Resistance of Short, Stiff Piles to Multidirectional Lateral Loadings
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Abstract Lateral loads applied to pile foundations in some cases are multidirectional. However, most of the past studies only considered soil-pile interaction under unidirectional horizontal loadings. This paper describes a comprehensive experimental study on a pile-sand system under both unidirectional and multidirectional horizontal loadings using a computer numerically controlled biaxial motion platform. The displacement paths at the pile head include unidirectional regular paths, cross paths, figure-8 paths, and unidirectional and multidirectional irregular paths with different displacement amplitudes and different aspect ratios of the displacement amplitudes along two horizontal directions (α). The test results indicate that the preloading along one horizontal direction influences the subsequent response along the orthogonal horizontal direction, in terms of the pile resistance and the direction of the force increment vector. In the figure-8 tests, the shapes of the force-displacement curves in most cases differ significantly from that obtained from the unidirectional regular test and different from the unidirectional regular test, the maximum forces appear before the displacements reach the maximum values. In these tests, the direction of the force increment vector always deviates from the direction of the displacement increment vector. According to the results of the regular and irregular loading tests, the lateral resistance of the pile under the multidirectional paths is generally lower than that under the unidirectional path, and the degree of reduction increases with the aspect ratio (α). The ratio of force (rF), defined as the maximum force in the multidirectional tests to that in the unidirectional test, can be expressed as an exponential function of α. Considering that the reduction in the resistance can reach as large as about 30%, overlooking the multidirectional loading effect can lead to unconservative analysis or design in some cases.Keywords:
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A perturbation method representing a nonlinear gravity wave is applied to the vertical displacement of the water surface of a standing wave for estimating wave overtopping. The presented method predicts the surface displacement when the crest of the breakwater is lowered below the maximum water‐surface elevation while wave overtopping occurs. A theoretical investigation is conducted to study the behavior of a wave overtopping a vertical barrier. A method based on the wave energy is used to formulate the discharge‐water quantity due to wave overtopping, and the total amount of wave overtopping is calculated by integrating the water surface elevation at the barrier. Experiments were performed in a two‐dimensional wave channel, where a vertical barrier model was placed to verify the predictions. The surface displacement of standing waves was measured at the barrier while the flow over the barrier was collected in a tank. The surface displacement, calculated by the finite‐amplitude approximation is in agreement with test data, and the wave‐overtopping model of this research agrees with measurements.
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The data measured by a thermal chain array covering depths of 4 to 46.6 meters in the North of the Yellow Sea in September 2008 is analyzed in this paper. Results show that the water particle vertical displacement of 15 meters occurs due to internal waves. The vertical displacement power spectrum of isotherm curves is conducted and the spectrum attenuation coefficients are between ‐1.93 and ‐2.19. The mean spectrum attenuation coefficient is ‐2.05, which is consistent with the G‐M internal wave spectrum with power law of ‐2. With these, the sound velocity fluctuation δc/c caused by internal waves is predicted at different ranges, depths and times respectively. The results show that mean δc/c is about 10−4 and varies strongly within the thermocline layer at the depth of 20–35 meters. It will be useful for deterministic modeling and stochastic modeling in a random sea.
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Particle velocity
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