## Final Report Summary - LIFTING TANKS (Seismic Analysis of Liquid-Storage Tanks with a Focus on Tank-Base Uplift)

Seismic Analysis of Liquid-Storage Tanks with a Focus on Tank-Base Uplift

At grade liquid storage tanks depending on their base fixity fall into two categories: (1) anchored and (2) unanchored tanks. A fixed base tank requires a substantial foundation and attachment mechanism in the form of bolts to carry the considerable overturning moment that occurs due to seismic loads. Therefore, because of the cost, liquid-storage tanks are often not fixed to their foundation even in seismic areas.The seismic response of unanchored tanks during earthquakes is highly nonlinear and much more complex than that implied in the design standards. Especially tank-base uplift provisions proposed by the current codes such as API 650 and Eurocode 8 are based on a mechanical spring-mass analogy, but this aproach has very little technical verification for unanchored tanks. The tank base plate uplift is a function of tank size, tank aspect ratio (liquid height to tank diameter ratio), tank foundation, local seismicity, and tank site classification. However, none of the current tank codes reflects the effects of all these parameters in calculation of tank-base uplift. There is a large number of both experimental and theoretical studies on seismic behavior of anchored liquid-storage tanks. However, the studies on seismic performance of unanchored tanks and effect of tank base uplift on the tank seismic performance are limited. In addition, most of the theoretical and computational studies on unanchored tanks do not include the effect of sloshing water breaking and the effect of tank base uplift on hydrodynamic loads during seismic loading.The objective of this study is to determine seismic performance of unanchored above ground liquid-storage tanks using 3D advanced finite element techniques, verify applicability of code mechanical spring-mass analogy, and to develop code adoptable simple models/tools for predicting tank base uplift and its effects on seismic performance of unanchored tanks.

Seismic performance of three unanchored liquid-storage tanks with tank diameter ranging from 24.4 m to 55.0 m and liquid height between 12.2 m to 21 m were investigated using three different analyses approaches. These are: (1) Coupled Eulerian Lagrangian (CEL), (2) mechanical spring-mass analogy in 3D, and (3) a simple single degree of freedom (SDOF) spring-stick model in 2D. The CEL method is computationally costly but has very high accuracy. The developed SDOF method is much simple and computationally very cheap, but it is an approximate approach. The seismic performance of the tanks was computed using five strong ground motion records. The computed tank base uplift versus time histories were monitored and compared to evaluate adequacy of these analyses methods to predict tank base uplift. In CEL modelling, the water and its interaction with tank walls was explicitly modeled. The CEL modeling approach includes the effects of higher modes of vibration for the tank and sloshing liquid including its breaking during seismic loading. During seismic loading, a part of the liquid in the tank moves in long-period sloshing motion, while the rest of the liquid moves rigidly with the tank wall during earthquake loading. The liquid that is moving in long-period sloshing motion is called convective liquid while the part of liquid moving rigidly with the tank is called impulsive liquid. In the mechanical model, the water is not modeled explicitly rather its impulsive and convective components are modeled separately as mass and spring systems. The modern seismic design provisions for liquid-storage tanks is based on this mechanical model. However, this modelling approach neglects the higher vibration modes for the sloshing water. Finally, a simple SDOF spring-stick model is developed for predicting tank base uplift. The model is very simple and has only one-degree of freedom.

There are some significant differences between the analyses approached employed. Both mechanical and SDOF models do not include the interaction of liquid-structure fully. For example, both models neglect the hoop stresses developed in the tank shell, and therefore the model cannot predict tank shell buckling or stability issues. In addition, the effects of higher modes of sloshing water are neglected. However, CEL modeling fully covers the liquid-structure interaction including hoop stresses, and the it can predict tank shell buckling. Tank shell buckling can be an issue especially for unanchored tanks. Another significant difference between these three modelling approaches is the computational costs and complexity of developing the analysis model. Developing CEL models is rather complex and require extensive experience and knowledge of both finite element modelling and structural engineering. In addition, to be able to run the model effectively super computers or powerful workstations are needed. The mechanical model can also be complicated, and it can take significant analysis time mainly due to contact interaction between the tank and its foundation. However, the developed SDOF model is very simple and feasible in terms of computational cost.

The results indicate that the traditional mechanical spring analogy model, which is the basis for the current seismic design provisions (e.g. API 650 and Eurocode 8), cannot be used to predict tank base uplift. It has an error between -60% to 254% with an average error of 40%. These results show that the mechanical spring-mass analogy, which is verified and commonly used for the anchored tanks, does not capture the full seismic behavior of unanchored tanks-liquid structure with tank base uplift. It is considered that the high order vibration modes of sloshing water, which are ignored in the mechanical model, become more effective for unanchored tank seismic behavior. In addition, these findings suggest that tank maximum base shear and moment computed using current seismic provisions for tanks may not be on the conservative side for unanchored tanks.

The tank base uplift time-history analyses results computed with the mechanical and SDOF methods were similar in terms of number of cycles and magnitude of the maximum base uplift. The computed error for the SDOF method were between -57% to 83% with an average error of -8% relative to the mechanical approach. Considering the simplicity of SDOF spring-mass model this level of error is considered to be reasonable.

At grade liquid storage tanks depending on their base fixity fall into two categories: (1) anchored and (2) unanchored tanks. A fixed base tank requires a substantial foundation and attachment mechanism in the form of bolts to carry the considerable overturning moment that occurs due to seismic loads. Therefore, because of the cost, liquid-storage tanks are often not fixed to their foundation even in seismic areas.The seismic response of unanchored tanks during earthquakes is highly nonlinear and much more complex than that implied in the design standards. Especially tank-base uplift provisions proposed by the current codes such as API 650 and Eurocode 8 are based on a mechanical spring-mass analogy, but this aproach has very little technical verification for unanchored tanks. The tank base plate uplift is a function of tank size, tank aspect ratio (liquid height to tank diameter ratio), tank foundation, local seismicity, and tank site classification. However, none of the current tank codes reflects the effects of all these parameters in calculation of tank-base uplift. There is a large number of both experimental and theoretical studies on seismic behavior of anchored liquid-storage tanks. However, the studies on seismic performance of unanchored tanks and effect of tank base uplift on the tank seismic performance are limited. In addition, most of the theoretical and computational studies on unanchored tanks do not include the effect of sloshing water breaking and the effect of tank base uplift on hydrodynamic loads during seismic loading.The objective of this study is to determine seismic performance of unanchored above ground liquid-storage tanks using 3D advanced finite element techniques, verify applicability of code mechanical spring-mass analogy, and to develop code adoptable simple models/tools for predicting tank base uplift and its effects on seismic performance of unanchored tanks.

Seismic performance of three unanchored liquid-storage tanks with tank diameter ranging from 24.4 m to 55.0 m and liquid height between 12.2 m to 21 m were investigated using three different analyses approaches. These are: (1) Coupled Eulerian Lagrangian (CEL), (2) mechanical spring-mass analogy in 3D, and (3) a simple single degree of freedom (SDOF) spring-stick model in 2D. The CEL method is computationally costly but has very high accuracy. The developed SDOF method is much simple and computationally very cheap, but it is an approximate approach. The seismic performance of the tanks was computed using five strong ground motion records. The computed tank base uplift versus time histories were monitored and compared to evaluate adequacy of these analyses methods to predict tank base uplift. In CEL modelling, the water and its interaction with tank walls was explicitly modeled. The CEL modeling approach includes the effects of higher modes of vibration for the tank and sloshing liquid including its breaking during seismic loading. During seismic loading, a part of the liquid in the tank moves in long-period sloshing motion, while the rest of the liquid moves rigidly with the tank wall during earthquake loading. The liquid that is moving in long-period sloshing motion is called convective liquid while the part of liquid moving rigidly with the tank is called impulsive liquid. In the mechanical model, the water is not modeled explicitly rather its impulsive and convective components are modeled separately as mass and spring systems. The modern seismic design provisions for liquid-storage tanks is based on this mechanical model. However, this modelling approach neglects the higher vibration modes for the sloshing water. Finally, a simple SDOF spring-stick model is developed for predicting tank base uplift. The model is very simple and has only one-degree of freedom.

There are some significant differences between the analyses approached employed. Both mechanical and SDOF models do not include the interaction of liquid-structure fully. For example, both models neglect the hoop stresses developed in the tank shell, and therefore the model cannot predict tank shell buckling or stability issues. In addition, the effects of higher modes of sloshing water are neglected. However, CEL modeling fully covers the liquid-structure interaction including hoop stresses, and the it can predict tank shell buckling. Tank shell buckling can be an issue especially for unanchored tanks. Another significant difference between these three modelling approaches is the computational costs and complexity of developing the analysis model. Developing CEL models is rather complex and require extensive experience and knowledge of both finite element modelling and structural engineering. In addition, to be able to run the model effectively super computers or powerful workstations are needed. The mechanical model can also be complicated, and it can take significant analysis time mainly due to contact interaction between the tank and its foundation. However, the developed SDOF model is very simple and feasible in terms of computational cost.

The results indicate that the traditional mechanical spring analogy model, which is the basis for the current seismic design provisions (e.g. API 650 and Eurocode 8), cannot be used to predict tank base uplift. It has an error between -60% to 254% with an average error of 40%. These results show that the mechanical spring-mass analogy, which is verified and commonly used for the anchored tanks, does not capture the full seismic behavior of unanchored tanks-liquid structure with tank base uplift. It is considered that the high order vibration modes of sloshing water, which are ignored in the mechanical model, become more effective for unanchored tank seismic behavior. In addition, these findings suggest that tank maximum base shear and moment computed using current seismic provisions for tanks may not be on the conservative side for unanchored tanks.

The tank base uplift time-history analyses results computed with the mechanical and SDOF methods were similar in terms of number of cycles and magnitude of the maximum base uplift. The computed error for the SDOF method were between -57% to 83% with an average error of -8% relative to the mechanical approach. Considering the simplicity of SDOF spring-mass model this level of error is considered to be reasonable.