Numerical investigation of reducing the seismic response of liquid storage tanks due to the use of seismic isolators

Dissertation for Master's degree (M.S)

Chapter One

History of dynamic analysis of liquid storage tanks and regulatory orders in this regard

Abstract

The main goal of this research is to investigate the effect of the presence of seismic isolators on the dynamic performance of liquid storage tanks during an earthquake. In this regard, it is necessary to first know the dynamic behavior of tanks during real earthquakes and to introduce the types of possible seismic damage in liquid storage tanks. These failures are the source of many researches regarding the dynamic analysis of reservoirs, the abstracts of which are reflected in valid regulations in the form of practical instructions. Therefore, in the final part of the chapter, the philosophy used in some valid regulations regarding the way of applying the dynamic effects of the behavior of tanks is reviewed and their regulations are examined and compared regarding the general and important issues in the field of dynamic analysis of tanks. During the application of seismic loads, it indicates that steel tanks are more vulnerable than concrete tanks. The experiences of past earthquakes have made valid regulations to constantly improve their regulations for dynamic analysis of tanks. Although the regulatory provisions regarding the investigation of some phenomena have reached the same understanding, but the philosophy used in different regulations to investigate some other phenomena is different and there is still no uniform summary regarding them. For example, the effect of the roof of the tanks on the redistribution of the design forces, how different factors affect the estimation of the height of the free top of the tanks, or the redistribution of stresses during the lifting of the tank and so on. They are among the cases for which there is still no uniform analytical model. Therefore, the topic of dynamic analysis of liquid storage tanks, although it is a familiar topic with a long history, but due to the multiplicity of phenomena involved in it, it still has many ambiguous aspects, which has caused the dynamics of research in this field. On the other hand, the presence of phenomena such as liquid-structure interaction and structure-soil interaction phenomenon add to the complexity of the dynamic analysis of reservoirs and the variety of failures observed in them. A detailed understanding of the types of failures caused by the application of seismic loads in storage tanks can provide an initial perspective regarding the research fields. In a general summary, the failures resulting in liquid storage tanks during an earthquake can be summarized in the following types. The top of the tank wall

3- Liquid leakage from the tank due to the creation of high cyclic stresses at the joints

4- Lifting of the tank from the foundation (for unrestrained tanks)

5- Buckling of the middle fixed columns that are used to hold the roof

6- Lateral movements of the tank structure (not using flexible joints at the junction of the liquid inlet and outlet pipes with the tank may cause the wall sheet to tear or damage the tank accessories

1-1-1-Failures resulting from the effects of hydrodynamic forces

The most important type of failure observed for steel liquid storage tanks is damage caused by tank wall buckling. This buckling occurs as a result of compressive hydrodynamic force resulting from the bending anchor produced during an earthquake. In general, two types of buckling have been reported in the walls of steel tanks. The buckling of the wall may occur in the case that the wall is not very thick, before the material flows completely, and this type of buckling is called rhomboid or diamond-shaped buckling. Also, the buckling may be accompanied by the material flowing, which is called papili buckling. These two types of buckling differ from each other in terms of the philosophy of formation, place of occurrence, and appearance.

1-1-1-1-Lomb shaped buckling[1]

As mentioned, this type of buckling is actually a type of elastic buckling (which of course can be geometrically inelastic) which is caused by axial compressive stresses caused by hydrodynamic loads of earthquakes. This type of buckling usually occurs in tanks with a large height-to-radius ratio and in the lower third of the wall.That is, where the stresses caused by hydrostatic pressure are smaller than the stress at the bottom of the wall.  The amount of compressive stress to create such buckling can be obtained from the theory of linear buckling. The value of the critical buckling stress for the skin cylinder under pure axial pressure is equal to the following value.

(1-1)

where E is the modulus of elasticity, t is the thickness of the shell, and R is the radius of the tank.  This theoretical value cannot be used as the allowable compressive stress in tanks under dynamic loads. Because in the reservoirs under earthquake load, firstly, the whole shell is not under uniform pressure. Secondly, the internal pressure of the liquid causes environmental stresses in the tank wall, and these environmental stresses affect the resistance of the wall against compressive stresses. Thirdly, the wall of the tank has initial defects that occurred in the manufacturing process and it cannot be assumed to be a uniform material. Therefore, the effects of these three factors, i.e. primary defects, liquid internal pressure and non-uniformity of compressive stresses, should be included in the theoretical relationship.

The effects caused by construction defects in the wall significantly reduce the allowable compressive stresses. But the hydrodynamic pressure of the liquid inside the shell reduces the effects caused by the initial defects and thus helps to increase the allowable compressive stress. Also, the third factor, i.e. the non-uniformity of the compressive stresses caused by the bending anchor, reduces the probability of the maximum compressive stress occurring at the location of the primary defects and increases the allowable compressive stress. However, the negative effect of the first factor, i.e. initial defects, is very high and neutralizes the positive effects of the other two factors. As a result, the allowable compressive stress in the elastic buckling state is practically lower than the value suggested by the equation (1-1). Examples of diamond or rhomboid buckling are shown in Figure (1-1).

1-1-1-2-Pafili buckling [2]

There is another type of buckling that usually occurs in the lower region of short tanks with a ratio of height to tank radius smaller than one. This buckling is caused by the combination of environmental stresses caused by the internal pressure of the liquid and compressive stresses caused by the earthquake. According to the studies conducted by previous researchers [1], papili buckling is caused by the participation of vertical stresses and tensile annular stresses [2]. It should be noted that in Pafili buckling, first the material flows and then the plastic buckling occurs. While in the diamond type, the wall of the tank buckles before the material flows. It should also be noted that the internal pressure of the liquid on the wall plays a positive role in the elastic buckling state and causes the effects of initial defects to be less and the allowable compressive stress to be increased.  But in the case of papili buckling, the internal pressure has a negative role and reduces the allowable stress. Figure (1-2) shows some examples of papili buckling.

In a general summary, it can be said that elastic buckling occurs mostly for thin and long tanks that have a low radius-to-thickness ratio. But papili buckling occurs mostly for short and wide tanks with a ratio of height to radius less than one.

1-1-2- Damages resulting from the movement of liquid waves at the location of the free surface of the fluid

During an earthquake, part of the liquid in the tank moves back and forth with a period much longer than the period of the earthquake. This part of the liquid creates surface waves in the place of the free surface, which may collide with the roof and wall of the tank. The failure mode of tanks with fixed and floating roofs is different when faced with the phenomenon of liquid waves. In general, the damages caused by the movement of wavy liquid on the top of the tank can be summarized as follows.

In the case of tanks with a fixed roof, the collision of the wavy liquid with the walls and roof of the tank may cause them to buckle near the roof (Figures 1-3, 1-4, 1-5, 1-6).

For open tanks, the eruption of liquid from the top of the tank may cause environmental pollution. This is especially important in the case of storage tanks for toxic substances (Figure 1-7).

In some cases, the contact of the liquid with the roof causes the joints between the roof and the wall to leak.

During an earthquake, the fluid inside the tank shows large movements, which may cause the liquid to escape from the floating roof of the tank, or due to the movement of the roof of the tank, sparks may occur at the junction of the wall and the roof, in which case there is a possibility of large fires. (Figure 1-8).