraki University
(4-12-4,Nakanarusawa,Hitachi,316-8511,
[email protected]) Member**of JSCE,Dr.Eng.,Asso.Prof.,Dept.of Urban & Civil Eng.Ibaraki University (4-12-4,Nakanarusawa,Hitachi,316-8511,
[email protected]) Member of JSCE,Dr.Eng.,Chief *** of Geophysical Analysis Section,Geophysics Department,Geological Survey of Japan (1-1-3,Higashi,Tsukuba,Ibaraki
305-0046,
[email protected])
In this paper,a finite element model is formulated to simulate the crustal of deformation of faultbend folding with the large scale features using the large deformation theory in which the fault surface is represented with the master-slave method.The viscous-plastic material properties modeled by the Perzyna viscoplasticity theory are used to simulate the pressure solution creep and cataclasis respectively.Moreover,an interfacial viscous-plastic model is adopted to represent the nonlinear behavior of the fault surface.Effects on different structural models and parameters of fault-bend folds are simulated.Contours and development of the stress invariant,horizontal strain, equivalent viscous plastic strain by following an individual particle and traction on the fault surface are shown.The numerical results comparing with kinematic models are also discussed in order to infer a sequence of the deformation mechanisms. Key Words:fault-bend folding,master-slave method,viscous plastic,crustal
1
INTRODUCTION
creep and cataclasis of fault-bend
The nature and history of rock deformation during movement over thrust-fault ramps have been investigated using kinematic and mechanical models as well as field observations1) 2) 3).Kinematic models of fault-bend folding assume flexural-slip or flexural-flow folding during movement over a rigid footwall in order to simulate the development of a hanging-wall anticline 5) Because layer thickness is constant in most of these kinematic models,there is layer-parallel slip or layerparallel shear strain but no layer-parallel shortening or extension.Analytical and numerical models have been also used to simulate deformation around a ramp.Berger & Johnson (1980)1) discuss the development of ramp anticline above a rigid footwall using a linear viscous material,with constant friction along the ramp and frictionless flats.They show that fault friction leads to thickening of the hanging wall above the lower ramp hinge and an increase in fold asymmetry.Erickson & Jamison(1995) use viscous and pressure-dependant plastic material properties to model pressure solution
― 585―
elements
deformation
respectively
folds,
where
the
during
are adopted6).Recently,in
general crustal displacement,a
Fig.1 Schematic
principle
drawing
spring
order to simulate
deformation with new finite element
based on the extended
the development
friction-contact
the
fault discontinuous model is developed
of virtual
work in which
of a fault-bend
fold
the large deformation is formulated by using an updated Lagrange description and the fault surface is represented with the master-slave method (Wu 2000).7) In spite of these accomplishments,the investigation of the effects on both geometry sizes of structures and fault material properties are quite insufficient.This paper is concerned with a viscous-plastic finite element model to simulate different structures of fault-bend folding using large deformation,the Perzyna viscoplasticity theory that there is a fault surface with the master-slave method.An interfacial viscous-plastic law is adopted to represent the behavior of the fault surface.
2FINITE
ELEMENT
FAULT
MODEL7)
FORMULATIOIN
Fig.2 viscous-plastic
model
yield condition F and Drucker-Prager viscous-plastic potential QVPare used as expressed as eq.(2) and (3).
AND
(2)
(3)
τ1,τ3is the 1
(1)
the
yielding is
the
first
stress first
and
and
stress
￠ is the
Considering
the
viscoplastic
prescribed and
external internal
displacement s}is
traction
{f0}
traction jump
Lagrange
on stress
a body
{fc0}
force on
force
by
V,
is
internal the
is
friction.
second
can
be
defined
as
rate
I
stress
proposed
stress-strain
by
relation
of
follows:
(4)
y
coefficient.
is
the
fluid
coefficient;cr
If an integral
step.As
a
is
node even though reach yielding to be in elastic
measure
equivalent
of
the
creep
it had being
surface at some status in current
the
viscous-plastic
viscous-plastic strain
s vp is
introduced.
So
relative
surface is
in
boundary
caused
discontinuous vector;{ƒÃ}
field {r0}
of
strain
Qvp>0,the
deformation,the to
angle
stress.σY
i
Perzyna(1966),when
time
subjected
principal
invariant;J2
yielded formerly doesn't time step,it is considered
is
third
nvarlant,
where
body
domain
8)
Consider a structural system in which the reference configuration of a body exhibiting large slipping along the fault surface so that the whole structural system is characterized by two constitutive relations.One is a volumetric constitutive law that relates stress and strain for the continuous body,while another is a cohesive and frictional surface constitute relation between the traction and displacement jumps for the fault. There are two contributions to the internal virtual works:a volumetric contribution and interface contribution.Based on a Lagrange description,therefore, an incremental formulation of the extended principle of virtual work for a body with an internal interface is written as
The
in continuous
(5)
Sc .Here
Lagrange
{ strain
vector.
where
2.1CONSTITUTIVE CONTINUOUS As
shown
equation
EQUATIONS
IN
DOMAIN in Fig.2,a
model
based on a mixed
(6) viscous-plastic
in continuous method
domain
constitutive is formulated
And
in which the Mohr-Coulomb
― 586―
a,K
are the function
of
a,
and 0
(7)
2.2
MASTER-SLAVE
PLASTIC
METHOD
MODEL
ON FAULT
AND
(10)
VISCOUS
To describe
SURFACE
the inelastic
a viscous-plastic
model Faults
behavior
as shown surface
1
Faults Fig.3 master-slave
slide line segment
the contact
between
surface and a segment the nodes
x2,x3
of the master
and x4.On
surface in which global on master
surface
interpolation be
displacement
surface
coordinates
the slave
described
by
is defined
friction
Ni of
the
node
by
x;on
determined.Moreover,the
(13tcon discontinuous
And
the force increment
displacement
relative
displacement
surface
at
On two
kinds
of
(12)
where{•¢ucvp}is
the
referring
to
traction
is
components,i.e.
the
time
function increment
is
the
incremental function
of
Fc,viscous-plastic
viscous-plastic fluid potential
component by
coefficient (VP
rc, and
A t
master
elastic
or
giving
offered
tangent
the
by
elastic
respectively.The
normal
is
which
relative
(13) surface,the
displacement
described
x1
by the viscous-plastic
m.
components,
either
be
step
discontinuous
inelastic of
time
node
caused
to the total force increment.
after slip
increment;{•¢uc}m of
is added
the
yielding displacement
surface as follows
relative
displacement
is
as
(11)
the
completely
of the node x1 can be obtained
{•¢u}
yielding function is considered
the function of yielding stress 0cY and angle of internal
are used, the point x
(8)
where
2
of the master
to the point x,on
position function
segment,can
x1,on
this segment
corresponding
slave surface,whose the
a node
surface
Fig.4 viscous-plastic model on discontinuous interface In this model,the
Consider
of the fault surface,
in Fig.4 is considered.
and
2.3 time integration
characters
component
and iteration
will
discontinuous
(1)stress
stiffness
in continuous
domain
matrix.
(9)
For update Lagrange formulation,in time step m,the Lagrange stresses {s}mis equal to Cauchy stresses {i}m
(14) As relationship elastic
for
elastic
behavior
between displacement{•¢(•¢u)}can
the
along force
the
increment be
fault and expressed
surface,the the
relative
In continuous domain,the
as
Kirchhoff stresses {tk}
({tk}=[J]{2}) obey the following relation
― 587―
(22)
(15)
where
n
is
the
load
Symmetrical the
tensor
composition
and
step
of
rotation
and
k
is
the
formulation the
iteration [•¢r]
Jaumann
In the total
step. of
vector
differential
{•¢t}
tensor
coordinate,it
can be rewritten
as
is
(23)
[•¢rk*]
tensor [n].
where [T] is the coordinates transformation matrix. (16)
On
the
basis
Lagrange
of
stress
the
vector
above {•¢s}
equations,the can
be
written
2.4 FINITE
incremental
ELEMENT
Considering
as
time
iteration,in
the
continuous upon
(17)
FORMULATION
domain finite
integration,large total and
element
incremental
the
which
can
be
to
finite
where
[Dc]
modified the
first
second and
is
elastic
stiffness order order
{•¢fvP}
(2)traction
stiffness
matrix
terms
of
for incremental
terms;{•¢Evp} is the
matrix large
corresponding
on discontinuous
is
strain the
and
[DGt*]
deformation;
viscous
and
as
plastic
(24)
where
is
{•¢e} {•¢n}
the
element
(18)
(19)
the
surface,
respect
{•¢a},the
obtained
of
fault with
variables
and
consist
viscous-plastic
discretization
nodal
formulation
deformation
system
is
is the strain
traction.
surface
On the discontinuous surface,the traction vector {fcL} can be expressed as the following relation where the super script L' refers to local coordinate and the sub script `c' refers to discontinuous surface.
(20)
Therefore,the incremental traction vector {AfcL}can be written as
Here,the
total
incremental
elastic
interfacial
(21)
{•¢PvP}
is
― 588―
stiffness,
geometrical
the
due
virtual
to
is
the
virtual behavior
the
residual
the
nodal
load
behavior
viscous-plastic {‚ä}is
matrix
stiffness
viscous-plastic {•¢PcvP}
stiffness
in nodal
vector.[B]
consists
discontinuous vector
vector
the
the
and surface.
produced
by
domain
strain
the and
produced
discontinuous is
of
stiffness
continuous load
on
[K*]
by
the
surface. matrix
and
[N] is the interpolation function where the subscript 'L' refers to linear component, subscript 'NL' refers to nonlinear component and 'C' refers to discontinuous component.
3
NUMERICAL
properties on the fault surface
SIMULATIONS
Fig.5 shows a finite element mesh of a structural model with fault-bend folds,which is similar with reference [6].Erickson & Jamison investigated the structure using a finite element model with independent viscous,plastic analysis and constant friction material behavior on the fault surface.In this paper,we focus on the effect of the ramp height and the viscous-plastic material behaviors on the fault surface.Each structural model contains 200 6-node isoparametric,quadratic triangle elements.Plane strain is assumed.The initial fault geometry consists of a 1000m long ramp connecting lower and upper flats.A surface pressure of 75 MPa is applied to the top of the model and the right side of the hanging wall,which simulates a 3km overburden.There is zero shear stress along this top surface of the model.A zero displacement boundary condition,Ux=Uy=0,is used along the left (hinterland) side of the footwall,Uy=0 along the base of the model and Ux=0 along the right (foreland) side of the footwall . A displacement of 25 m per 2500 y time step is imposed on the left side of the hanging wall,a velocity (1 cm y-1) that is consistent with estimates of natural thrust sheet motion.The models are run to a maximum displacement of the left side of the model of 2.5km(100 time steps).
Fig.5 initial,undeformed model,showing
Table
Table 2.Material
1.Description
Six sets of structural models are used to simulate different fault-bend folds as shown in Table 1.All materials of the structural models have same density 2500 kg m-3,Young's modulus 3x104 MPa,Poisson's ratio 0.25,yield strength 27 MPa,Stress-strain slope 2300 MPa,viscous-plastic fluid coefficient r=5x10-14s-1, creep coefficient cr=1.On the fault surface,all materials have same normal stiffness Kn=3x1010MN/m,but the tangent stiffness and the viscous-plastic fluid coefficient are chosen as Table 2.In the corresponding figures,the unit of I1 and (J2)1/2is MPa;traction is MN;slip displacement is m;dip of backlimb and forelimb is degree;time increment is 2500 year.
grid for the finite-element boundary
conditions
of the structure
models
Fig.6Contoursof (a)I1(b)(J2)1/2 (c)Exx(d) ~vp after250,000 yearsfor uniformviscous-plasticmodelA3
― 589―
Fig.6 shows the results of the numerical simulations for the Model A3 which contains a hanging wall and footwall with the uniform viscous-plastic material properties.I1 is higher around the foreland of footwall and in the area from above the upper ramp hinge to the upper backstage of hanging wall(Fig.6a).Higher (J2)112 occurs above the upper ramp hinge,although the maximum value above the lower ramp hinge moves up the ramp during the late stage of the model.Maximum values in (J2)112 also develop below the ramp and in the upper forelimb of the hanging wall (Fig. 6b). The strains Fxxare negative in the trailing syncline and right leading syncline where there are horizontal shortenings and the maximum is in the upper late stage.Maximum negative Fxxis observed from above the upper ramp hinge to the upper backstage of hanging wall. Corresponding to this
result,in the hanging wall anticline syncline,the strains Fxx are positive horizontal extensions and decrease backlimb.Maximum positive Exx is
and left leading where there are from the upper observed in the
place where the hanging wall anticline meets in the left leading syncline (Fig. 6c).The highest viscous-plastic strain is found above the upper plat and nearby the upper ramp hinge with an ellipse shape in the hanging wall (Fig.6d). The numerical results for Model B3 which contains a viscous-plastic hanging wall and a rigid footwall are shown in Fig.7.From these figures,I1 is higher in the area from above the upper ramp hinge to the upper backstage of hanging wall,however,the maximum value is larger than Model A3(Fig. 7a).(J2)1/2 is higher in the area above the low and upper ramp hinge.Also,the maximum value is larger than Model A3(Fig. 7b).The strains Fxx are negative in the trailing syncline but the maximum value which is larger than Model A3 is above the ramp.Maximum negative Fxxis observed in the area from above the upper ramp to the upper backstage of hanging wall.Corresponding to this,in the hanging wall anticline,the strains Fxxare positive and decrease from the upper backlimb where the maximum value is smaller than Model A3.Maximum positive Fxxalso produces in the place where the hanging wall anticline meets in the left leading syncline but smaller than in uniform viscousplastic materials (Fig. 7c).The highest viscous-plastic strain is found in the area from above the upper ramp and nearby the upper ramp hinge with an ellipse shape and the maximum value is larger than Model A3 (Fig.7d).
Fig.8 Position
Fig.7 Contours of (a)I1 (b)(J2)1/2(c)xx(d)v,after
of particle
viscous-plastic
250,000
years for rigid footwall model B3
―590―
after 250,000
and rigid footwall
years on
By
following
and Fig.8,the shown
an individual
stress
paths
in fig.9a.When
hinge,a
particle
in J space
the particle
as shown in Fig.5 can be tracked
passes
peak value will appear.The
as
over a ramp
value,especially
the
peak value produced by high ramp is larger than by low ramp.Because of the different length of the ramp,the peak value by h=500m emerges later height.Viscous-plastic strain accumulates stress
status
is on the yield
lower hanging shortening contacts lower
surface.The
wall undergoes
over
the lower
hinge,it
shortening.When
flat
because
is
path
passes over the
to undergo
particle
in the
horizontal
its stress
the particle
continues the
particle
viscous-plastic
the yield surface.As ramp
than by small only when the
horizontal
above the ramp,
Fig.10development of (a)(J2)1/2 (b) Exx in 100 time steps for differentfootwallwith h=500m
Fig.9 development of (a)(J2)1/2(b) Exx(c)tvp 100 time
steps
for different
ramp
(d)traction in
height with uniform
viscous-plastic material
Fig.11 development of (a)(J2)1/2(b) XX (c)traction steps for different Kt with h=500m
― 591―
in 100 time
displacement.In time step 40 when the ramp height is 500m,it reaches the largest value and then trends to similar value approximately. For a structure with a rigid footwall,even though the horizontal extension is smaller,not only the peak value of (J2)1/2 is higher,but also horizontal shortening, extension and the average viscous-plastic strain are larger.The viscous-plastic footwall deforms more smoothly and results in smaller shear effect,however, there is practically no footwall deformation in series of model B,and consequently,the ramp shape remains relatively unchanged (Fig.10).
Fig.12 development time
of (a)(J2)1/2(b) Exx (c)traction
in 100
steps for different rt with h=500m
the stress status falls below the yield surface because of increasing I1 and decreasing (J2)112and,thus,further viscous-plastic strain temporarily ceases.The incremental strain changes from horizontal shortening to extension approximately midway up the ramp.Over the upper ramp hinge,I1 decreases and (J2)1/2increases,and the stress state returns to the yield surface,resulting in additional viscous-plastic strain.This second phase of viscous-plastic deformation is horizontal extension, which is superposed on the earlier phase of horizontal shortening.As the particle moves over the upper flat, (J2)1/2decreases and the stress state falls below the yield surface.After all the viscous-plastic deformation is distinctly episodic.When the ramp height exceeds 300m, the areas of horizontal shortening and extension are classified evidently.On the fault surface, from the development of traction of right low corner node of the triangle element (Fig.9d),the value rises and drops episodically.It rises as it isn't yielding,otherwise drops due to amendment by the viscous-plastic incremental
― 592―
Fig.13 (a)slip displacement(b)backlimb dip
(c)forelimb dip
(d)thickness variation after 250,000 years for different height with uniform viscous-plastic model
ramp
For
different
viscous-plastic though
the
times
of
tangent
stiffness
footwall
when
traction by
produced
MN/m
similar
but
,the
strain
Exx
increase
different
fluid
MN/m,the
peak with
first
50
of
is is
the
however,in s-1
shapes
of
that
to
50
rc
two
but
material
to
relationships
Kt.
same
evolution.The
by (J2)1/2
c=3x10-11
by
s-1,the
models
are
rc
(J2)1/2
more
similar
The
value
of
ramp
height
condition direction
angle
thickening
the
to
forelimb
increase
h.Comparing
with
in
the
with h=500m,
hanging
smaller
with
advanced is
the the there
than
forced
final
initial
ramp
the
later
shallow will
evolution 32•K.According
initial
layer
decrease is
the
or
rc over
and
28%
layer
the
finite
the
it leaves
layer
wall(Fig.13).
the
equivalent
But
when
DISCUSSION
the
In the form of kinematical models proposed by Rich(1934),bed-duplication folding requires:(1) translation of hanging wall rocks sub-parallel to the thrust surface;(2)steps or curves in the thrust surface; (3)continuous contact between hanging wall and footwall rocks across the detachment surface;(4)stiff or rigid footwall.Suppe(1983)added three requirements to constrain the geometry of bed-duplication folds.These are:(5)constant length of beds;(6)planar fold limbs;(7) constant thickness (normal) of beds within planar limbs. Actual fault-bend folds may not develop precisely with the assumptions of parallel behavior, because the kinematic details depend on the mechanical properties of the layers applied.In this paper,the finite element models simulate both fold geometry and the distribution,
•\ 593•\
other
initial
ramp
evident these In
are
fault
creep
effect
are
used,the
be
observed
coefficient the
in
shorter
by
second
shortening,extension also
have
lower,the occurs
larger
to the
after
ramp,the small.On
is
used,the the
ramp
end.If
the
are
more
the
all,
ramp.
of
of
Kt
rc means the
same
stiffness
same
structures
hysteresis or
shape
can
smaller
and
fluid
peak
value strain
viscous-plastic the
shear
means
the
similar.Horizontal
average
of
the very
value
difference.When
tangent
or
evidently.
to
stiffness but
are
will
ramp
shear-effect
tangent
surface
shown
footwall.After
value
of
as
varieties
due
higher
phenomenon by
footwall beginning
and
large
of
are
same,these
invariant
by
degree
above
period.When
larger
fault
finally
steep
increase
varieties
phenomenon
on
decrease
displacement
model,higher
but
is
shortening,extension
forward
dominant
surface
2
A3,there
at the
a viscous-plastic
cohesion
synclines
particle
strain
from is
trailing
the the
arrives
goes
angle
varieties our
of
a rigid
using
addition,
model
advanced
relative
change
than
stronger
of
particle
dip.In
a viscous-plastic
horizontal
hand,when
doesn't
its
particle
their
in
will
viscous-plastic
of
from
Al,there is
wall.If effect
ramp,the
the
angle
angle
but
the
and
in the
but
hanging
increase
range
as h=500m.
shear
decrease.Before
the
forelimb,whereas
models,when ramp
the
affected element
models,layer
model
h=100m
element
increases,the
differences
4
as
of
will
constant
26•K. only
during
dips
forelimb
models.In
is used,the
in Fig.5
the
not
thickening
squeezing
ramp
than and
are element
be
degrees
the
the
24•Kto
finite
geometric
increase decrease
model
depends not
forelimb
some
element h=500m,
from
the
few
final
to
thickening
footwall
ramp
thickness,
of 20%
rc
layer
In
the
a
fault-
the
dip
ramp.In
by
should should
finite
range
would
the
a
finite
during
forelimb
of
of
26.5•Kas
degrees dips
the
geometric
geometry.In
the
initially
backlimb
and
thicknesses
22
The the
larger of
7%
opposite
than is
the
few
increase
31•Kto
the
dip.In
is
geometry,and
model
of
fold dip fb
ramp
a
the
backlimb
dip
fold
fundamentally
although
models,the
the
relate
kinked-hinge
the
by
by
layer
a
to
geometric
those
angular
are
curved
ramp
on
and
velocity
has
decrease
h.
Kt
velocity.
smaller
(5f which the
and of
which
dip with
Kt,rc
increase is
side
traction
which
and
h.When
left
(Fig.1)
to
rc and
model,it of
increases of
relates of
referring bh
variation
increase
each
of
angle of
h.In
because
(26.5•K)
increase
decrease
particles
dip
ramp
displacement
the
of
while
backlimb
the
slip
with
displacement
the
the
folds
are
decrease
thinning
decreases
the
the
thickening
(Fig.12).
It
equal
with
configuration.The
use
is
compared
fold
folds,which
first-mode
when
folds.The
be
fault-bend
hinges
models,it
similar,
produced
will
In
rc.In
of
can
models,the
fold
it
fault-bend
models
generally
bend
in
fault
geometric
models,
produced
more
the
average
s-1,the
are
if
the
the
for
appears
of
traction
=3x10-11
traction r
geometry
are
with
decrease
models
by
models
Kt=1x105
similar
the
by
geometric
models
surface and
the
steps,the
approaches
this
with
material
last
fault
is
of
(Fig.11).For
strain Exx,the
found
close
two
the
.1x10-10
(J2)112
increase
steps,it s-1
shapes
of
strain
rc=1x10-11
the
Kt
h=500m
rc.Horizontal
viscous-plastic the
on
geometry
viscous-plastic of
deformation
6 Kt
larger
of
s-1,
by
(J2)1/2
by
average
when
value
smaller
of
timing
is
of
value
increase
coefficient
with
c=1x10-11
times
lately
the
footwall
surface r
MN/m
3
peak
appears
the
fault and
and
and
and
with
viscous-plastic
lately
shape value
the
Kt=1x105
MN/m
peak
Horizontal strain
by
Kt=1x104
=3x104
on h=500m
ramp
effect or
strain height
is
hysteresis
also
smaller
fluid
coefficient invariant
on fault surface has large
In a word,the regular
but peak value of the second
difference
cohesion
despite
of similar
and creep on fault surface
shape.
On the other hand,
the cohesion
surface
effect for the total system.
have regular
Classic
have
effect for the total system.
relations that
geometry and,
would
models
in which
and creep
suggest
backlimb
not be affected
and the
backlimp forelimb
during
the
increase
dip will decrease
simulates
Fig.14
Schematic drawing of possible deformation mechanisms
sequence
cataclasis
From reference[6],pressure-dependent viscous-plastic deformation can simulate cataclasis and pressure solution creep,so the results of our models can also be used to infer a sequence of deformation mechanisms for a particle moving over a ramp(Fig.14):(1)viscous plastic shortening,(2)shortening,(3)shortening,(4)extension, (5)shortening.From these results,the sequence of deformation mechanisms can be obtained:(1)transportperpendicular stylolites,(2)transport-perpendicular stylolites,(3)transport-perpendicular stylolites,(4) bedding-parallel stylolites with viscous plastic extension, (5)transport-perpendicular stylolites.Kilsdonk & Wiltschko(1988),in a study of the ramp region of the Pine Mountain fault,recognized an early deformational phase characterized by transport-perpendicular stylolites, which may correlate with our stages 1-3.Wiltschko et al. (1985) recognized early transport-perpendicular stylolites,which may correlate with our stage 1,and later bedding-plane slip,which may correlate with our stages 2 and 4.Thus,our model results are consistent with field observations,although the complete suit of deformational stages indicated by these models has not been recognized in the observational studies. 5
material
finite
properties
element
models
to simulate
Throughout
most
of
the fault-bend the
model
that the shear effect,the
shortening,extension,equivalent and advanced
with
both in continuous
fault surface
conclude
degrees would
would
decrease
plastic
results
our
deformational been recognized
which
creep,so
is the
composition
bedding-parallel
shortening model
stages
solution
can be used to infer a sequence
and
observations,although
deformation
are
of of
stylolites
and extension.Thus,the consistent
the indicated
the
with
complete by these
in the observational
models
field
suit
of
has not
studies.
REFERENCES 1)Berger & Johnson:First-order analysis of deformation of a thrust sheet moving over a ramp,Tectonophysics Vol 70,924,1980. 2)Suppe:Geometry and kinematics of fault-bend folding,Am. J.Sci.Vol283,684-721,1983. 3)Kilsdonk & Wiltschko:Deformation mechanisms in the southeastern ramp region of the Pine Mountain block, Tennessee.Bull.Geol.Soc.Am.Vol 100,653-664,1988 4)Johnson & Berger:Kinematics of fault-bend folding,Eng. Gelo,Vol27,181-200,1989 5)Rich:Mechanics of low-angle overthrust faulting illustrated by the Cumberland thrust block,Virginia,Kentucky and Tennessee,Bull.Am.Ass.Petrol.Geol.Vol18,15841596,1934 6)Erickson & Jamison:Viscous-plastic finite-element models of fault-bend folds,Jour.Stru.Geol,Vol 17,No.4,561-573, 1995 7)Zhishen Wu,Yun Gao & Murakami:A finite element model for crustal deformation with large slipping on fault surface, International workshop on solid earth simulation and ACES
CONCLUSIONS We use
a few
thickening
thinning
and pressure
mechanisms
with viscous of
by
viscous-plastic
transport-perpendicular
of
increase
dip.
of our models
deformation
of the
by a few degrees
evolution.Layer
Pressure-dependent
results
dip
to our finite element
the forelimb,whereas
the forelimb
of angular
by the later shallow
dip will
model
a series
dip and forelimb
ramp will keep constant.According models,the
on the fault
displacement
viscous
WG meeting,2000 8)Koji Sekiguchi:Time step selection for 6-noded non-linear
plastic
body
and on the
folding
structures.
evolutions,we varieties
can
of horizontal
viscous-plastic are dominant
joint element in elasto-viscoplasticity analyses,Computers and Geotechnics,vol10,33-58,1990
strain
due to the ramp.
― 594―
(Received April 21,2000)
