Strong ground motions were recorded at Port Island, Kobe, by a borehole array during the 1995 Hyogo-ken Nanbu (Kobe) earthquake. These records indicate that, while the horizontal peak accelerations were reduced as seismic waves traveling from the bottom to the surface, motions in the vertical direction were significantly amplified at the surface, with peak value of 1.5 to 2 times larger than the horizontal components. Some studies have discussed local site effects on the horizontal motions, whereas the available study on the vertical amplification is limited. In this article, we present a possible mechanism to explain the observed vertical amplification in detail. We consider that the observed large vertical amplification is mainly associated with incomplete saturation of near-surface soils, which causes substantial amplification of P waves but does not affect the propagation of S waves. Based on the concept of homogeneous pore fluid and Biot's theory of two-phase media, we discuss the characteristics of P-wave velocity, Poisson's ratio and degree of saturation in shallow soil layers, and show evidence of incomplete saturation of near-surface soils at the array site. We analyze a simple model to theoretically investigate the effects of saturation on vertical-motion amplification. The results show that the degree of saturation may produce substantial influence on the amplification, both amplitude and frequency content. Using a solid-fluid coupled finite element procedure, we perform a simulation of the observed vertical motions at the array site by including the effects of saturation. The results demonstrate the mechanism of large amplification caused by incomplete saturation of near-surface layers. The present study indicates that vertical-component motions may significantly be affected by pore-water saturation of soils, suggesting that we may need to carefully examine the condition of saturation in the study of vertical site amplification.

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Uncertainty involved in the experiment data prohibits the wide applications of the finite element (FE) model updating technique into engineering practices. In this article, the Markov Chain Monte Carlo approach with a Delayed Rejection Adaptive Metropolis algorithm is investigated to perform the Bayesian framework for FE updating under uncertainty. A major advantage of this algorithm is that it adopts global and local adaptive strategies, which makes the FE model updating be robust to uncertainty. Another merit of the studied method is that it not only quantitatively predicts structural responses, but also calculates their statistical parameters such as the confidence interval. Impact test data of a grid structure are investigated to demonstrate the effectiveness of the presented FE model updating technique, in which the uncertainty parameters include the vertical and longitudinal spring stiffness that simulate the boundary
 conditions, the end‐fixity factor for modeling semi‐rigid connections, and the elastic modulus for simulating the uncertainty associated with material property.

SUMMARYAnalysis of large deformation of geomaterials subjected to time-varying load poses a very difficult problem for the geotechnical profession. Conventional finite element schemes using the updated Lagrangian formulation may suffer from serious numerical difficulties when the deformation of geomaterials is significantly large such that the discretized elements are severely distorted. In this paper, an operator-split arbitrary Lagrangian-Eulerian (ALE) finite element model is proposed for large deformation analysis of a soil mass subjected to either static or dynamic loading, where the soil is modelled as a saturated porous material with solid-fluid coupling and strong material non-linearity. Each time step of the operator-split ALE algorithm consists of a Lagrangian step and an Eulerian step. In the Lagrangian step, the equilibrium equation and continuity equation of the saturated soil are solved by the updated Lagrangian method. In the Eulerian step, mesh smoothing is performed for the deformed body and the state variables obtained in the updated Lagrangian step are then transferred to the new mesh system. The accuracy and efficiency of the proposed ALE method are verified by comparison of its results with the results produced by an analytical solution for one-dimensional finite elastic consolidation of a soil column and with the results from the small strain finite element analysis and the updated Lagrangian analysis. Its performance is further illustrated by simulation of a complex problem involving the transient response of an embankment subjected to earthquake loading.

We report a procedure by which structural parameters and input ground motion are identified from measured responses only. We have assumed that the coda of the response time history represents the free vibration response of the structural system. Because the coda is not effected by the input ground motion, we can first identify such structural parameters as the masses, damping coefficients and spring constants from this part of the record. Input ground motion then is estimated from the full record and the identified parameters. The identification and estimation are made with the Kalman filter. To verify the effectiveness of this procedure, we have simulated the responses of a linear, three-degree-of-freedom system for different earthquake inputs and made estimations using the simulated responses as observed records. The estimated accelerograms, the identification of which usually more difficult than the identifications of velocitigrams and displacementgrams, are in good agreement with the recorded ones for the actual earthquakes.

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