This paper presents numerical analysis of soil-structure-interaction (SSI) of tall reinforced concrete chimneys with piled raft foundation subjected to El Centro ground motion (1940) using finite element method. Seismic analysis in time domain was performed on the basis of direct method of SSI on the three-dimensional SSI system. The chimney, foundation, and soil were assumed to be linearly elastic in the analysis. The stress resultants and settlement of raft of piled raft foundation were evaluated under different soil properties and different geometrical features of raft and chimney. Soil properties were selected based on the shear wave velocity corresponding to sand in the loose to dense range. Chimneys with different elevations of 100 m, 200 m, and 400 m were taken with a ratio of height to base diameter of chimney of 17. Raft of different thickness was considered to evaluate the effect of stiffness of foundation. Results were analysed to assess the significance of characteristic of the ground motion. It is found that the response in the raft depends on the different parameters of chimney, foundation, and soil. It is also found that the higher modes of SSI system are significant in determining the response in the raft.
We study the fair division problem of allocating multiple resources among a set of agents with Leontief preferences that are each required to complete a finite amount of work, which we term "limited demands." We examine the behavior of the classic Dominant Resource Fairness (DRF) mechanism in this setting and show it is fair but only weakly Pareto optimal and inefficient in many natural examples. We propose as an alternative the Least Cost Product (LCP) mechanism, a natural adaptation of Maximum Nash Welfare to this setting. We characterize the structure of allocations of the LCP mechanism in this setting, show that it is Pareto efficient, and that it satisfies the relatively weak fairness property of sharing incentives. While we prove it satisfies the stronger fairness property of (expected) envy freeness in some special cases, we provide a counterexample showing it does not do so in general, a striking contrast to the "unreasonable fairness" of Maximum Nash Welfare in other settings. Simulations suggest, however, that these violations of envy freeness are rare in randomly generated examples.
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