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196 CHAPTER 8 Seismic risk of RC water storage elevated tanks

the formation of surface waves. This phenomenon is called the hydrodynamic effect,
and its appreciation can be given by the Housner method [12], which is based on the
decomposition of the water action in impulse and oscillation action. Under the seis-
mic action effect, the overall stability of the tank to collapse must be satisfied. The
overall stability relating to rigid body behavior can be lost by sliding or overturning.
For this purpose, it is necessary that the stabilizing moment be greater than the over-
turning moment. The classification of this parameter is done according to a safety
factor “F s ” defined as the ratio of the stabilizing moment and overturning moment.

5.3.1 Hydrodynamic effect assessment by the approximate
method of Housner
It is futile to try to protect a structure against the effects of earthquakes simply by
virtue of the calculations said antiseismic. Experience has shown that structures
whose design was correct and the rules correctly applied have a fairly high proba-
bility to support adequately a seismic action of moderate intensity. The choice of
the calculation method and the structure modeling must have the objective that best
reproduces the real behavior of the structure. During the seismic design of water stor-
age elevated tank with a capacity more or less important, it may be a matter of study-
ing the hydrodynamic effect of water on the structure in accordance with the
3
Algerian Seismic Code [13] when the capacity is equal or greater than 1500 m in
seismic zones (II and III). The evaluation of hydrodynamic forces is a crucial step.
For this reason, we use the analytical method of Housner to estimate the response of a
liquid in rigid tanks (cylindrical or rectangular), seismically excited. In the case of a
water storage elevated tank, we cannot consider the vessel as being rigidly related to
the soil and therefore undergoing the same value of the maximum acceleration that
the soil. Indeed when the vessel is on top of a structure, we must consider the flex-
ibility of the latter. Approached calculation by the Housner method consists of
modeling all the water storage elevated tank represented by its equivalent mechan-
ical and mathematical model (Figure 8.3).
The action of the liquid is divided into two actions: A passive action causing pulse
actions and active action causing oscillation actions [14]. The pulse efforts come
from of that a portion of the liquid mass, called passive mass, reacts by inertia to
the translation of a tank walls. Its equivalent mechanical system is obtained by con-
sidering a mass M i , rigidly connected to the tank at a height h i as it applies on the
walls, the same horizontal forces that the equivalent water mass. As for oscillation
efforts, they come from that another part of the liquid mass, called active mass is set
in oscillation motion under the earthquake action.
In summary, the total water mass M e can be divided into a passive mass M i and an
active mass M 0 rigidly connected on the one hand and by means of a spring constant
K 1 on the other hand.
In the adopted mathematical model for a water storage elevated tank (Figure 8.3),
the mass M 0 is connected to the structure by a rod of the same stiffness K 1 ensuring
direct coupling with M 1 , while M 1 is connected to the ground by a rod representing