Shearing along Interfaces
Thursday, March 11, 2010
11:43 AM
There are several instances in geomechanics in which it is desirable
to represent planes on which sliding or separation can occur:
○ joint, fault or bedding planes in a geologic medium
○ interface between a foundation element and the soil
○ contact plane between a bin or chute and the material that it
contains
○ contact between two colliding objects.
FLAC provides interfaces that are characterized by Coulomb sliding
and/or tensile separation. Interfaces have one or more of the
following properties:
○ Friction
○ Cohesion
○ Dilation
○ Normal stiffness
○ Shear stiffness
○ Tensile Strength
Although there is no restriction on the number of interfaces or the
complexity of their intersections, it is generally not reasonable to
model more than a few simple interfaces with FLAC because it is
awkward to specify complicated interface geometry. The program
UDEC (Itasca 2004) is specifically designed to model many interacting
bodies; it should be used instead of FLAC for the more complicated
interface problems.
An interface can also be specified between structural elements and a
grid, or between two structural elements. Interfaces may also be
used to join regions that have different zone sizes. In general, the
ATTACH
command should be used to join sub-grids together. However, in
some circumstances it may be more convenient to use an interface
for this purpose. In this case, the interface is prevented from sliding
or opening because it does not correspond to any physical entity.
Steven F. Bartlett, 2010
Interfaces Page 1
Interfaces (cont.)
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11:43 AM
Interface Properties
Steven F. Bartlett, 2010
Interfaces Page 2
Interfaces (cont.)
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Steven F. Bartlett, 2010
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Interfaces (cont.)
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Shear and normal stiffness (cases)
○ Interface Used to Join Two Sub-Grids
○ Real Interface — Slip and Separation Only
○ Real Interface — All Properties Have Physical Significance
Interface Used to Join Two Sub-Grids
Steven F. Bartlett, 2010
Interfaces Page 4
Interfaces (cont.)
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Real Interface — Slip and Separation Only
Steven F. Bartlett, 2010
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Interfaces (cont.)
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Real Interface — All Properties Have Physical Significance
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Dilation Angle
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Steven F. Bartlett, 2010
Interfaces Page 7
Dilation Angle (cont.)
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Solution for dilation angle for Fig. 3.58 in FLAC manual
.
solving for the dilation angle:
Note: A negative sign was added here to be
consistent with Salgado Eq. 4-15. Also, the
relation between dev and de1 and de3 is
from Eq. 4-17 in Salgado
taking the sin of the dilation angle:
simplifying:
from Eq. 4.18 in Salgado
simplifies to:
the results are the same
Steven F. Bartlett, 2010
Interfaces Page 8
Dilation Angle (cont.)
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11:43 AM
Steven F. Bartlett, 2010
Interfaces Page 9
Simple Interface Model
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Interface
config
set large
g 20 21
model elas
gen 0,0 0,10 21,10 21,0
; scales model to 1 cm
ini x mul 0.01
ini y mul 0.01
; creates horz. gap in grid
model null j 11
; creates gap on both sides of upper part of grid
model null i 1,4 j 12,21
model null i 17,20 j 12,21
; reconnects the grid
ini x add .005 j 12 22
ini y add -.00475 j 12 22
Steven F. Bartlett, 2010
Interfaces Page 10
Simple Interface Model (cont.)
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11:43 AM
; creates interface
int 1 Aside from 1,11 to 21,11 Bside from 5,12 to 17,12
int 1 kn 10e6 ks 10e6 cohesion 0 fric 35 dil 5
; elastic properties for model
prop dens 2000 bulk 8.3e6 shear 3.85e6
; boundary conditions
fix x y j=1
fix x i=1 j 1,11
fix x i=21 j=1,11
; apply pressure at top of model
apply p=50e3 i=5,17 j=22
;
his 999 unb
; consoldates sample under applied pressure
solve
;
; starts shear part of test
ini xvel 5e-7 i= 5,17 j 12,22
fix x i= 5,17 j 12,22
; reinitializes displacements to zero
ini xdis 0.0 ydis 0.0
Steven F. Bartlett, 2010
Interfaces Page 11
Simple Interface Model (cont.)
Thursday, March 11, 2010
11:43 AM
; functions to calculate shear stress and displacements
call int.fin ; this needs to be in default folder
def ini_jdisp
njdisp0 = 0.0
sjdisp0 = 0.0
pnt = int_pnt
loop while pnt # 0
pa = imem(pnt+$kicapt)
loop while pa # 0
sjdisp0 = sjdisp0 + fmem(pa+$kidasd)
njdisp0 = njdisp0 + fmem(pa+$kidand)
pa = imem(pa)
end_loop
pa = imem(pnt+$kicbpt)
loop while pa # 0
sjdisp0 = sjdisp0 + fmem(pa+$kidasd)
njdisp0 = njdisp0 + fmem(pa+$kidand)
pa = imem(pa)
end_loop
pnt = imem(pnt)
end_loop
end
ini_jdisp
;
Steven F. Bartlett, 2010
Interfaces Page 12
Simple Interface Model (cont.)
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11:43 AM
def av_str
whilestepping
sstav = 0.0
nstav = 0.0
njdisp = 0.0
sjdisp = 0.0
ncon = 0
jlen = 0.0
pnt = int_pnt
loop while pnt # 0
pa = imem(pnt+$kicapt)
loop while pa # 0
sstav = sstav + fmem(pa+$kidfs)
nstav = nstav + fmem(pa+$kidfn)
jlen = jlen + fmem(pa+$kidlen)
sjdisp = sjdisp + fmem(pa+$kidasd)
njdisp = njdisp + fmem(pa+$kidand)
pa = imem(pa)
end_loop
pa = imem(pnt+$kicbpt)
loop while pa # 0
ncon = ncon + 1
sstav = sstav + fmem(pa+$kidfs)
nstav = nstav + fmem(pa+$kidfn)
jlen = jlen + fmem(pa+$kidlen)
sjdisp = sjdisp + fmem(pa+$kidasd)
njdisp = njdisp + fmem(pa+$kidand)
pa = imem(pa)
end_loop
pnt = imem(pnt)
end_loop
if ncon # 0
sstav = sstav / jlen
nstav = nstav / jlen
sjdisp = (sjdisp-sjdisp0) / (2.0 * ncon)
njdisp = (njdisp-njdisp0) / (2.0 * ncon)
endif
end
Interfaces Page 13
Simple Interface Model (cont.)
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11:43 AM
hist sstav nstav sjdisp njdisp
step 22000
save directshear.sav 'last project state'
Steven F. Bartlett, 2010
Interfaces Page 14
Simple Interface Model (cont.)
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11:43 AM
JOB TITLE : .
FLAC (Version 5.00)
(10
04
)
LEGEND
6-Oct-10 6:59
step 27927
HISTORY PLOT
Y-axis :
Rev 1 sstav
X-axis :
3 sjdisp
3.500
3.000
(FISH)
2.500
(FISH)
2.000
1.500
1.000
0.500
2
4
6
8
10
(10
-03
)
Steven Bartlett
University of Utah
JOB TITLE : .
FLAC (Version 5.00)
(10
-04
)
LEGEND
6-Oct-10 6:59
step 27927
HISTORY PLOT
Y-axis :
4 njdisp
(FISH)
X-axis :
3 sjdisp
(FISH)
5.000
4.000
3.000
2.000
1.000
0.000
2
4
6
8
10
(10
Steven Bartlett
University of Utah
Steven F. Bartlett, 2010
Interfaces Page 15
-03
)
Interface Example
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11:43 AM
Typical freestanding geofoam embankment at bridge approach. Note
that continuous horizontal planes are created by the block placement
pattern. Question: Could sliding occur along these interface planes
during a major earthquake?
Steven F. Bartlett, 2010
Interfaces Page 16
Interface Example (cont.)
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11:43 AM
Horizontal acceleration response spectra for earthquakes used in
sliding evaluation.
Steven F. Bartlett, 2010
Interfaces Page 17
Interface Example (cont.)
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Pavement Section
Geofoam
Foundation soil
FLAC X-sectional model (2D plane strain)
Steven F. Bartlett, 2010
Interfaces Page 18
Interface Example (cont.)
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11:43 AM
More on interface properties
Normal and shear stiffness at the interfaces are also required by FLAC.
These are spring constants that represent the respective stiffness
between two planes that are in contact with each other. Interfacial
stiffness is often used in FLAC to represent the behavior of rock joints
where some elastic deformation in the joint is allowed before slippage
occurs. However for geofoam block placed in layers, such elastic
behavior before slippage occurs is probably small. Thus, for the case
where only slippage and separation are considered at the interface (i.e.,
one geofoam subgrid is allowed to slide and/or open relative to
another subgrid), the normal and shear stiffnesses used in the FLAC
model are not important (Itasca. 2005). For this case, the FLAC user’s
manual recommends that the normal and shear interface stiffness (kn
and ks, respectively) be set to ten times the stiffness of the neighboring
zone.
Steven F. Bartlett, 2010
Interfaces Page 19
Interface Example (cont.)
Thursday, March 11, 2010
11:43 AM
More on interface properties
Normal and shear stiffness at the interfaces are also required by FLAC.
These are spring constants that represent the respective stiffness
between two planes that are in contact with each other. Interfacial
stiffness is often used in FLAC to represent the behavior of rock joints
where some elastic deformation in the joint is allowed before slippage
occurs. However for geofoam block placed in layers, such elastic
behavior before slippage occurs is probably small. Thus, for the case
where only slippage and separation are considered at the interface (i.e.,
one geofoam subgrid is allowed to slide and/or open relative to
another subgrid), the normal and shear stiffnesses used in the FLAC
model are not important (Itasca. 2005). For this case, the FLAC user’s
manual recommends that the normal and shear interface stiffness (kn
and ks, respectively) be set to ten times the stiffness of the neighboring
zone.
Steven F. Bartlett, 2010
Interfaces Page 20
Interface Example (cont.)
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11:43 AM
Steven F. Bartlett, 2010
Interfaces Page 21
Interface Example (cont.)
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CONCLUSIONS
In general. the majority of the evaluated cases suggest that interlayer sliding is
within tolerable limits (0.01 to 0.1 m) however, two input time histories produced
interlayer sliding that was greater than 0.5 in.. which is considered unacceptable
from a performance standpoint Because the model predicted a wide range of
interlayer sliding displacement for the cases analyzed, this suggests that sliding is
a highly nonlinear process and is strongly governed by the frequency content and
long period displacement pulses present in the input time histories.
The model also suggests that interlayer sliding displacement can, in some cases1
increase when the vertical component of strong motion is included in the analysis
For cases where interlayer sliding is just initiating, the sliding displacement
increases by a factor of 2 to 5 times when the vertical component of strong
motion is added to the analyses However, when the interlayer sliding
displacements are larger. the presence of the vertical component in the model is
less important and the displacements remain the same or only slightly increase.
Thus, we conclude that it is generally unconservative to ignore the vertical
component of strong motion when estimating sliding displacement, but its
inclusion is less important when the interlayer sliding displacement is well
developed. All models showed that the interlayer sliding is generally concentrated
in the basal layers and diminishes greatly in the higher layers. The potential for
interlayer sliding displacement in geofoam embankments can be resolved by
constructing shear keys within the geofoam mass to disrupt continuous horizontal
layers that are being created by current construction practices
The numerical model also suggests that internal deformation caused by rocking
and sway can cause local tensile yielding of some blocks within the embankment,
usually near the base.. In some cases, this yielding can propagate upward and
cause the embankment to begin to decouple dynamically. Consideration should
be given to using blocks with higher strengths than Type VIII geofoam in the basal
zones of geofoam embankments undergoing high levels of strong motion.
Steven F. Bartlett, 2010
Interfaces Page 22
More Reading
Thursday, March 11, 2010
11:43 AM
○ FLAC User's Manual, Theory and Background, Section 4 Interfaces
○ FLAC User's Manual, Section 3.4.7.1, Shear Dilatancy
○ Bartlett, S. F. and Lawton E. C., 2008, “Evaluating the Seismic
Stability and Performance of Freestanding Geofoam Embankment,”
6th National Seismic Conference on Bridges and Highways,
Charleston, S.C., July 27th –30th 2008, 17 p.
Steven F. Bartlett, 2010
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