Effects of topography on dynamic responses of single piles under vertical cyclic loading

This paper describes model tests of single piles subjected to vertical cyclic compressive loading for three kinds of topography: sloping ground, level ground, and inclined bedrock. Comprehensive dynamic responses involving cyclic effects and vibration behaviours are studied under various load combinations of dynamic amplitude, mean load,frequency and number of cycles. Test results show that permanent settlement can generally be predicted with a quadratic function or power function of cycles.Sloping ground topography produces more pronounced settlement than level ground under the same load condition. For vibration behaviour,displacement amplitude is weakly affected by the number of cycles, while load amplitude significantly influences dynamic responses. Test results also reveal that increasing load amplitude intensifies nonlinearity and topography effects. The strain distribution in a pile and soil stress at the pile tip are displayed to investigate the vibration mechanism accounting for sloping ground effects. Furthermore, the dynamic characteristics among three kinds of topography in the elastic stage are studied using a three-dimensional finite method. Numerical results are validated by comparing with experimental results for base inclination topography. An inclined soil profile boundary causes non-axisymmetric resultant deformation, though a small difference in vertical displacement is observed.

Seismic response analysis of continuous rigid frame bridge considering canyon topography effects under incident SV waves

To evaluate the importance of the canyon topography effects on large structures, based on a rigid frame bridge across a 137-m-deep and 600-m-wide canyon, the seismic response of the canyon site is analyzed using a two-dimensional finite element model under different seismic SV waves with the assumptions of vertical incidence and oblique incidence to obtain the ground motions, which are used as the excitation input on the pier foundations of the bridge with improved large mass method. The results indicate that canyon topography has significant influences on the ground motions in terms of inci- dent angle. The peak ground acceleration values vary greatly from the bottom of the canyon to the upper comers. Under ver- tical incident SV waves, at the upper comers of canyon the peak ground accelerations greatly increase; whereas the peak ground accelerations diminish at the bottom comers of canyon. Under oblique incident SV waves, the shaking of the canyon slope perpendicular to the incidence direction is much more severe than that of the opposite side of canyon. And the ground surface has been characterized by larger deformations in the case of oblique incident waves. It is also concluded that the low piers and frame of the continuous rigid frame bridge ape more sensitive to the multi-support seismic excitations than the flexible high piers. The canyon topography as well as the oblique incidence of the waves brings the continuous rigid frame bridge severe responses, which should be taken into account in bridge design.

Effects of topography on the sub-tidal circulation in the southwestern Huanghai Sea(Yellow Sea)in summer

A nested circulation model system based on the Princeton ocean model （POM） is set up to simulate the currentmeter data from a bottom-mounted Acoustic Doppler Profiler （ADP） deployed at the 30 m depth in the Lunan（South Shandong Province, China） Trough south of the Shandong Peninsula in the summer of 2008, and to study the dynamics of the circulation in the southwestern Huanghai Sea （Yellow Sea）. The model has reproduced well the observed subtidal current at the mooring site. The results of the model simulation suggest that the bottom topography has strong steering effects on the regional circulation in summer. The model simulation shows that the Subei （North Jiangsu Province, China）coastal current flows north- ward in summer, in contrast to the southeastward current in the center of the Lunan Trough measured by the moored currentmeter. The analyses of the model results suggest that the southeastward current at the mooring site in the Lunan Trough is forced by the westward wind-driven current along the Lunan coast, which meets the northward Subei coastal current at the head of the Haizhou Bay to flow along an offshore path in the southeastward direction in the Lunan Trough. Analysis suggests that the Subei coastal current, the Lunan coastal current, and the circulation in the Lunan Trough are independent current systems con- trolled by different dynamics. Therefore, the current measurements in the Lunan Trough cannot be used to represent the Subei coastal current in general.

Topography effect on ambient noise tomography using a dense seismic array

With the rapid increase of dense seismic array deployment, more and more ambient noise studies have been applied on short period surface waves tomography. For arrays with inter-station distance of several hundred meters,the effect of surface topography has to be considered. In this study, we investigate topography effect on ambient noise surface wave tomography using synthetic data from different topographic models. Our travel times are synthetized considering surface topography, and shear wave inversions are performed by incorporating and not incorporating topography respectively. Our inversion results suggest that topography does affect subsurface shear wave velocity inversion. If topography is not considered, although the pattern of the structure may be recovered reasonably well, the depth distribution of velocity structure can be distorted. The maximum distortion depth is generally correlated with the relief of the topography and the amplitude of the velocity anomalies. Finally, our example of real data inversion in a mountain area demonstrates good correlation between shear velocity and the geological settings, as well as the core sample in that area.

The plurality effect of topographical irregularities on site seismic response

Topography can have signifi cant eff ects on seismic ground response during an earthquake because topographic irregularities cause considerable diff erences between the seismic waves emitted by the source and the waves reaching the ground surface. When a seismic motion happens in a topographically irregular area, seismic waves are trapped and refl ected between the topographic features. Therefore, the interaction between topographies can amplify seismic ground response. In order to reveal how interaction between topographies infl uences seismic response, several numerical fi nite element studies have been performed by using the ABAQUS program. The results show that topographic features a greater distance between the seismic source and the site would cause greater seismic motion amplifi cation and is perceptible for the hills far away from the source and the ridges. Also, site acceleration response is impacted by surrounding topography further than site velocity and displacement response.

mKdV Equation for Solitary Rossby Waves with Linear Topography Effect in Barotropic Fluids

The modify Korteweg-de Vries(mKdV) equations,governing the evolution of the amplitude of solitary Rossby waves,are derived from quasi-geostrophic vorticity equation by using the perturbation method.The result manifests that the linear topography effect with the change of latitude can induce solitary Rossby wave.

Effects of Topography and Current on Horizontal Irrotational Waves in Shallow Water

Based on the Boussinesq assumption, derived are couple equations of free surface elevation and horizontal velocities for horizontal irrotational flow, and analytical expressions of the corresponding pressure and vertical velocity. After the free surface elevation and horizontal velocity at a certain depth are obtained by numerical method, the pressure and vertical velocity distributions can be obtained by simple calculation. The dispersion at different depths is the same at the O (epsilon) approximation. The wave amplitude will decrease with increasing time due to viscosity, but it will increase due to the matching of viscosity and the bed slope, thus, flow is unstable. Numerical or analytical results show that the wave amplitude, velocity and length will increase as the current increases along the wave direction. but the amplitude will increase, and the wave velocity and length will decrease as the water depth decreases.

Effects of Land-Sea Distribution, Topography and Diurnal Change on Summer Monsoon Modeling

The effects of the land-sea distribution, the topography and the diurnal change of the solar radiation on the summer monsoon modelings are studied by use of a coupled modeling system with a 5-layer primitive equation model of the atmosphere and a 2-layer soil or ocean thermodynamic model which are all solved in a zonal model domain between 60°S and 60°N. The results of numerical simulations show that the quasi-stationary patterns of the mean monsoon circulations are mainly affected by the land-sea distribution and the topography, the effect of the diurnal change is the secondary. However, the inclusion of the diurnal change into the model system may improve the intensity of the simulated monsoon circulation, it can influence the distributive pattern of precipitation to a larger extent,without the diurnal change precipitation in the interior of land would decrease and in the coastal regions it would increase.

A Fluid Experiment of Large-Scale Topography Effect on Baroclinic Wave Flows

The effects of topography on baroclinic wave flows are studied experimentally in a thermally driven rotating annulus of fluid.Fourier analysis and complex principal component (CPC) analysis of the experimental data show that, due to topographic forcing, the flow is bimodal rather than a single mode. Under suitable imposed experimental parameters, near thermal Rossby number ROT = 0.1 and Taylor number Ta = 2.2 × 107, the large-scale topography produces low-frequency oscillation in the flow and rather long-lived flow pattern resembling blocking in the atmospheric circulation. The 'blocking' phenomenon is caused by the resonance of travelling waves and the quasi-stationary waves forced by topography.The large-scale topography transforms wavenumber-homogeneous flows into wavenumber-dispersed flows, and the dispersed flows possess lower wavenumbers.

EFFECTS OF BOTTOM TOPOGRAPHY ON THE STANDING WAVES IN CIRCULAR BASINS

Standing waves in the cylinder hasins with inhomogeneous bottom are considered in this paper. We assume that the inviscid, incompressible fluid is in irrotational undulatory motion. For convenience sake, cylindrical coordinates are chosen. The velocitv potentials, the wave profiles and the modified frequencies are determined (to the third order) as power series in terms of the amplitude divided by the wavelength. Axisymmetrical analytical solutions are worked out. When w=0 , the second order frequency are gained.As an example, we assume that cylinder bottom is an axisymmetricat paraboloid. We find out that the uneven bottom has influences on standing waves. In the end. we go into detail on geometric factors.

The Effect Analysis of Topography on the Spectrum Properties of Anti-Plane Movement

An explicit finite difference method is performed to evaluate the significance of topography effects on the seismic response of viscoelastic sites.The real accelerograms and bell-shape impulse wavelets,slope angle of cliff and angle of incidence on the spectrum property of the incoming waves are all discussed in detail.The conclusions show that the presence of topographic factors and the direction of the incident waves not only significantly affect the peak ground acceleration of a site,but also affect the spectrum properties of the incoming waves,and the effect on the direction of the incident waves is especially remarkable.The study also finds that it is reasonable to analyse spectrum properties with the input of impulse wavelets in the finite element simulation of wave motion.

Numerical and test study on vertical vibration characteristics of pile group in slope soil topography

Topography effects on the vertical vibration responses of pile group are revealed though numerical analysis and model tests.First,a series of model tests with different topography of ground and bedrock are conducted.The results indicate that displacement amplitude of the pile head in sloping ground topography is larger than in horizontal ground.Differential displacement at various positions of the pile cap is observed in non-horizontal topography.Afterwards,a numerical algorithm is employed to further explore the essential response characteristics in group piles of different topography configurations,which has been verified by the test results.The lengths of the exposed and frictional segment,together with the thickness of the subsoil layer,are the dominant factors which cause non-axisymmetric vibration at the pile cap.

Rossby waves with linear topography in barotropic fluids

Rossby waves are the most important waves in the atmosphere and ocean,and are parts of a large-scale system in fluid.The theory and observation show that,they satisfy quasi-geostrophic and quasi-static equilibrium approximations.In this paper,solitary Rossby waves induced by linear topography in barotropic fluids with a shear flow are studied.In order to simplify the problem,the topography is taken as a linear function of latitude variable y,then employing a weakly nonlinear method and a perturbation method,a KdV(Korteweg-de Vries) equation describing evolution of the amplitude of solitary Rossby waves induced by linear topography is derived.The results show that the variation of linear topography can induce the solitary Rossby waves in barotropic fluids with a shear flow,and extend the classical geophysical theory of fluid dynamics.

Seismic analysis of high-speed railway irregular bridge–track system considering V-shaped canyon effect

To explore the effect of canyon topography on the seismic response of railway irregular bridge-track system that crosses a V-shaped canyon, seismic ground motions of the horizontal site and V-shaped canyon site were simulated through theoretical analysis with 12 earthquake records selected from the Pacific Earthquake Engineering Research Center(PEER) Strong Ground Motion Database matching the site condition of the bridge.Nonlinear seismic response analyses of an existing 11-span irregular simply supported railway bridge-track system were performed under the simulated spatially varying ground motions. The effects of the V-shaped canyon topography on the peak ground acceleration at bridge foundations and seismic responses of the bridge-track system were analyzed. Comparisons between the results of horizontal and V-shaped canyon sites show that the top relative displacement between adjacent piers at the junction of the incident side and the back side of the V-shaped site is almost two times that of the horizontal site, which also determines the seismic response of the fastener. The maximum displacement of the fastener occurs in the V-shaped canyon site and is 1.4 times larger than that in the horizontal site. Neglecting the effect of V-shaped canyon leads to the inappropriate assessment of the maximum seismic response of the irregular high-speed railway bridge-track system. Moreover, engineers should focus on the girder end to the left or right of the two fasteners within the distance of track seismic damage.

Large-scale two-dimensional nonlinear FE analysis on PGA amplification effect with depth and focusing effect of Fuzhou Basin

Based on the explicit finite element(FE) method and platform of ABAQUS,considering both the inhomogeneity of soils and concave-convex fluctuation of topography,a large-scale refined two-dimensional(2D) FE nonlinear analytical model for Fuzhou Basin was established.The peak ground motion acceleration(PGA) and focusing effect with depth were analyzed.Meanwhile,the results by wave propagation of one-dimensional(1D) layered medium equivalent linearization method were added for contrast.The results show that:1) PGA at different depths are obviously amplified compared to the input ground motion,amplification effect of both funnel-shaped depression and upheaval areas(based on the shape of bedrock surface) present especially remarkable.The 2D results indicate that the PGA displays a non-monotonic decreasing with depth and a greater focusing effect of some particular layers,while the 1D results turn out that the PGA decreases with depth,except that PGA at few particular depth increases abruptly; 2) To the funnel-shaped depression areas,PGA amplification effect above 8 m depth shows relatively larger,to the upheaval areas,PGA amplification effect from 15 m to 25 m depth seems more significant.However,the regularities of the PGA amplification effect could hardly be found in the rest areas; 3) It appears a higher regression rate of PGA amplification coefficient with depth when under a smaller input motion; 4) The frequency spectral characteristic of input motion has noticeable effects on PGA amplification tendency.

Effects of site conditions on earthquake ground motion and their applications in seismic design in loess region

The Loess Plateau is an earthquake prone region of China, where the effects of loess deposit on ground motion were discovered during the 2008 Wenchuan earthquake(Ms8.0) and the 2013 Minxian-Zhangxian earthquake(Ms6.6). The field investigations, observations, and analyses indicated that large number of casualties and tremendous economic losses were caused not only by collapse and damage of houses with poor seismic performance, landslides, but also amplification effects of site conditions, topography and thickness of loess deposit, on ground motion. In this paper, we chose Dazhai Village and Majiagou Village as the typical loess site affected by the two earthquakes for intensity evaluation, borehole exploration, temporary strong motion array, micro tremor survey, and numerical analysis. The aim is to explore the relations between amplification factors and site conditions in terms of topography and thickness of loess deposit. We also developed site amplification factors of ground motion for engineering design consideration at loess sites. The results showed that the amplification effects are more predominant with increase in thickness of loess deposit and slope height. The amplification mayincrease seismic intensity by 1 degree, PGA and predominant period by 2 times, respectively.

THE EFFECTS OF A SLOPING BOTTOM ON THE EQUATORIAL WAVE-INDUCED DEEP RESIDUAL CURRENTS

Based on an inverted one-and-one-half inviscid reduced gravity shallow water model with bottom topography representing an abyssal layer under a stagnant upper layer on the equatorial β-Plane, a set of field equations governing the wave-induced Lagrangian residual currents is developed. The equations show that the wave-induced Lagrangian residual ot satisfies generalized geostrophic dynamics. The relation of meridional residual current to vertical residual current resulted from the varied bottom is similar to the Sverdrup transport relation. The tranport process of potential vorticity for zeroth order approximation is determined by the advection whose velocity is equal to that of the weve-induced Lagrangian residual current.A Kelvin wave solution and the reated solution of Kelvin wave-induced Lagrangian residual current for the case of slowly varying topography are obtained anaytically. The wave solution shows that a shoaling eastward bottom can decrease the propagation speed of the Kelvin wave and cause it to take a longer time to transmit the energy from the west to the central and easterm parts of the basin, and can also shorten the wavelength and enhance the wave amplitude. The wave-induced residual current solution reveals that the existence of a sloping bottom can result in a onier meridional component of wave-induced mesidual current and that Kelvin wave-induced Lagrangian currents’s responses to bottom variation are greater than those of Kelvin wave orbital currents.

Edge Effects and Coupling Effects in Atomic Force Microscope Images

The AFM images were obtained by an atomic force microscope (AFM) and transformed from the deformation of AFM micro cantilever probe. However, due to the surface topography and surface forces applied on the AFM tip of sample, the deformation of AFM probe results in obvious edge effects and coupling effects in the AFM images.The deformation of AFM probe was analyzed,the mechanism of the edge effects and the coupling effects was investigated, and their results in the AFM images were studied. It is demonstrated by the theoretical analysis and AFM experiments that the edge effects make lateral force images more clear than the topography images,also make extraction of frictional force from lateral force images more complex and difficult. While the coupling effects make the comparison between topography images and lateral force images more advantage to acquire precise topography information by AFM.

Substructure Method of Three-Dimensional Semi-Analytic Boundary Element and Its Application to Seismic Scattering of Hill Topography

In this paper,a substructure method of three-dimensional semi-analytic boundary element is established.The seismic scattering by three-dimensional topography of a hill can be analyzed by the method in frequency domain.Using this method,the computational effort and storage space are reduced considerably.Finally,analytic results are given.

Scattering of Plane P Waves by Circular-arc Canyon Topography:High-frequency Solution

Through the Fourier-Bessel series expansion of wave functions,the analytical solution to the two-dimensional scattering problem of incidental plane P waves by circular-arc canyon topography with different depth-to-width ratio is deduced.Unlike other existing analytical solutions,in order to ensure that the analytical solution is valid for higher frequency incident waves,the asymptotic properties of cylindrical functions are in this paper introduced to directly determine the unknown coefficients of scattering waves,avoiding the solution of linear equation systems and corresponding numerical issues,which in turn expand the frequency band in which the analytical solution is valid.Comparison with other existing analytical solutions demonstrates that the proposed analytical solution is correct.Furthermore,the scattering effects of a circular-arc canyon on the incident plane P wave are analyzed in a comparatively broad frequency band.