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<br />(1) Sufficient foundation and abutment exploration, <br />material testing, and strengthening, if necessary, to <br />ensure foundation and abutment integrity. The importance <br />of foundation and abutment integrity cannot be <br />overemphasized. Adequate drainage is usually the first <br />line 0 f de fense against foundation instabi li ty. <br /> <br />(2) The best geome tr ic a1 design, such as cu rved transitions, <br />minimal mass at the crest, gradual changes in arch and <br />cantilever stiffness in the top half of arch dams, and a <br />downstream face slab for buttress dams. The objective is <br />to limit the concentration, magnitude, and extent of <br />excessive compressive and tensile stresses from <br />earthquake-induced ground motion. <br /> <br />(3) Sufficient strength of the concrete and lift joints, <br />especially in the upper half of the dam where the tensile <br />stresses can be the greatest. <br /> <br />(4) Effective quality control during construction to ensure <br />adequate foundation preparation, strengths of the concrete <br />and lift joints, and placement of the reinforcement when <br />used. <br /> <br />c. Methods of Analyses <br /> <br />(1 ) Genera 1 <br /> <br />Three methods currently being applied to various levels of <br />studies and types of dams, in the order of complexity, <br />are: the pseudostatic, response spectrum, and time- <br />history methods. All commonly used methods assume the dam <br />is made of linearly elastic, homogeneous, and isotropic <br />material. <br /> <br />(2) Pseudostatic Method <br /> <br />This method consists of determining a set of loads acting <br />on the dam to prescribed average horizontal and vertical <br />ground accelerations based on a seismic zone map and <br />applying these loads statically to the dam. The <br />acceleration is assumed either constant or varying over <br />the height of the dam, depending on the flexibility of the <br />dam. The earthquake loadings consist of those resulting <br />from hydrodynamic pressures from the reservoir and inertia <br />forces of the dam. The hyrodynamic forces are determined <br />using Westergaard's approximation for an equivalent mass <br />of water to move with the dam. Westergaard's me thod is <br />more applicable to stiff gravity-type dams. The <br />pseudostatic method is commonly used for checking sliding <br />and overturning stabi li ty for gravi ty and bu ttress dams. <br /> <br />-19- <br />