Earthquake pressures on fluid containers

The dynamic fluid pressures developed during an earthquake are of importance in the design of structures such as dams, tanks and caissons. The first solution of such a problem was that by Westergaard (1933) who determined the pressures on a rectangular, vertical dam when it was subjected to horizontal acceleration. Jacobsen (1949) solved the corresponding problem for a cylindrical tank containing fluid and for a cylindrical pier surrounded by fluid. Werner and Sundquist (1949) extended Jacobsen's work to include a rectangular fluid container, a semicircular trough, a triangular trough and a hemisphere. Graham and Rodriguez (195Z) gave a very complete analysis of the impulsive and convective pressures in a rectangular container. Hoskins and Jacobsen (1934) measured impulsive fluid pressures and Jacobsen and Ayre (1951) gave the results of similar measurements. Zangar (1953) presented the pressures on dam faces as measured on an electrical analog. The foregoing analyses were all carried out in the same fashion, which requires finding a solution of Laplace's equation that satisfies the boundary conditions. With these known solutions as checks on accuracy it is possible to derive solutions by an approximate method which avoids partial differential equations and series and presents solutions, for a number of cases in simple closed form. The approximate method appeals to physical intuition and makes it easy to see how the pressures arise. It thus seems to be particularly suitable for engineering applications. To introduce the method the problem of the rectangular tank is treated in some detail. Applications to other types of containers are treated more concisely. The essence of the method is the estimation of a simple type of flow which is similar to the actual fluid movement and this simple flow is used to determine the pressures. The method is analogous to the Rayleigh-Ritz method used in the theory of elasticity, and it always overestimates the forces. The method is capable of solving a wide variety of problems but if it is required that the solutions be in simple form, which they should to be practically useful, the number of problems that can be handled satisfactorily are limited, just as in the case of the Rayleigh-Ritz method. Acknowledgement is due C. M. Cheng for carrying out the calculations in this report