EARTHQUAKE SAFETY EVALUATION OF ATATURK DAM

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comparable materials. Possible ranges of the most important dynamic properties were considered by analysing a number of cases. The Poisson’s ratios of the shells (including filters) and the core were assumed to be equal to 0.30 and 0.47, respectively. The total mass densities of the dam materials corresponded to the total unit weights listed in Table 2. The principal features of the dynamic properties of the dam materials are explained below. Maximum dynamic shear modulus in upstream and downstream shells The maximum dynamic shear modulus Gmax of a cohesionless geotechnical material can be expressed as (Seed and Idriss, 1970) 0. 5 G max = 220 k 2max ( σ′ m ) (in kPa) where k2max is a material constant that depends primarily on the relative density and σ′ m is the mean effective static stress. Conventionally, the shear modulus for a cyclic shear strain amplitude of 10 -4 % is designated as Gmax, since the dynamic shear modulus is practically constant for strain amplitudes below this level. The possible range of values of k2max considered for the upstream and downstream shells was as follows (Seed et al., 1984): • Lower bound: k2max = 90 • Average: k2max = 120 • Upper bound: k2max = 150 Maximum dynamic shear modulus in clay core The maximum dynamic shear modulus Gmax of the clay core depends primarily on the undrained shear strength su (Seed and Idriss, 1970). The approximate relationship between the two quantities can be expressed as ⎧1200 lower bound G max ⎪ = ⎨2400 average s u ⎪ ⎩3600 upper bound The undrained shear strength su of the clay core varies from approximately 100 kPa at the top to 220 kPa at the bottom of the dam. It is assumed to vary linearly over the dam height. Strain-dependence of dynamic shear modulus and damping ratio The dynamic shear modulus and the damping ratio of a fill material subjected to a cyclic loading vary substantially with the amplitude of the shear strain. In general, the shear modulus diminishes and the damping ratio grows when the dynamic shear strain amplitude becomes larger. The strain-dependence of the dam materials for the earthquake analysis is briefly discussed below. • Upstream and downstream shells: The dynamic shear modulus and the damping ratio of the upstream and downstream shells (including the filters) were assumed to vary with shear strain amplitude as shown in Fig. 1. These curves were proposed by Seed et al. (1984) based on a large number of cyclic triaxial tests made on gravelly soils, including the rockfill materials used in the Pyramid and Oroville Dams in USA. • Clay core: The strain-dependence of a clayey soil is strongly influenced by its plasticity index. The plasticity index of the core material of the Ataturk dam lies within the range of 20 to 45. The corresponding variation of the shear modulus and the damping ratio of the clay core with the dynamic shear strain are plotted in Fig. 2, in which the average curves as well as the upper and lower bounds are indicated.
Fig. 1: Dependence of dynamic shear modulus (left) and damping ratio (right) of rockfill on cyclic shear strain amplitude Fig. 2: Dependence of dynamic shear modulus (left) and damping ratio (right) of clay core on cyclic shear strain amplitude <strong>EARTHQUAKE</strong> ANALYSIS Brief description of analysis method The dynamic analysis was performed with the computer program QUAD4M (Hudson et al., 1994). This program evaluates the seismic response of any soil deposit or earth structure using the finite element procedure in the time domain. The equations of motion are solved by direct step-by-step numerical integration. The shear modulus and damping ratio are based on dynamic tests using constant-amplitude strain cycles. The strain response during an earthquake, however, consists of cycles with variable amplitudes. This was taken into account by using an equivalent, uniform dynamic shear strain amplitude equal to 65% of the peak dynamic shear strain for the evaluation of the dynamic shear modulus and the damping ratio. An iterative procedure, based on the equivalent linear method, was applied to obtain the strain-compatible shear modulus and damping ratio of each finite element. The solution was found to converge satisfactorily in 5 iterations. The integration of the dynamic equations of motion was done in time steps of 0.01 s. The dynamic solution was obtained for the total duration of the input motion plus an additional 5 s of the free vibration phase after the earthquake. Cases analysed
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EARTHQUAKE SAFETY EVALUATION OF ATATURK DAM

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