EP 1110-2-12
30 Sep 95
(1) The PGA associated with the vertical compo-
participation factor and the mode coefficient for a
nent. In some instances the vertical component PGA
particular mode and direction of excitation may be
may be as great or greater than the horizontal compo-
used to judge the order of importance of the modes,
and which modes will make a significant contribution
nent PGA. Refer to paragraph 5-6a.
to the dynamic response.
(2) The shape of the vertical component design
response spectrum. The frequency content of the
c. Equivalent added mass system. The added
vertical component of ground motion is usually
mass associated with the equivalent mass system
higher than the frequency content of the horizontal
discussed in paragraph 7-5c should be active in the
component. This causes the vertical spectrum shape
horizontal direction, and inactive in the vertical direc-
to be different than the horizontal spectrum shape.
tion. Added mass representing backfill or silt depos-
The vertical component will excite modes in the
its against vertical or near vertical surfaces of the
lower frequency range less than will the horizontal
dam should also be active horizontally and inactive
component.
vertically. If the backfill is placed on the sloping
face of the dam, the magnitude of the added mass
(3) The depth of the reservoir. Vertical ground
acting vertically should be determined as described in
motion causes hydrodynamic pressure waves to be
paragraph 6-3b.
generated which exert a lateral load against the face
of the dam (this hydrodynamic load is in addition to
d. Hydrodynamic loading. The vertical compo-
that discussed in paragraph 7-5). When considering
nent of ground motion causes hydrodynamic pressure
stresses caused by the vertical component of ground
waves to be generated from the reservoir bottom into
motion, the stress induced by the hydrodynamic pres-
the impounded water above. These pressure waves
sure waves can be larger than the stress caused by the
act horizontally against the vertical or near vertical
inertia response associated with the mass of the dam.
face of the dam. In the composite finite element
For a nonabsorptive reservoir bottom, the hydrody-
method, the equivalent mass system discussed in
namic load theoretically reaches infinity at the natural
paragraph 7-5 accounts for the hydrodynamic reser-
vibration frequencies of the reservoir. This is in con-
voir effects caused by the horizontal component of
trast to stresses caused by the horizontal component
ground motion, but it does not account for the effect
of ground motion where the stress caused by the
of the hydrodynamic pressure waves generated by the
hydrodynamic load is small compared to the stress
vertical component of ground motion. To account for
caused by the inertia response associated with the
the effect of the pressure waves, a finite element-
mass of the dam.
substructure model configuration is required as dis-
cussed in Chapter 8.
(4) Reservoir bottom absorption. Reservoir
e. Combining component responses. The indi-
bottom absorption greatly reduces the added hydrody-
vidual vertical and horizontal component dynamic
namic load due to vertical ground motion and elimi-
responses are not in phase. They are independent
nates the unbounded peaks in the response, described
maximum component responses that do not occur at
above, at excitation frequencies equal to the natural
the same point in time during the period of ground
vibration frequencies of the reservoir.
motion activity. Each pair of horizontal and vertical
ground motion records representing a single earth-
b. Method of analysis. Except for the hydrody-
quake event would have a unique phase relationship.
namic load contribution which is discussed later,
Since the response spectrum method encompasses
determining the response due to the vertical compo-
many possible ground motion events which make up
nent of ground motion follows the same general
the design earthquake, the maximum vertical and
procedures and recommendations that apply in deter-
horizontal component responses are combined by a
mining the horizontal component response. The
statistical method to produce a total dynamic response
vertical component design response spectrum, and the
with reasonable probability of occurrence. It is rec-
PGA associated with vertical excitation are used to
ommended that the phasing of the two maximum
define the design earthquake. It should be noted that
component responses be treated as two unrelated
for vertical direction excitation, the fundamental
random occurrences, and they be combined by the
mode and some or all of the significant higher modes
square root of the sum of the squares method (SRSS).
are often different than for horizontal excitation. The
7-11
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