Performancebased assessment of response reduction factor of RCelevated water tank considering soil flexibility: a case study
 1k Downloads
Abstract
The seismic design codes/standards of most countries include the nonlinear response of a structure implicitly through a response reduction/modification factor (R). It is the factor by which the actual base shear should be reduced to find the design base shear during design basic earthquake considering nonlinear behavior and deformation limits of structures. In the present study, attempts are made to determine the ‘R’ factors of four existing RC staging elevated water tanks, which are designed as per draft Indian standards for seismic design of liquid and RC designs and having a ductile detailing considering the effects of soil flexibility. The elevated RC water tanks are analyzed using displacement controlled nonlinear static pushover analysis to evaluate the base shear capacity and ductility of tank considering soil flexibility. The ‘R’ factor is obtained for four realistic designs of elevated RC water tanks having different capacities at two performance levels. The evaluated values of ‘R’ factor are compared with the values suggested in the design code. The results of the study show that the flexibility of supporting soil has considerable effect on response reduction factor, period and overall performance of water tank, indicating that idealization of fixity at base may be seriously mistaken for soft soils. All the studied water tanks were designed with higher safety margin than that of specified in Indian Standards.
Keywords
Response reduction factor Soil flexibility Ductility factor Strength factor Pushover analysisIntroduction
Different aspects of the response reduction factor of various structural systems have been investigated and essential weaknesses have been pointed out by many researcher. Mondal et al. (2013) estimated the real values of response reduction factor of actual RC moment frame structure designed and detailed using the Indian codes for earthquake and RC designs and for ductile detailing. Authors concluded that codes recommend higher than real value of ‘R’ for RC frame. Tamboli and Amin (2015) evaluated the ‘R’ factor of RC frame strengthened using the different types of bracing systems and concluded that type and arrangement of bracing systems have significant impact on the ‘R’ factor. Masoudi et al. (2012) discuss the seismic behavior and failure mechanism of RC frame and shaftsupported tanks under severe earthquakes considering the P–∆ effects by performing linear and nonlinear response history analyses. Ghateh et al. (2015) presented a methodical approach to determine the response modification factors for total 48 elevated tanks of different capacities and RC frame dimensions commonly used in industry. They have suggested not to use the same response reduction factor for tanks having a different staging height and capacity. Patel et al. (2014) evaluated componentwise response reduction factor of elevated water tanks having equal staging height and different capacities. They concluded that the value of response reduction factor for RC staging tank is significantly influenced by time period, capacity of tank, and seismic zone. The possible serious effects of neglecting soil flexibility and their effects on structural safety have been evaluated by many researchers (Dutta et al. 2004; Halabian and Erfani 2013; Livaoglu and Dogangun 2007). Dutta et al. (2004) studied the effect of soil flexibility on the dynamic characteristics of RC frame staging tanks having different configurations and concluded that analysis without considering soil flexibility may lead to lower or higher estimation of seismic base shear of RC frame staging tanks considering fluid–structure interaction. Halabian and Erfani (2013) evaluated the effect of foundation flexibility and structural strength on response reduction factor of RC frame buildings.
The aim of the present study is componentwise evaluation of response reduction factor of the four existing realistic RC water tanks considering the effects of soil flexibility and comparing these values with the values given in the seismic design code. All tanks are located in different parts of Gujarat, India and were designed and detailed as per the Indian codal provisions IS: 4562000 (BIS IS 456 2000), IITKGSDM guidelines/Draft IS 1893 (PartII) and IS: 139201993 (BIS IS 13920 1993) by different design engineers.
Concept of ‘R’ factor
Strength factor (R _{s})
Ductility factor (R _{µ})
Redundancy factor (R _{R})
Yielding at one location in the structure does not indicate yielding of the whole structure. Hence, the load distribution, due to redundancy of the structure, provides additional safety margin. RC structure with multiple lateral loadresisting frames is normally considered as redundant structure, because each of the seismic frames is designed and detailed to transfer the seismic forces to the soil. Following the conservative assumption, R_{R} = 1.0 is used in this study.
Damping factor (R _{ζ})
The damping factor (R_{ζ}) takes into accounts the effect of ‘added’ viscous damping for a structures having supplementary energy dissipating devices. Without any such devices, the damping factor is generally taken as one.
Description of the existing water tank considered in this study
Detailed descriptions of RC tanks and members
Capacity (m^{3})  140  480 

Earthquake zone  ZoneIII  ZoneIII 
Type of soil  Medium soil  Medium soil 
Diameter of staging (m)  6  9 
Height of staging (m)  18  18 
Tie beam levels  Plinth + 4.5 m c/c  Plinth + 4.5 m c/c 
No. of columns  6  8 
Top dome (mm)  100  100 
Top ring beam (mm)  170 × 300  350 × 300 
Cylindrical wall (mm)  170  170 
Bottom ring beam (mm)  300 × 300  400 × 300 
Lower circular ring beam (mm)  400 × 800  500 × 1000 
Bottom dome (mm)  170  175 
Conical dome (mm)  170  200 
Braces (mm)  300 × 530  300 × 600 
Columns (mm)  500  600 
Reinforcement in tie beam and plinth beam  4–16 #  6–16 # 
Reinforcement in columns  12–16 #  12–16 # 
Reinforcement in lower circular beam  6–20 + 2–16#  3–25 + 2–20 # 
Detailed descriptions of RC tanks and members
Capacity(m^{3})  1000  2200 

Zone  ZoneV  ZoneIII 
Soil type  Hard soil  Medium soil 
Height of staging (m)  20  23 
Diameter of staging (m)  16.25  22.75 
Height of container (m)  5  7 
Wall thickness (mm)  230  250 
Top slab thickness (mm)  170  175 
Bottom slab thickness (mm)  230  250 
Height of staging (m)  15  18.4 
Tie beam levels (m)  Plinth + 5 m c/c  Plinth + 4.6 m 
Column size (mm)  650  600 
Reinforcement in column (Nodia)  16–20 mm  8–20 mm 
Plinth beam (mm × mm)  400 × 600  300 × 500 
Tie of beam (mm × mm)  400 × 600  300 × 500 
Bottom slab beam (mm × mm)  350 × 1200  350 × 950 
No. of column  12  24 
Length of column (m)  5  4.6 
Reinforcement in columns (Nodia)  16–20#  8–20# 
Ground beam 1,2  2–16# + 4–20#(top) 6–16#(bottom)  2–16# + 3–20#(top) 4–16#(bottom) 
Ground beam 3,4  4–16# + 4–20#(top),4–16# + 2–20#(bottom)  2–16# + 3–20#(top),4–16#(bottom) 
Ground beam 5,6  –  2–16# + 5–20#(top),4–20#(bottom) 
Tie beam 1,2  4–16# + 3–20#(top)4–16# + 2–20#(bottom)  2–16# + 4–20#(top)4–16#(bottom) 
Tie beam 3,4  4–16# + 4–20#(top),4–16# + 3–20#(bottom)  2–16# + 5–20#(top),4–16#(bottom) 
Tie beam 5,6  –  5–20#(top),4–20#(bottom) 
Lower ring beam B1,B2  4–20# + 6–25#(top),5–25# + 3–12#(bottom)  2–20# + 2–16#(top),5–16# + 3–10#(bottom) 
Lower ring beam B3,B4,B5  4–20# + 8–25# + (top),1025#  4–20# + 5–25# (top),6–20# 
Lower ring beam B6,B7,B8  2–16# + 6+20# + (top),6–20#  3–20# + (top),7–20# 
Lower ring beam B9,B10,B11  4–16# + 5–20#(top),8–20#(bottom)  2–20#(top),4–20#(bottom) 
Lower ring beam B12,B13,B14  –  4–20# + 3–25#(top),5–20#(bottom) 
Modeling of soil flexibility
Equivalent spring stiffness for raft foundation
Mode  Vertical  Horizontal  Rocking  Torsion 

Stiffness  \(\frac{{4{\text{G}}R}}{1  \mu }\)  \(\frac{{8{\text{G}}R}}{2  \mu }\)  \(\frac{{8{\text{G}}R^{3} }}{3(1  \mu )}\)  \(\frac{{16{\text{G}}R^{3} }}{3}\) 
Mass ratio  \(\frac{m(1  \mu ) }{{4\rho R^{3} }}\)  \(\frac{m(2  \mu ) }{{8\rho R^{3} }}\)  \(\frac{{3I_{x} (2  \mu ) }}{{8\rho R ^{3} }}\)  \(\frac{{I_{z} }}{{\rho R ^{5} }}\) 
Damping ratio  \(\frac{0.425}{{\bar{m}^{0.5} }}\)  \(\frac{0.29}{{\bar{m}^{0.5} }}\)  \(\frac{0.15}{{(1 + \bar{m})\bar{m}^{0.5} }}\)  \(\frac{0.50}{{(1 + 2\bar{m})}}\) 
Elastic soil properties and spring stiffness considered in water tank
Type of soil  Degrees of freedom  Spring constant 140 m^{3}  Spring constant 480 m^{3}  Spring constant 1000 m^{3}  Spring constant 2200 m^{3} 

(kN/m/m^{2})  (kN/m/m^{2})  (kN/m/m^{2})  (kN/m/m^{2})  
Hard  Horizontal  42096.2  37678.88  15852.45  12533.36 
Vertical  63144.3  56518.32  23778.69  18800.04  
Rocking  604674.18  677375.95  1613908  2043851  
Torsion  604674.18  677375.95  1613908  2043851  
Medium  Horizontal  24177.77  21640.7  9104.78  7198.47 
Vertical  36266.66  32461.05  13657.18  10797.72  
Rocking  347291.9  389047.91  926941.1  1173877  
Torsion  347291.9  389047.91  926941.1  1173877  
Soft  Horizontal  5766.29  5161.21  2171.45  1716.807 
Vertical  8649.68  7741.82  3257.18  2575.211  
Rocking  83827.6  92786.29  221071.6  279964.7  
Torsion  83827.6  92786.29  221071.6  279964.7 
Pushover analysis of finite element model of study water tanks
Seismic performance levels (based on Table C13, FEMA 356)
Immediate occupancy (IO)  Life safety (LS)  Collapse prevention (CP)  

Overall  Light  Moderate  Severe 
Damage  Extensive cracking and hinge formation in ductile elements. Limited cracking and/or splice failure in some nonductile columns. Severe damage in short columns.  Extensive damage to beams. Spalling of cover and shear cracking (< 1/8″width) for ductile columns. Minor spalling in nonductile columns. Joint cracks < 1/8″ wide.  Minor hairline cracking. Limited yielding possible at a few locations. No crushing (strains below 0.003). 
Lateral drift limit  1% transient; negligible permanent  1% transient; 2% permanent  1% transient; 4% permanent 
Plastic rotation limits for RC beams as per FEMA 356
\(\frac{p  p'}{{p_{bal} }}\)  Trans reinf  \(\frac{v}{{b_{w} d\surd f_{c} }}\)  Acceptance criteria  

IO  LS  CP  
≤ 0.0  C  ≤ 3  0.010  0.02  0.025 
≤ 0.0  C  ≤ 6  0.005  0.01  0.02 
Plastic rotation limits for RC columns as per FEMA 356
\(\frac{p  p'}{{p_{\text{bal}} }}\)  Trans reinf  \(\frac{v}{{b_{w} d\surd f_{c} }}\)  Acceptance criteria  

IO  LS  CP  
≤ 0.1  C  ≤ 3  0.005  0.015  0.020 
≤ 0.1  C  ≥ 6  0.005  0.012  0.016 
≥ 0.4  C  ≤ 3  0.003  0.012  0.015 
≥ 0.4  C  ≥ 6  0.003  0.010  0.012 
Deformation limits for different performance level
Performance level  

Immediate occupancy  Damage control  Life safety  Structural stability  
Maximum drift ratio  0.01  0.01–0.02  0.02  0.33V_{i}/P_{i} 
The performance limit PL1 is defined at the member/local level in terms of the maximum plastic rotation at the ends of RC frame member. This limit state is monitored continuously at each step of the pushover analysis, and the performance point PL1 is noted when the plastic rotation of any beam or column member reaches to limit states defined as given in Tables 7 and 8, respectively. The second performance limit state PL2 is defined at the global/structural level as the point on the pushover curve corresponding to the maximum base shear or point corresponding to the maximum drift ratio of 0.02, whichever attained earlier. For all considered water tanks, the maximum base shear capacity of structures on pushover curve reached earlier than the maximum drift ratio of 0.02 during NSPA. Therefore, the performance limit state PL2 is considered corresponding to the maximum base shear on pushover/capacity curves in this study. The results of pushover analysis show that the beams of RC frame staging enter into inelastic range before the columns. Generally, design of staging using IS 13920, i.e., capacity design concept leads to strong column weak beam design. The behavior of frame staging elevated water tank supporting a large convective and impulsive mass at the top is completely different than SMRF typically used in building, because in building the mass of the structure is distributed at different story levels.
Computation of ‘R’ factor for the study water tanks
Componentwise evaluation of ‘R’ based on PL1 for 140 m^{3} tank (ZoneIII)
Type of soil  T_{i (sec)} (impulsive)  V _{0} (kN)  V _{d} (kN)  R_{s} = V_{0}/V_{d}  Δ_{m} ^{(mm)}  Δ_{y} ^{(mm)}  µ = Δ_{m}/Δ_{y}  R _{ μ}  R _{R}  R 

Fixed  1.22  340  70  4.85  211  92  2.29  2.67  1  12.94 
Hard  1.31  336  66  5.09  211  103  2.05  2.34  1  11.93 
Medium  1.36  336  84  4.01  209  107  1.97  2.23  1  8.92 
Soft  1.64  335  85  3.94  211  110  1.91  2.29  1  9.02 
Componentwise evaluation of ‘R’ based on PL1 for 480 m^{3} tank (ZoneIII)
Type of soil  T_{i (sec)} (impulsive)  V _{0} (kN)  V _{d} (kN)  R_{s} = V_{0}/V_{d}  Δ_{m} ^{(mm)}  Δ_{y} ^{(mm)}  µ = Δ_{m}/Δ_{y}  Rμ  R _{R}  R 

Fixed  1.22  663  175  3.78  189  83  2.27  2.61  1  9.86 
Hard  1.24  659  173  3.80  190  86  2.20  2.53  1  9.61 
Medium  1.25  657  230  2.85  186  92  2.02  2.34  1  6.66 
Soft  1.28  653  273  2.39  186  94  1.97  2.35  1  5.61 
Componentwise evaluation of ‘R’ based on PL1 for 1000 m^{3} tank (ZoneV)
Type of soil  T_{i (sec)} (impulsive)  V _{0} (kN)  V _{d} (kN)  R_{s} = V_{0}/V_{d}  Δ_{m} ^{(mm)}  Δ_{y} ^{(mm)}  µ = Δ_{m}/Δ_{y}  R _{ μ}  R _{R}  R 

Fixed  1.21  2000  987  2.02  176  83  2.12  2.42  1  4.88 
Hard  1.25  1996  954  2.09  179  87  2.05  2.35  1  4.91 
Medium  1.29  1996  1232  1.62  180  90  2.00  2.29  1  3.70 
Soft  1.35  1988  1446  1.37  194  102  1.90  2.27  1  3.10 
Componentwise evaluation of ‘R’ based on PL1 for 2200 m^{3} tank (ZoneIII)
Type of soil  T_{i (sec)} (impulsive)  V _{0} (kN)  V _{d} (kN)  R_{s} = V_{0}/V_{d}  Δ_{m} ^{(mm)}  Δ_{y} ^{(mm)}  µ = Δ_{m}/Δ_{y}  R _{ μ}  R _{R}  R 

Fixed  1.55  2505  659  2.79  218  110  1.81  2.05  1  7.79 
Hard  1.57  2505  650  3.85  224  120  1.70  1.91  1  7.35 
Medium  1.61  2500  835  2.99  235  124  1.70  1.82  1  5.44 
Soft  1.70  2485  966  2.57  258  148  1.50  1.75  1  4.49 
The ‘R’ values corresponding to PL1 for the tanks resting on medium soil range from 3.17 to 8.92 for the four tanks considered, and are all higher than the IITKGSDM guidelines/Draft IS 1893 (Part2) specified value of R (= 2.5) for ductile/special moment resistance RC frame staging water tanks. The ‘R’ values corresponding to PL1 for 140, 480 and 2200 m^{3} water tanks supported on different soil types range from 4.49 to 11.93, and are all higher than the IS 1893 (Part2) 2014 specified value of R (= 4) for ductile/special moment resistance RC frame staging water tanks. It is worth to mention that all the studied water tanks are constructed before the year 2014, and therefore, in this study it is assumed that it was designed using IITKGSDMA guidelines/Draft IS 1893 (Part2). This indicates that all the study water tanks were designed with higher safety margin than that of specified in Indian standards. It is worth to mention that the strength factor in a water tanks depends on various factors, such as the safety margins specified in the code, partial safety factors for loads and material strength. Furthermore, in same design code, strength factor becomes subjective to the individual designer’s selection of crosssectional dimension depending on the demand, because the section and the percentage of reinforcement provided for a member are never exactly as per the demand requirements. For example, the same section will be provided for all the columns, although the design requirement usually varies for these. Additionally, the reinforcements provided are typically slightly more than the required due to the availability of discrete rebar sizes at site. This conservative decision imparted through a designer’s choice adds to R_{s}.
The pushover curves reflect that for all tanks, PL2 is reached after PL1 (i.e., at a larger displacement). According to pushover curves and their bilinearisation, maximum shear is almost the same as that of PL1. Since design shear do not change, reserve strength factor is also the same as in PL1. There is no change in yield displacement values for PL2 as compared to PL1. Ultimate displacement values for PL2 are larger as compared to PL1 values, and therefore, the ductility values are higher for PL2 as compared to PL1. Among the various components of ‘R’ presented in Tables 14, 15, 16 and 17, reserve strength factor R_{s} remains the same as in PL1, while ductility factor R_{µ} comes out to be higher, which finally results in higher ‘R’ factors overall. For PL2, ‘R’ ranges from 3.30 to 13.53 for all studied water tanks. Based on PL2, the IS 1893(Part2): 2002 recommendation is on the conservative side. It should, however, be noted that this limit does not consider any member level behavior such as maximum plastic rotation at the ends. However, The actual value of ‘R’ of study water tanks needed to be even lower than what is evaluated in this study, because of many reasons, such as irregularity in dimensions leading to torsional effects, poor quality control and construction practice, not following ductile detailing requirements exactly as per the standards, and deterioration in concrete with time. If soil flexibility is not taken into account in estimating ‘R’ factor of elevated water tank properly, the accuracy in evaluating seismic base shear and assessing the structural safety for a structure subjected to earthquakes could not be reliable.
The effect of soil flexibility considerably increases the impulsive time period of the elevated water tank, indicating that modification in soil stiffness could have considerable effect on the fundamental period of vibration. It is observed that flexibility of supporting soil has considerable effect on base shear, ductility factor and response reduction factor of water tank. Considering soil flexibility, particularly when the tank supported on relatively soft soil is crucial. The increase in the flexibility of the soil reduces the overstrength factor as well as ductility factor of study water tanks. The consideration of soil flexibility in analysis reduces the values of ‘R’ factor of study water tanks as compared to fixed base condition. The overstrength factor as well as ductility factor reduce with increase in the size of the study water tank. Consideration of flexibility of soft and medium soil in analysis reduces the values of ‘R’ factor as much as 25 and 40% for the considered tanks, respectively, as compared to fixed base condition. The effect of the soil flexibility is the least in case of hard soil.
Component of ‘R’ for 140 m^{3} based on PL1 and PL2 for seismic zoneIII and IV
140 m^{3} capacity (zoneIII)  140 m^{3} capacity (zoneIV)  

Type of soil  R _{s}  R _{R}  PL1  PL2  R _{s}  R _{r}  PL1  PL2  
R _{ µ}  R  R _{ µ}  R  R _{ µ}  R  R _{ µ}  R  
Fixed  4.85  1  2.67  12.94  2.79  13.53  3.26  1  2.67  8.70  2.79  9.09 
Hard  5.1  1  2.34  11.93  2.58  13.15  3.42  1  2.34  8.0  2.58  8.82 
Medium  4.01  1  2.23  8.92  2.55  10.19  2.68  1  2.23  5.97  2.55  6.83 
Soft  3.94  1  2.29  9.02  2.53  9.96  2.63  1  2.29  6.02  2.53  6.65 
Component of ‘R’ for 480 m^{3} based on PL1 and PL2 for seismic zoneIII and IV
480 m^{3} capacity (zoneIII)  480 m^{3} capacity (zoneIV)  

Type of soil  R _{s}  i_{R}  PL1  PL2  R _{s}  R _{R}  PL1  PL2  
R _{ µ}  R  R _{ µ}  R  R _{ µ}  R  R _{ µ}  R  
Fixed  3.78  1  2.61  9.86  2.96  11.18  2.52  1  2.61  6.57  2.96  7.45 
Hard  3.8  1  2.53  9.61  2.76  10.48  2.53  1  2.53  6.41  2.76  6.98 
Medium  2.85  1  2.34  6.66  2.50  7.12  1.90  1  2.34  4.46  2.50  4.75 
Soft  2.39  1  2.35  5.61  2.46  5.87  1.59  1  2.35  3.75  2.46  3.91 
Component of ‘R’ for 2200 m^{3} based on PL1 and PL2 for seismic zoneIII and IV
2200 m^{3} capacity (zoneIII)  2200 m^{3} capacity (zone IV)  

Type of soil  R _{s}  R _{R}  PL1  PL2  R_{s}  R_{R}  PL1  PL2  
R _{ µ}  R  R _{ µ}  R  R _{ µ}  R  R _{ µ}  R  
Fixed  3.79  1  2.05  7.79  2.27  8.60  2.54  1  2.05  5.20  2.27  5.76 
Hard  3.85  1  1.91  7.35  2.11  8.12  2.57  1  1.91  4.92  2.11  5.42 
Medium  2.99  1  1.82  5.44  2.04  6.11  1.99  1  1.82  3.64  2.04  4.05 
Soft  2.57  1  1.75  4.49  2.09  5.37  1.71  1  1.75  3.00  2.09  3.57 
Component of ‘R’ for 1000 m^{3} based on PL1 and PL2 for seismic zoneV
1000 m^{3} capacity (zoneV)  

Type of soil  R _{s}  R _{R}  PL1  PL2  
R _{ µ}  R  R _{ µ}  R  
Fixed  2.02  1  2.42  4.88  2.62  5.30 
Hard  2.09  1  2.35  4.91  2.50  5.230 
Medium  1.62  1  2.29  3.70  2.50  4.07 
Soft  1.37  1  2.27  3.1  2.40  3.30 
Conclusions
In this study, the ‘R’ factors of four existing RCelevated water tanks designed using IS 456, Draft IS 1893 *PartII) and detailed as per IS 13920 are evaluated considering soil flexibility. The focus has been given in methodical assessment of the R factor, consideration of soil flexibility; realistic performancebased limit states at both structure and member levels. The schematic procedure for evaluating the realistic values of response reduction factor of RC staging elevated water tank incorporating the effect of soil flexibility, is also presented. The use of realistic values of response reduction factor may prove useful for safe and economic seismic design of elevated water tank. The significant observations of the present study are summarized as follows:

The R values corresponding to PL1 for the tanks resting on medium soil range from 3.17 to 8.92 for the four tanks considered, and all are higher compared to the IITKGSDM guidelines/Draft IS 1893 (PartII) suggested value of R (= 2.5) for ductile/special moment resistance RC frame staging water tanks. This indicates that all the studied water tanks were designed with higher safety margin.

Based on PL2, R factor ranges from 3.30 to 13.53, indicating the IITKGSDM guidelines recommendation is on the conservative side.

As the soil spring stiffness decrease from hard to soft soil, the impulsive time period of elevated water tank model increases and response reduction factor decreases. This means that the impulsive time period and response reduction factor is also a function of soil flexibility.

The overstrength factor as well as ductility factor reduce with the increase of the size of the studied water tanks.

The flexibility of supporting soil has considerable effect on displacement ductility and response reduction factor of water tanks. Consideration of flexibility of medium and soft soil in analysis reduces the values of ‘R’ factor as much as 25 and 40% for the considered tanks, respectively, as compared to fixed base condition. The effect of the soil flexibility is the least in case of hard soil. The analysis of water tank with fixed base assumption may lead to underestimation or overestimation of seismic base shear of elevated tanks with any staging configurations.

Consideration of flexibility of medium and soft soil during analysis increases yield and ultimate displacement response demands compared to that of fixed base model Consideration of flexibility of medium and soft soil during analysis reduces the displacement ductility ratio (µ) of water tank models as much as 12% and 16% for the considered tanks, respectively, as compared to fixed base condition.

The actual value of ‘R’ of study water tanks needed to be even smaller than what is evaluated in this study, because of various reasons, such as poor quality control and workmanship during the construction, irregularity in dimensions leading to torsional effects, and not following the ductile detailing requirements exactly as per the standards which would lead to deterioration in concrete with time.
Notes
Acknowledgements
The authors acknowledge the financial support from a project sanctioned by Gujarat Council on Science and Technology, Government of Gujarat, Gujarat, India (Order No. GUJCOST/MRP/1516/1905) for successful completion of this work.
References
 ACI 350.3 (2001) Seismic design of liquid containing concrete structures. American Concrete Institute Standard, Farmington HillsGoogle Scholar
 ATC 19 (1995) Structural response modification factors. Applied Technology Council, Redwood City, USAGoogle Scholar
 ATC40 (1996) Seismic evaluation and retrofit of concrete building, vol 1. Seismic Safety Commission, Redwood City, USAGoogle Scholar
 AWWA D110 (1995) Wire and strandwound circular, prestressed concrete water tanks. American Water Works Association, Colorado, USAGoogle Scholar
 BIS IS 13920 (1993) Ductile detailing of reinforced concrete structure subjected to seismic forcescode of practise. Bureau of Indian Standards, New Delhi, IndiaGoogle Scholar
 BIS IS 1893 (2014) Criteria for earthquake resistant design of structures, Part 2. Bureau of Indian Standards, New Delhi, IndiaGoogle Scholar
 BIS IS 456 (2000) Plain and reinforced concretecode of practice. Bureau of Indian Standards, New Delhi, IndiaGoogle Scholar
 Draft IS 1893 (2006) Criteria for earthquake resistant design of strucutres, Part 2. Liquid retaining tanks. Bureau of Indian Standards, New Delhi, India (Doc No. CED 39 (7231)) Google Scholar
 Dutta SC, Jain SK, Murty CVR (2000) Assessing the seismic torsional vulnerability of elevated tanks with RC frametype staging. Soil Dyn Earthq Eng 19:183–197CrossRefGoogle Scholar
 Dutta S, Mandal A, Dutta SC (2004) Soilstructure interaction in dynamic behavior of elevated tanks with alternate frame staging configurations. J Sound Vib 277:825–853CrossRefGoogle Scholar
 FEMA 356 (2000) Prestandard and commentary for the seismic rehabilitation of buildings. Federal Emergency Management Agency, Washington D.C., USAGoogle Scholar
 FEMA 368 (2000) NEHRP recommended provisions for seismic regulations for new buildings and other structures  part 1: provisions. Building Seismic Safety Council, Washington D.C., USAGoogle Scholar
 Ghateh R, Kianoush MR, Pogorzelski W (2015) Seismic response factor of RC pedestal in elevated water tanks. Eng Struct 87:32–46CrossRefGoogle Scholar
 Ghazetas G (1983) Analysis of machine foundation vibrations: state of art. Soil Dyn Earthq Eng 2(1):2–42Google Scholar
 Halabian AM, Erfani M (2013) The effect of foundation flexibility and structural strength on response reduction factor of RC frame structures. Struct Des Tall Spec Build 22:1–28CrossRefGoogle Scholar
 IBC (2000) International Building Code 2000. International Code Council, Falls ChurchGoogle Scholar
 IITKGSDM guidelines for Seismic design of liquid storage tanks (2007), NICEE, Indian Institute of Technology, Kanpur, IndiaGoogle Scholar
 IS 1893 (2002) Indian standard criteria for earthquake resistant design of structures, Part1, Bureau of Indian Standards, New Delhi, IndiaGoogle Scholar
 Krawinkler H, Nassar A (1992) Nonlinear seismic analysis of reinforced concrete buildings. Seismic design based on ductility and cumulative damage demands and capacities. CRC Press, New York, pp 27–47Google Scholar
 Livaoglu R, Dogangun A (2007) Effect of foundation embedment on seismic behavior of elevated tanks considering fluid–structuresoil interaction”. Soil Dyn Earthq Eng 27:855–863CrossRefGoogle Scholar
 Miranda E, Bertero V (1994) Evaluation of strength reduction factors for earthquake resistantdesign. Earthq Spectra 10:357–379CrossRefGoogle Scholar
 Mondal A, Ghosh S, Reddy GR (2013) Performance based evaluation of the response reduction factor for ductile RC frames. Eng Struct 56:1808–1819CrossRefGoogle Scholar
 Mostafa M, Sassan E, Mohsen G (2012) Evaluation of response modification factor (R) of elevated concrete tanks. Eng Struct 39:199–209CrossRefGoogle Scholar
 Newmark N, Hall W (1982) Earthquake spectra and design. Engineering monograph. Earthquake Engineering Research Institute, BerkeleyGoogle Scholar
 Patel T, Amin JA, Patel B (2014) Evaluation of response reduction factor of RC framed staging elevated water tank using static pushover analysis. Int J Civil Struct Eng 4(3):215–226Google Scholar
 Rai DC (2003) Performance of elevated tanks in Mw 7.7 Bhuj earthquake of January 26th, 2001. Proc Indian Acad Sci Earth Planet Sci 112:421–429Google Scholar
 Riddell R, Newmark N (1979) Statistical analysis of the response of nonlinear systems subjected to earthquakes, vol 468. Structural research series. Dept. of Civil Engineering, University of Illinois, UrbanaGoogle Scholar
 Structural Analysis software (2000) Advance, static and dynamic finite element analysis of structures, SAP 2000. Computer and Structures, Inc, BerkeleyGoogle Scholar
 Tamboli K, Amin JA (2015) Evaluation of response reduction factor of RC braced frame. J Mater Eng Struct 2:120–129Google Scholar
Copyright information
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.