Civil Engineering Reference
In-Depth Information
pressure, base shear and overturning base moment for the largest expected
peak responses. A few parametric variations are carried out to study the
effects of various governing parameters, e.g. height of liquid in the tank,
height-radius ratio of the tank, ratio of total liquid mass to mass of founda-
tion, shear wave velocity in the soil medium, etc.
As seen in Chapter 2, like any other nonstationary system response, the
nonstationary ground displacement and ground acceleration may also be
expressed in terms of wavelet coefficients as
Kb
a
∑∑
xt
()
=
Wx ab
(,)
ψ
( )
t
(4.27)
g
ψ
gj
i
ab
j
,
i
j
i
j
Kb
a
∑∑
xt
()
=
Wx ab
(,)
ψ
( )
t
(4.28)
g
ψ
gj
i
ab
j
,
i
j
i
j
On differentiating Equation (4.27) two times and subsequently taking
the Fourier transform of both sides, one may get
Kb
a
∑∑
ˆ
x
ω=
Wx ab
ψω−ω
2
(4.29)
()
(,)
( )(
)
g
ψ
gj
i
ab
j
,
i
j
i
j
On taking the Fourier transform of both sides of Equation (4.28), one
may also get
Kb
a
∑∑
ˆ
x
ω=
Wx ab
(,
)
ψω
( )
(4.30)
()
g
ψ
gj
i
ab
j
,
i
j
i
j
On comparing Equations (4.29) and (4.30), one may obtain the follow-
ing important relation, which we will make use of:
Kb
a
1
Kb
a
∑∑
∑∑
(,) ˆ
ψω=−
ω
()
(,) ˆ
ψω
()
Wx ab
Wxab
ψ
ψ
gj
i
ab
,
gj
i
ab
,
2
j
i
j
i
j
j
i
j
i
j
(4.31)
The above equation relates the wavelet coefficients of ground displace-
ment to the wavelet coefficients of ground acceleration. As also explained
