Tomoyo Taniguchi

Estimation of Peak Ground Acceleration from Horizontal Rigid Body Displacement: A Case Study in Port-au-Prince, Haiti

The M 7.0 Haiti earthquake of 12 January 2010 caused catastrophic da- mage and loss of life in the capital city of Port-au-Prince. The extent of the damage was primarily due to poor construction and high population density. The earthquake was recorded by only a single seismic instrument within Haiti, an educational seis- mometer that was neither bolted to the ground nor able to record strong motion on scale. The severity of near-field mainshock ground motions, in Port-au-Prince and elsewhere, has thus remained unclear. We present a detailed, quantitative analysis of the marks left on a tile floor by an industrial battery rack that was displaced by the earthquake in the Canape Vert neighborhood in the southern Port-au-Prince metropolitan region. Results of this analysis, based on a recently developed formula- tion for predicted rigid body displacement caused by sinusoidal ground acceleration, indicate that mainshock shaking at Canape Vert was approximately 0:5g, correspond- ing to a modified Mercalli intensity of VIII. Combining this result with the weak- motion amplification factor estimated from aftershock recordings at the site as well as a general assessment of macroseismic effects, we estimate the peak acceleration to be ≈0:2g for sites in central Port-au-Prince that experienced relatively moderate damage and where estimated weak-motion site amplification is lower than that at the Canape Vert site. We also analyze a second case of documented rigid body dis- placement, at a location less than 2 km from the Canape Vert site, and estimate the peak acceleration to be approximately 0:4g at this location. Our results illustrate how observations of rigid body horizontal displacement during earthquakes can be used to estimate peak ground acceleration in the absence of instrumental data.

Rocking Mechanics of Flat-Bottom Cylindrical Shell Model Tanks Subjected to Harmonic Excitation

The rocking motion of the tanks is complex and not fully understood. Using model tanks that possess concentric rigid-doughnut-shaped bottom plates, this paper tries to clarify its fundamental mechanics through the analog of rocking motion of rigid bodies. Introducing an effective mass for the internal liquid for rocking motion enables the development of a dynamical system including the rocking-bulging interaction motion and the effective mass of liquid for the interaction motion. Since the base shear and uplift displacement observed during shaking tests match well with computed values, the proposed procedure can explain the mechanics of the rocking motion of the model tanks used herein.

Experimental and Analytical Study of Free Lift-Off Motion Induced Slip Behavior of Rectangular Rigid Bodies

The mechanism of the slip of a rectangular rigid body during free lift-off motion is investigated analytically and experimentally. Equations of motion of slipping rectangular rigid body during free lift-off motion are derived by the variational approach. The time histories of both slip and lift-off motions are numerically computed and compared with corresponding experimental results to discuss the analytical accuracy; given an initial enforced lift-off angle to the rectangular rigid body and then gently released. The mechanical energy balance of simultaneous slip and lift-off motions is clarified to explain the considerable reduction of lift-off angle due to the slip.

Masses of Fluid for Cylindrical Tanks in Rock With Partial Uplift of Bottom Plate

This study proposes the use of a slice model consisting of a set of thin rectangular tanks for evaluating the masses of fluid contributing to the rocking motion of cylindrical tanks; the effective mass of fluid for rocking motion, that for rocking-bulging interaction, effective moment inertia of fluid for rocking motion and its centroid. They are mathematically or numerically quantified, normalized, tabulated, and depicted as functions of the aspect of tanks for different values of the ratio of the uplift width of the tank bottom plate to the diameter of tank for the designers convenience.

Effective Mass of Fluid for Rocking Motion of Flat-Bottom Cylindrical Tanks

In analyzing the rocking motion of the flat-bottom cylindrical tanks subjected to severe earthquakes, the effective mass of fluid for the rocking motion and its moment inertia around the pivoting bottom edge of the tank would be indispensable dynamical properties, because they couples the fluid-shell interaction motion, the so-called bulging motion, with the rocking motion. This paper quantifies them based on the equilibrium of the fluid pressure and inertia force accompanying the angular acceleration acting on the pivoting bottom edge of the tank. Employing a general mathematical solution for the fluid pressure that can calculate either fully or partially uplifted tank bottom, this paper presents mathematical formulae of the effective mass of fluid for the rocking motion and its moment inertia. These quantities are given by an explicit function of dimensional variables of the tank but with Fourier series. For designer’s convenience, the effective moment inertia and effective mass of fluid for the rocking motion and its center of gravity from the pivoting bottom edge are normalized accordingly and are depicted on diagrams.Copyright

Numerical Investigation Into Significant Reduction in Coefficient of Restitution for Fluid-Container Combined Systems

The analysis procedure of rocking motion of unanchored flat-bottom cylindrical shell tanks should include an impact problem between the tank bottom plate and tank foundation. To evaluate the rocking motion of tanks based on a simple analytical procedure developed by a senior author, adequate estimation of a coefficient of restitution is necessary. This paper numerically examines the coefficient of restitution suitable for the fluid-container combined system used in such simple analysis procedure. Employing free rocking motion, an empty container and fluid-container combined system are computed. The velocity vectors of the empty container turn their direction simultaneously just after the uplifted edge hits the ground, while those of the fluid-container combined system need a time to turn their direction. This implies that the coefficient of restitution should be evaluated with effects of fluid stored in the tank.Copyright

Experimental and Analytical Studies of Rocking Mechanics of Unanchored Flat-Bottom Cylindrical Shell Model Tanks

Employing a few feasible physical quantities of liquid related to the rocking motion of tanks, this paper tries to understand the fundamental dynamics of the rocking motion of tanks. Introducing the effective mass of liquid for rocking motion and for rocking-bulging interaction motions, the equations of motion are derived by analogue of rocking motion between rigid bodies and tanks. Using the exclusive tanks that possess the rigid-doughnuts-shape bottom plate that guarantees the uplift region of the bottom plate and the extent of the effective mass of liquid for rocking motion, the harmonic shaking tests are carried out. The proposed procedures can stepwise trace the base shear and the uplift displacement of the model tanks used herein.© 2004 ASME

Effective Mass of Fluid for Rocking-Bulging Interaction of Rigid Rectangular Tank Whose Bottom Plate Rectilinearly Uplifts

In experimental and analytical studies of the rocking response of a circular cylindrical tank under the action of the purely horizontal and translational ground motion, the author analogically quantified the mass of fluid contributing to both bulging and rocking motion of the tank. It was called “the effective mass of fluid for the rocking-bulging interaction.” Its dynamical role in the rocking motion of the tank was thoroughly investigated. However, applying it to design process requires us to use its rigorous definition. To date, the fluid pressure on the tank induced by the impulsive (= bulging) motion and the rocking motion and their effective masses of fluid for each motion were mathematically defined, respectively. Therefore, this paper tries to define the effective mass of fluid for the rocking-bulging interaction based on the fluid pressure on the tank mathematically. The effective mass of fluid for the rocking-bulging interaction is understood as a part of the effective mass of fluid for the bulging motion that is also under the action of the rotational inertia. The influence of the rotational inertia on the effective mass of fluid for the bulging motion is measured by a ratio of the apparent density of fluid contributing to the rocking motion to the original density of fluid. The distribution of the apparent density of fluid contributing to the rocking-bulging interaction is drawn for the various aspects of tanks. The ratio of the effective mass of fluid for the rocking-bulging interaction to the total mass of fluid of the tank is given as the function of the aspect ratio of the tank and the ratio of the uplift width of the tank bottom.Copyright

Fluid Pressure on Rectangular Rigid Tanks Due to Uplift Motion

This paper mathematically derives fluid pressure on a rectangular rigid tank with unit depth, which models a section of a center part of a flat-bottom cylindrical shell tank, accompanied with uplift motion. Employing boundary conditions consisting of fluid velocity imparted by motion of the side walls and bottom plate of the tank along with uplifting, the equation of continuity of fluid given by the Laplace equation is solved as the parabolic partial differential equation of Neumann problem. The fluid pressure is given by a function of the velocity potential. Comparison of mathematical results with numerical ones based on explicit FE analysis corroborates its accuracy and applicability on design procedure of flat-bottom cylindrical shell tanks.Copyright

Mathematical Solution for Evaluating Fluid Pressure on Rigid Flat-Bottom Cylindrical Shell Tanks Due to Uplift Motion

Solving the equation of continuity given by the Laplace equation on the cylindrical coordinates, the mathematical solution for evaluating fluid pressure on rigid flat-bottom cylindrical shell tanks is derived. However, since difficulty of applying asymmetric boundary conditions on the cylindrical coordinates which trace realistic uplift motion of tanks restricts application of the preceding mathematical solution to the actual case scenario, the slice model consisting of a rigid rectangular tank with unit depth on a parallel plane to the uplift motion and offsetting from a center of tanks is developed. Comparison reveals applicability of the slice model for evaluating the fluid pressure on the rigid flat-bottom cylindrical rigid shell tanks.© 2007 ASME