Effect of Depth of Water and Container Diameter in Seismic Analysis of R. C. Elevated Circular Water Tank

Safety of water tanks is very important as they are very important life living structures. Tanks shall always be functional for the access to drinking purpose as well as for the requirement of fire fighting in the area of occurrence of earthquake. The study focus on analysis of RC water tank of circular shape in accordance with IS 1893 (Part-2):2014. The analysis of tank is carried out for zones II, III, IV and V and Rocky or Hard Soil, Medium Stiff Soil and Soft Soil conditions in accordance to Indian standard. Further three different depth of water with constant diameter ratios with tank full, half-filled and tank empty condition are considered for analysis. From the analysis, it is found that tank design is governed in full tank condition. Values of seismic horizontal design coefficient in impulsive mode (Ahi) are less than those for convective mode (Ahc), for full tank condition. This is due to lower values of time period in impulsive mode. For the same soil condition, values of Ahi and Ahc increases for higher seismic zone. The values of highest shear and moment at bottom of container are found to be governing in full tank condition as compared with half-filled and empty tank condition.


Introduction
Safety of water tanks is very important as they are very important life living structures.Tanks shall always be functional for the access to drinking purpose as well as for the requirement of fire fighting in the area of occurrence of earthquake.Earthquake loads are infrequent loads [9,10] acting on the structure.So it is not advisable to allow structure to remain elastic or unharmed which in result will be improvident.In common design practice it is consent some structural and non-structural damages at the time of occurrence of earthquake.Ultimately this shall not lead to complete fall of structure so that human life is saved in the worst case [4, 6, and 7], however tolerable destruction of structural components is acceptable.In tolerable destruction of structural components in case of earthquake, it is be designed for earthquake forces significantly lower than predicted in occurrence of earthquake if structure is expected to be elastic linear [8,10].Actual lateral base shear is lowered to determine the design lateral force by using Response reduction factor, R [11].
Design lateral force for the elastic structure as per Indian seismic code [1][2][3] is determined by dividing by 2R.Reduction factor is the amount of ductility & over-strength of a structure [12,13].For construction of a structure for considerably less force than expected to be at the time of strong shaking, over strength, redundancy and ductility factors shall be considered for prevention of complete collapse of structure.
In the occurrence of earthquake water mass inside container vibrates as two dissimilar modes.Impulsive mass is the amount of water vibrating with the container and convective or sloshing mass is the part of water vibrating relative to tank container.Impulsive as well as convective mass of liquid contributes to hydrodynamic force.Water in elevated tanks are modelled by two approaches [5, 6, and 7] as Single DOF 2-DOF system.In SDOF system, total water weight is taken as impulsive in addition to container and staging mass.Housner in 1963 [5] recommended an equivalent mechanical model for 2-DOF system.It consist of first degree of freedom for impulsive mass along with container & staging mass and second degree of freedom for convective mass.As per model recommended by Housner [5], total hydrodynamic force embraces of convective and impulsive components [14].

Base Shear
Impulsive and convective modes are considered in IS1893 (Part-2) [3].Combined lateral shear for water tanks shall be calcualted with consideration of impulsive and convective mode lateral base shear using square root of sum of squares rule and is give as: V= √(Vi 2 + Vc 2 )…………………………………………….....Eq.1 Just above the staging base, shear in impulsive mode, is given as: Design seismic coefficient in horizontal direction, Ah is individually calculated in impulsive (Ah) i &S convective (Ah) c modes.

Results
The values of maximum shear as well as moment are found out in full tank,half-filled and empty condition for different zone factors, soil conditions, tank full, half-filled and empty condition.Graphical reprentation of results from Table 1, 2 and 3 is given as below.
… … … … … … … … … … ..…… ..Eq.5 equation, S a /g = response acceleration coefficient; Z = zone of seismic factor; W = Weight of container plus (1/3) rd staging weight; I = Factor of Importance (1.5); R = Response factor.'R' values ranges from 2 to 4 for water tank.t As per Indian code [3], the base moment 'M' for tank, shall be considered as combining the impulsive mode moment (M i ) and convective mode base moment (M c ) using SRSS and is given as follows M*= M i * 2 + M c * 2 ……………………………………..Eq.6 Impulsive moment at base, is calculated as: M i * = (Ah) i x [m i x (h i * + h s ) + m s x h cg ] x g......................Eq.7 and convective mode base moment in is calculated as: M c * = (Ah) c x m c x (h c * + h s ) x g ……………………..Eq.8Where h i * = impulsive mass height above tank wall bottom h c * = convective mass height above tank wall bottom h s = staging elevation; h cg = C.G. of empty container of above footing = M i * 2 + M c * 2 … ([Z/2][I/R])/[S a /g] 3. Methodology In the present study of RC circular water tank in accordance with Indian standard is analyzed for seismic loads.The analysis of tank is carried out for zones II to V with Rocky or Hard Soil, Medium Stiff Soil and Soft Soil conditions as per Indian standard.Further three different depth of water with constant diameter ratios with tank full condition, tank half-filled condition and tank empty condition are considered.Seismic analysis of water tank is performed using following parameters.Circular Water container capacity = 200Cu.m,Height of container, H =5m, Free board =0.3m,Depth of water, h = 4.7m (Tank full), 2.5m (Tank Half full), 0 (Tank empty) Diameter of container, D = 7.5m (Constant in all cases), Seismic zone = Zone II to V, Factor of Importance, I =1.5, Response factor, R =4, Soil Site condition = Rocky or Hard, Medium stiff & Soft soil For detailed geometry of circular water tank refer Figure 1.

Figure 2 : 6 Figure 3 :
Figure 2: Variation of Ahi in various seismic zones and soil

Figure 4 : 7 Figure 5 :
Figure 4: Variation of Maximum Shear at base in various seismic zones and soil .1, 2 ,3 and Figure 2 to 5. From these results, following conclusions can be drawn.• Values of horizontal seismic coefficient in impulsive mode (Ahi) are lesser than those for convective mode (Ahc), for tank full condition.This is due to lower values of time period in impulsive mode.• Values of horizontal seismic coefficient in impulsive mode (Ahi) increases in tank half filled condition and tank empty condition as compared with tank full condition.• Values of horizontal seismic coefficient in impulsive mode (Ahi) are more than the values for convective mode (Ahc), for tank half-filled condition.This is due to lower values of impulsive mass of liquid.[For tank half-filled condition, mass of water is less than that of tank full condition].• For the same soil condition, values of horizontal seismic coefficient in impulsive mode (Ahi) and convective mode (Ahc) increases as zone factor increases [higher seismic zone] • As soil conditions, changes from Rocky hard to medium stiff and soft soil, horizontal seismic coefficient value in impulsive mode (Ahi) and convective mode (Ahc) increases for higher zones.• Maximum shear & moment is higher at full tank with that for tank half-filled and tank empty condition.• Maximum shear & moment increases with higher seismic zone.• Maximum shear & moment values are governing in rocky hard soil condition as compared with medium stiff and soft soil.

Table 1 ,
2 and 3 presented in summary of various calculated parameters.