Geoscience Reference
In-Depth Information
GRID A NON ABSORBING
x 10 6
6
amplitude
4
2
0
2
4
6
3
10
9
2.5
8
2
7
6
1.5
distance along sample axis
5
time
1
4
0.5
3
0
2
Fig. 6.4. Propagation of waves through cylindrical sample withnon-absorbing boundary
(Arroyoet al.,2006)
a pure shear mode of deformation in the soil but it will certainly generate other modes
of deformation including compression waves which will travel at the compression wave
velocity.
Numericalsimulationsofexcitationofabenderelementintheendofacylindricalelastic
soil sample have been performed using the three dimensional finite difference program
FLAC-3D confirming the non-ideal nature of the wave (Arroyo et al., 2006). Figure 6.4
shows the time history of the wave (a single sinusoidal pulse at input) as it propagates
along the axis of the cylinder with non-absorbing boundaries. Local effects, especially
reflectionsfromthelateralboundaries,turntheinputtraceintosomethingmorecomplex.
As the distance along the axis increases the second peak actually becomes bigger than
the firstone.
Thesyntheticsignalsfromthenumericalsimulationcanbeinspectedinanattempttodis-
coveranobjectiveprocedureforestimatingthearrivaltimesothattheshearwavevelocity
can be calculated (Figure 6.5). People have proposed various geometrical characteristics
of the received wave that can be extracted more or less automatically (Figure 6.5): the
most obvious one would be when the receiving bender element starts to move (T0); but
themomentoffirstsignificantreversal(T1)orthefirstcrossingofthetimeaccess(T2)or
eventhesecondpeak(T3)mightprovidemoregeometricalconsistency.Oneofthediffi-
cultiesofusingthefirstpointofmovement(T0)isthatveryoftenthereceivedtracemay
well be preceded by a small movement associated with the arrival of the compression or
p -wave—which is evident also in a typical experimental record (Figure 6.6). With these
geometrical definitions (Figure 6.5), the received signal of the numerical calculations
can be interpreted automatically to estimate the values of apparent shear wave velocity.
 
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