Seismic Design of Liquid Storage TanksPraveen K. Malhotra

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1-6 P. K. Malhotra, 2006

Earthquake Damage to Tanks

Tank farm damaged by the 1995 Kobe Earthquake

Tanks have suffered significant damage during past earthquakes. The seismic design standards have been revised several times to improve the performance of tanks during future earthquakes.

Photo: Courtesy of University of California, Berkeley

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1-7 P. K. Malhotra, 2006

Shell Buckling

Elephant-foot buckling (broad tanks)

Diamond buckling (slender tanks)

Caused by combination of outward pressures generated by verticalmotion and compressive stresses generated by horizontal motion

Shell buckling is caused by combined action of outward hydrodynamic wall pressures generated by vertical ground motion and axial compressive stresses caused by overturning moment generated by horizontal ground motion. For broad tanks, shell buckling takes the form of an axisymmetric bulge (elephant foot). For slender tanks, buckling is in the form of a diamond pattern.

Photos: Courtesy of University of California, Berkeley

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1-8 P. K. Malhotra, 2006

Inlet-outlet Pipe Breaks

Shell buckling has caused this pipe break. Base uplifting or sliding can also cause pipe breaks

Unanchored or partially anchored tanks experience base uplifting. This can cause a break in the inlet/outlet piping connections which are not designed to accommodate the vertical movement. Pipe breaks can also result from horizontal movement (sliding) of the base.

Photo: Courtesy of University of California, Berkeley

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1-9 P. K. Malhotra, 2006

Flexible Connection

Flexible connections that accommodate horizontal and vertical movements prevent pipe breaks

Source: unknown

Flexible connections that accommodate vertical and horizontal movement prevent pipe breaks. Note that even an anchored tank is expected to undergo some uplift during design ground shaking, because the anchors are designed for a fraction of the full elastic moment induced in the tank. This will become clear in Session 3.

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1-12 P. K. Malhotra, 2006

Base Sliding

This broad motor-spirit storage tank slid at its base during the 2001 Bhuj, India Earthquake. Notice extensive damage to inlet/outlet piping.

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1-13 P. K. Malhotra, 2006

Sloshing Damage to Upper Tank Shell and Roof

Tanks that are not provided with sufficient freeboard can be damaged by the sloshing waves. This oil tank suffered a leak at the roof-shell junction. Note also uneven bulging of the roof due to impacts from the sloshing liquid.

Photo: Courtesy of University of California, Berkeley

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1-15 P. K. Malhotra, 2006

Sloshing Damage to Floating Roof Tanks

1999 Turkey earthquake. Photo by Gayle Johnson

Tanks with floating roofs have generally performed poorly during earthquakes. In the left photo, the floating roof of the tank was overtopped by the liquid inside the tank. Some floating roofs have sunk during earthquakes. In the right photo, the oil tanks caught fire due to sparks generated by up-down movement of the roof against the guides.

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1-16 P. K. Malhotra, 2006

Elevated Tanks

The substructures need to be designed for the hydrodynamic moments and shears generated in the superstructure. In the left photo, concrete link beams of an elevated tower have suffered shear failure. In the right photo, the steel elevated tank has collapsed.

Photos: Courtesy of University of California, Berkeley

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1-17 P. K. Malhotra, 2006

Implosion Caused by Rapid Loss of Contents

Rapid loss of contents caused the implosion of these tanks during the 1999 Taiwan Earthquake. Adequate venting can prevent implosion

Lack of proper venting caused these tanks to implode. Rapid loss of contents due to leaks near the base generated ‘vacuum’ in the tank, which caused the top shell and roof to implode. Softening of material due to nearby fires also played a role.

Photo: Courtesy of University of California, Berkeley

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1-20 P. K. Malhotra, 2006

Impulsive and Convective Masses

Convective

Convective

Impulsive

Impulsive

Broad tank Slender tank

For tanks with H/R = 0.9 (~1), half the liquid is impulsive and half the liquid is convective. For broad tanks (H/R < 1), more liquid is convective than impulsive. For slender tanks (H/R > 1), more liquid is impulsive than convective. Intuitively, this makes sense because in slender tanks more liquid is constrained to move with the tank wall.

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1-31 P. K. Malhotra, 2006

Elevated Tank Model

hi

mi

cm

ch

The substructure should be included in the model of the elevated tank. The flexibility of the substructure will change the impulsive and convective periods. Note that the impulsive and convective masses are at heights hi’ and hc’ (not hi and hc).

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4-17 P. K. Malhotra, 2006

Resistance to Base Uplifting

An important part of nonlinear tank analysis is calculating the moment-rotation relationship of base uplifting. A tank has significant resistance to uplifting due to the weight of the contained liquid. However, this resistance cannot be mobilized unless a portion of the base plate has been uplifted by the tank wall; larger the overturning base moment higher the base rotation, hence higher the base uplift. The moment-rotation relationship is established for the base plate by taking into account the nonlinearities associated with plastic yielding, membrane forces and varying contact of base with the foundation. The plot on the left shows a typical moment-rotation relationship. The loading and unloading paths are not the same in the moment-rotation relationship. The area enclosed between the loading and unloading paths is the energy dissipated through plastic yielding at the plate-shell junction. The skeleton stiffness is separated from the hysteresis loop and the two are shown on the right side.

The damping is estimated from the area enclosed by the hysteresis loop.