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عنوان فارسی مقاله:

یک مدل غیر خطی ساده شده نوسانی- جنبشی جهت ارزیابی پاسخ لرزه ای سازه های قرار گرفته بر روی فونداسیون های سطحی

عنوان انگلیسی مقاله:

A simplified Nonlinear Sway-Rocking model for evaluation of seismic response of structures on shallow foundations

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2. Problem definition

The problem investigated in this study (Fig. 1) is a seismicallyexcited building founded on a half-space consisting of saturated soft clay layers, where undrained shear strength su and stiffness G increase linearly with depth (Poisson’s ratio ν and density ρ remain constant). The foundation is assumed to be rigid, which is appropriate for a mat foundation that is much stiffer than the soil. Foundation movements are described by the translations w (vertical) and u (horizontal) as well as rotation angle θ, which are correlated, respectively, with the forces V, H and moment M with respect to the base centre. The interface between the foundation and clay is assumed to sustain tension. This simplifying assumption is suitable for the problem being investigated: buildings supported on soft clay deposits and subjected to undrained seismic loading where the foundation uplift resistance is provided by structural weight and potential suction within the underlying soil. The overall SSI system is initially subjected to the self-weight V of the structure, followed by the radial load paths in the M–H plane representing the seismically loaded structures with a predominant mode of vibration. Fig. 1(b) displays the simplified NSR model where the mass of the structure m is lumped at an effective height heff above a circular mat foundation with an equivalent radius R¼ ffiffiffiffiffiffiffiffiffi A=π p , where A is the area of the foundation. In the proposed model, the soil half-space is replaced by an assemblage of springs and dashpots. The plastic spring (placed closer to the foundation) simulates the large-displacement behaviour of the soil-foundation system, whereas the spring and dashpot arranged in parallel are used to model, respectively, the small-displacement response and the radiation damping. The strength and stiffness of the springs and the damping coefficient of the dashpots were derived from existing analytical solutions and rigorous FD analyses. Though independent springs are used for the individual degrees of freedom of the foundation, coupling between the nonlinear sway and rocking responses is also incorporated in the model by expressing the spring properties as a function of the load paths experienced by the foundation in V:H:M space. The load paths are controlled by the factor of safety against vertical bearing capacity failure FSv, the moment-to-shear ratio M/H, and the failure envelope defining the ultimate limit states of the foundation in V:H:M space.