•
•
•
the original program. The intent
of
the modifications was to make the program more
convenient for use with a personal computer.
MODIFICATIONS IMPLEMENTED
IN
SHAKE91
The main modifications incorporated in SHAKE91 include the following:
• The number
of
sublayers was increased from 20 to 50; this should permit a more
accurate representation
of
deeper and/or softer soil deposits.
• Removed
all
built-in modulus reduction and damping relationships. These
relationships are now specified by the user; up
to
13
different relations
of
modulus
reduction,
G/G
max
> versus shear strain and damping ratio,
J...,
versus shear strain can
be specified as part
of
the input file. A number
of
published variations
ofG/G
max
and
J...
with shear strain are available in the literature (eg, Hardin and Dmevich, 1970; Seed
and Idriss, 1970; Seed et
aI,
1986; Sun et
aI,
1988; Vucetic and Dobry, 1991).
• The maximum shear velocity
or
the maximum modulus are now specified for each
sub layer; again these are part
of
the input and therefore the program no longer
calculates modulus values as a function
of
either confining pressure
or
shear strength.
The user specifies the maximum values, which are derived by the user.
• Object motion is now read from a separate
file;
the number
of
header lines and format
are specified by the user.
• Other clean-up included: renumbering
of
options, elimination
of
infrequently used
options, user specified periods for calculating spectral ordinates ... etc.
DESCRIPTION
OF
THE
PROGRAM
The soil profile is idealized as a system
of
homogeneous, visco-elastic sub layers
of
infinite
horizontal extent; the idealized soil profile
is
shown in Fig.
1.
The response
of
this system
is
calculated considering vertically propagating shear waves. The algorithm in the original
program
SHAKE
(Schnabel
et
al, 1972)
is
based on the continuous solution
to
the wave
equation (Kanai, 1951; Matthiesen
et
al, 1964; Roesset and Whitman, 1969; Lysmer et
al
1971), which was adapted for transient motions using the Fast Fourier Transform
techniques
of
Cooley and Tukey (1965). The program SHAKE91 retains this feature
of
the original program. Details pertinent to the derivation
of
the applicable equations
of
motion and solution
of
these equations are summarized in the original
SHAKE
manual,
in
the aforementioned references and in most textbooks on wave propagation.
An equivalent linear procedure (Idriss and Seed, 1968; Seed and Idriss, 1970)
is
used to
account for the nonlinearity
of
the soil using an iterative procedure to obtain values for
modulus and damping that are compatible with the equivalent uniform strain induced in
each sublayer. Thus, at the outset, a set
of
properties (shear modulus, damping and total
2
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