Single beam analogy for describing soil–pile group interaction

Most laterally loaded piles are flexible in the sense that they are not deformed over their entire lengths. Instead, pile deflections become negligible below an ‘active pile length’ L_a. This L_a is an important parameter that governs the overall behavior of a rigidly capped pile group. In the present approach, piles closely grouped together beneath a superstructure are viewed as a single equivalent upright beam whose stiffness matrix determines L_a. This idea is verified for different cases of pile spacing, and is further extended for nonlinear behavior of soils surrounding grouped piles.     

Centrifuge modelling of raked piles

Inclined piles are prohibited by many codes in seismic areas. Nevertheless the battered effect has not yet been clarified because very few data are available. The present work is a comparison, at reduced scale in the centrifuge, of the response of two simplified pile groups: a 1 × 2 vertical piles and 1 × 2 pile group with one inclined pile. Two configurations are considered: end-bearing and floating pile group, both with pile heads rigidly fixed with a massive cap. First, repeatability tests under horizontal cyclic loading were performed on both floating pile groups. Secondly, repeated horizontal impact tests were performed on both end-bearing pile groups. These impact tests, which highlight the influence of inclined piles on the inertial response of a group, are a first step for the more complex analysis of the performance of such groups under seismic loads where inertial and kinematic interactions are combined. The first part of this work revealed the influence of sand structure around the inclined pile tip on the repeatability of the tests performed on floating pile groups. The second part highlighted differences in the dynamic response between the two end-bearing pile groups through measurements of the pile cap acceleration, the bending moment profile and the axial load in the piles.     

Modelling of raked pile foundations in liquefiable ground

Raked piles are believed to behave better than vertical piles in a laterally flowing liquefied ground. This paper aims at numerically simulating the response of raked pile foundations in liquefying ground through nonlinear finite element analysis. For this purpose, the OpenSees computer package was used. A range of sources have been adopted in the definition of model components whose validity is assessed against case studies presented in literature. Experimental and analytical data confirmed that the backbone force density–displacement (p–y) curve simulating lateral pile response is of acceptable credibility for both vertical and raked piles. A parametric investigation on fixed-head piles subject to lateral spreading concluded that piles exhibiting positive inclination impart lower moment demands at the head while those inclined negatively perform better at liquefaction boundaries (relative to vertical piles). Further studies reveal substantial axial demand imposed upon negatively inclined members due to the transfer of gravity and ground-induced lateral forces axially down the pile. Extra care must be taken in the design of such members in soils susceptible to lateral spreading such that compressive failure (i.e. pile buckling) is avoided.     

Model tests and numerical analyses on horizontal impedance functions of inclined single piles embedded in cohesionless soil

Horizontal impedance functions of inclined single piles are measured experimentally for model soil-pile systems with both the effects of local soil nonlinearity and resonant characteristics.Two practical pile inclinations of 5° and 10° in addition to a vertical pile embedded in cohesionless soil and subjected to lateral harmonic pile head loadings for a wide range of frequencies are considered.Results obtained with low-to-high amplitude of lateral loadings on model soil-pile systems encased in a laminar shear box show that the local nonlinearities have a profound impact on the horizontal impedance functions of piles.Horizontal impedance functions of inclined piles are found to be smaller than the vertical pile and the values decrease as the angle of pile inclination increases.Distinct values of horizontal impedance functions are obtained for the ’positive’ and ’negative’ cycles of harmonic loadings,leading to asymmetric force-displacement relationships for the inclined piles.Validation of these experimental results is carried out through three-dimensional nonlinear finite element analyses,and the results from the numerical models are in good agreement with the experimental data.Sensitivity analyses conducted on the numerical models suggest that the consideration of local nonlinearity at the vicinity of the soil-pile interface influence the response of the soil-pile systems.     

Pulsating of the generalized ion and neutral polar winds

A three-dimensional, time-dependent model of the ion and neutral polar winds was used to study their dynamic evolution during the May 4, 1998 magnetic storm. The simulation tracked the dynamics of five species (O⁺, H⁺, H_s, O_s, and electrons) and covered a 9-h period. During the storm, D_st decreased to −210 nT, Ap reached 300, and K_p was elevated. The IMF B_z component was southward at the start of the storm and for several hours thereafter and then turned northward. However, the magnetospheric energy input to the ionosphere exhibited a 50-min oscillation, with the plasma convection and particle precipitation patterns expanding and contracting in a periodic manner. As a consequence, the ion and neutral polar winds pulsated with an approximate 50-min period. The H⁺ and O⁺ ions displayed cyclic upflows and downflows in the topside ionosphere as well as a highly structured spatial distribution that varied with time. The vertical flux of the neutral H_s atoms was upward at the top of the ionosphere, but the magnitude varied in a cyclic manner in response to the oscillating stormtime energy input. The vertical flux of neutral O_s atoms was downward at the top of the ionosphere and varied significantly with the stormtime energy input. For H⁺, O⁺, and H_s, the maximum total (integrated) vertical flux during the storm was upward at the top of the ionosphere, with values of 8–9×10²⁵ particles/s for H⁺, 2–4×10²⁶ particles/s for O⁺, and 2–3×10²⁷ particles/s for H_s. The corresponding total vertical O_s flux was predominately downward, with only localized areas with positive fluxes.     

Centrifuge modeling of batter pile foundations under sinusoidal dynamic excitation

Batter pile (or inclined pile) foundations are widely used in civil engineering structures. However, their behavior under dynamic loadings is not yet thoroughly understood. This paper presents an experimental work on the behavior of batter and vertical piles considering dynamic soil-pile-superstructure interactions. A series of dynamic centrifuge tests were performed using sinusoidal excitations. The influence of the base shaking (frequency content and amplitude) and of the height of the center of gravity of the superstructure is investigated. Seismic responses are analyzed considering the pile cap displacements and forces (total base shear, overturning and residual moments, axial forces). It is found that in certain cases batter piles play a beneficial role on the dynamic behavior of the pile foundation system. This novel experimental work provides an important database on the behavior of batter pile foundations under dynamic loadings.     

Experimental study of the effect of inclined pile on the seismic behavior of pile group

Seismic behavior of inclined piles has been considered detrimental for years. However, recent researches show that battered piles can have a beneficial effect. In this framework, a series of centrifuge tests on an inclined pile group is performed. The analysis is based on the comparative response of two 2×1 simplified pile groups: one with vertical piles and the other with one vertical and one inclined pile. The response of these pile groups to repeated earthquakes or sinusoidal inputs is analyzed through the response frequencies, the envelop curves of bending moment profiles, the axial loads measured in both piles and the kinematic response of the cap. Results highlight that the effect of inclined pile is highly influenced by the frequency content of the input. In addition, the inclined pile induces non-negligible residual bending moments, higher horizontal stiffness at the pile cap and larger rotation.     

Dynamic stiffness of deep foundations with inclined piles

The influence of inclined piles on the dynamic response of deep foundations and superstructures is still not well understood and needs further research. For this reason, impedance functions of deep foundations with inclined piles, obtained numerically from a boundary element–finite element coupling model, are provided in this paper. More precisely, vertical, horizontal, rocking and horizontal–rocking crossed dynamic stiffness and damping functions of single inclined piles and 2 × 2 and 3 × 3 pile groups with battered elements are presented in a set of plots. The soil is assumed to be a homogeneous viscoelastic isotropic half‐space and the piles are modeled as elastic compressible Euler–Bernoulli beams. The results for different pile group configurations, pile–soil stiffness ratios and rake angles are presented. Copyright © 2010 John Wiley & Sons, Ltd.     

Free Wobble of the Triaxial Earth: Theory and Comparisons with International Earth Rotation Service (IERS) Data

Earth’s free wobble is often referred to as the Euler wobble (for the rigid case) or the Chandler wobble for the real case. In this study, we investigate the theory of the free wobble of the triaxial Earth and demonstrate that: (1) the Euler period should actually be expressed by the complete elliptic integral of first kind, and (2) the trace of the free polar motion is elliptic, with the orientations of its semi-minor and major axes being approximately parallel to the Earth’s principal axes A and B, respectively. Numerical calculations show that, due to the triaxiality of the Earth, the spin rate ω ₃ fluctuates with the semi-Euler/Chandler period, although its amplitude (about 10⁻¹⁹ rad/s) is rather small and beyond the present measurement accuracy; the tilt of the instantaneous spin axis (or the amplitude of the free wobble), θ, has a fluctuation whose amplitude is around 0.34 milli-arcsecond (mas), which could be detected by present observations. Thus, we conclude that the Earth’s triaxial nature has little impact on ω ₃, but has an influence on the polar motion which should not be ignored. On the other hand, our study shows that there is a mechanism of frequency–amplitude modulation in the Chandler wobble which might be a candidate to explain the correlation between the amplitude and period of the Chandler wobble. We compare the theoretical polar parameters (m ₁, m ₂) with the observed values for the Chandler components obtained from the data EOP (IERS) C 04, and find that they coincide with each other quite well, especially for recent years. In addition, a polar wander towards 76.7°W, which is in agreement with previous results given by other scientists, is also obtained.     

Inversion of breakout data from inclined boreholes for stress state of the upper crust in Jizhong depression

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Kinematic internal forces in deep foundations with inclined piles

This paper presents a parametric study that looks into the influence of pile rake angle on the kinematic internal forces of deep foundations with inclined piles. Envelopes of maximum kinematic bending moments, shear forces and axial loads are presented along single inclined piles and 2 × 2 symmetrical square pile groups with inclined elements subjected to an earthquake generated by vertically incident shear waves. Inclination angles from 0° to 30° are considered, and three different pile–soil stiffness ratios are studied. These results are obtained through a frequency–domain analysis using a boundary element–finite element code in which the soil is modelled by the boundary element method as a homogeneous, viscoelastic, unbounded region, and the piles are modelled by finite elements as Euler–Bernoulli beams. The rotational kinematic response of the pile foundations is shown to be a key factor on the evolution of the kinematic internal forces along the foundations. Copyright © 2015 John Wiley & Sons, Ltd.     

Vertical response of single piles: transient analysis by time-domain BEM

The transient dynamic response of single piles in a layered half-space under a time-dependent vertical force is analyzed by an FEM-BEM coupling approach. The pile is modeled by FEM and the layered half-space is modeled by a general cylindrical coordinates time-domain BEM. Only one-dimensional discretization is necessary on the boundaries of the three-dimensional layered half-space by virtue of the Fourier theory, while the pile shaft can be discretized as a one-dimensional elastic beam. The compatibility and equilibrium conditions between pile shaft and soil layers are employed to assemble respective equations into one. Fairly good agreement between two unknown solutions and the current approach is found. Parametric studies reveal the influences of several dimensionless factors, such as E_p/E_s, l/r₀, _p/_s and ν_s. The effect of soil layering and the support condition of the pile tip is also reported by numerical examples.     

Dynamic pile-soil-pile interaction. Part II: Lateral and seismic response

A simplified three-step procedure is proposed for estimating the dynamic interaction between two vertical piles, subjected either to lateral pile-head loading or to vertically-propagating seismic S-waves. The starting point is the determination of the deflection profile of a solitary pile using any of the established methods available. Physically-motivated approximations are then introduced for the wave field radiating from an oscillating pile and for the effect of this field on an adjacent pile. The procedure is applied in this paper to a flexible pile embedded in a homogeneous stratum. To obtain analytical closed-form results for both pile-head and seismic-type loading pile-soil and soil-pile interaction are accounted for through a single dynamic Winkler model, with realistic frequency-dependent ‘springs’ and ‘dashpots’. Final- and intermediate-step results of the procedure compare favourably with those obtained using rigorous formulations for several pile group configurations. It is shown that, for a homogeneous stratum, pile-to-pile interaction effects are far more significant under head loading than under seismic excitation.     

Effects of inertial and kinematic interaction on seismic behavior of pile with embedded foundation

Effects of inertial and kinematic forces on pile stresses are studied based on large shaking table tests on pile-structure models with a foundation embedded in dry and liquefiable sand deposits. The test results show that, if the natural period of the superstructure, T_b, is less than that of the ground, T_g, the ground displacement tends to be in phase with the inertial force from the superstructure, increasing the shear force transmitted to the pile. In contrast, if T_b is greater than T_g, the ground displacement tends to be out of phase with the inertial force, restraining the pile stress from increasing. With the effects of earth pressures on the embedded foundation and pile incorporated in, pseudo-static analysis is conducted to estimate maximum moment distribution in pile. It is assumed that the maximum moment is equal to the sum of the two stresses caused by the inertial and kinematic effects if T_b<T_g or the square root of the sum of the squares of the two if T_b>T_g. The estimated pile stresses are in good agreement with the observed ones regardless of the occurrence of soil liquefaction.     

Cyclic behavior of laterally loaded concrete piles embedded into cohesive soil

Modern seismic design codes stipulate that the response analysis should be conducted by considering the complete structural system including superstructure, foundation, and ground. However, for the development of seismic response analysis method for a complete structural system, it is first imperative to clarify the behavior of the soil and piles during earthquakes. In this study, full‐scale monotonic and reversed cyclic lateral loading tests were carried out on concrete piles embedded into the ground. The test piles were hollow, precast, prestressed concrete piles with an outer diameter of 300 mm and a thickness of 60 mm. The test piles were 26 m long. Three‐dimensional (3D) finite element analysis was then performed to study the behavior of the experimental specimens analytically. The study revealed that the lateral load‐carrying capacity of the piles degrades when subjected to cyclic loading compared with monotonic loading. The effect of the use of an interface element between the soil and pile surface in the analysis was also investigated. With proper consideration of the constitutive models of soil and pile, an interface element between the pile surface and the soil, and the degradation of soil stiffness under cyclic loading, a 3D analysis was found to simulate well the actual behavior of pile and soil. Copyright © 2007 John Wiley & Sons, Ltd.     

Response of fixed offshore platforms to wave and current loading including soil–structure interaction

Fixed offshore platforms supported by pile foundations are required to resist dynamic lateral loading due to wave forces. The response of a jacket offshore tower is affected by the flexibility and nonlinear behaviour of the supporting piles. For offshore towers supported by clusters of piles, the response to environmental loads is strongly affected by the pile–soil–pile interaction. In the present study, the response of fixed offshore platforms supported by clusters of piles is investigated. The soil resistance to the pile movement is modelled using dynamic p–y curves and t–z curves to account for soil nonlinearity and energy dissipation through radiation damping. The load transfer curves for a single pile have been modified to account for the group effect. The wave forces on the tower members and the tower response are calculated in the time domain using a finite element package (ASAS). Several parameters affecting the dynamic characteristics of the platform and the platform response have been investigated.     

均质介质中排桩对瑞利波的阻隔试验分析

本文通过室外试验的方法并绘制二维等值线图以及将波长和双桩变量进行归一化处理来分析瑞利波通过双桩时周边土体振动的变化,结果表明：在桩间、桩前存在振动加强的现象,其中桩间以及桩角处振动强度最大;桩长与波长的比值的增加会使得桩前、桩间土体振动加强,同时也会使得双桩的隔振效果提升。当比值为0.691~0.781的范围内时,各点处变化幅度趋于平缓;桩间距的增加会使得双桩失去相互影响作用,当桩间距与波长的比值在0.34~0.42时,桩前、桩间以及桩后的A_r值趋近于1,即不存在振动加强以及衰减现象;桩径的增加可提升双桩的隔振效果,同时随着桩径与波长的比值增加,桩前、桩间的A_r值均有较小幅度的增加;振源距的增加会使得双桩的隔振效果增强,随着振源距与波长的比值的增加,桩前的A_r值降低了0.13左右,桩间仅仅降低了0.068左右,而桩后的A_r值降低了0.108左右,隔振效果增强,但增强的幅度较小。     

The Effect of Velocity Inversions on H/V

We analyzed the phenomenology of microtremor H/V curves under inversions in the shear-wave velocity (V_s) profile in the subsoil. Under no V_s inversion the spectral signature of the H/V peaks is found to be ‘eye-shaped’ with the horizontal components higher than the vertical. Conversely, under negative velocity gradients, numerous of differences emerge. I) A H/V ratio below 1 is observed for a wide range of frequencies, due to the decrease of the horizontal components below the vertical one. II) In the presence of persistent H/V < 1, small bumps in the H/V ratio given by local minima in the vertical spectral component may represent the relics of the peaks indicating resonances and stratigraphic discontinuities. As a consequence, in the presence of velocity inversions the H/V > 2 SESAME (2004) criterion fails but a stratigraphic interpretation may still be possible. III) The H/V curves should always be interpreted together with the single component spectra. IV) Microtremor H/V measurements for stratigraphic/microzonation purposes on stiff artificial soils, (asphalt, concrete, cement, pavements) should always be avoided since the latter often produce velocity inversions. This may have consequences in the intermediate to high frequency domain ( > 1 Hz) also in the application of reference site methods, like H_site/H_bedrock, to microtremor. Theoretical modeling confirms these experimental findings.     

Ground magnetic characteristics of the storm-time ring current Asymmetry

Using the minute data of the H component of geomagnetic field from the 20°E magnetic meridian chain and the 30°N magnetic latitudinal chain, the temporal evolution characteristics of the equatorial ring current during the storm on November 7-10, 2004 are studied. It is indicated that the UT-MLT and UT-MLAT graphics extremely exhibit the local time distribution, latitudinal variation and temporal evo- lution of the H component. The results show: (1) The UT-MLT contour clearly shows the increasing of the H component mostly around noon during the initial phase, representing the geomagnetic effect from the magnetopause current system. During the main phase, most negative values of the H com- ponent appear around the dusk-side, indicating the dawn-dusk asymmetric distribution of the ring cur- rent. (2) The contour of UT-MLAT suggests the latitudinal variation of the H component decreasing with the enhancement of the latitudes during geomagnetic storm, which is in good agreement with the Dst index. The latitudinal variations provide a new sight for describing the temporal characteristics of the intensity of the storm-time ring current. (3) Both the contours of UT-MLT and UT-MLAT are useful to monitor the space-time distribution of the equatorial ring current.     

Grain-size variation of tephra derived from volcanic umbrella clouds

The relationships among the thickness and grain-size of tephra-fall deposits and the volumetric flow rate of their source umbrella clouds are analytically obtained. The logarithm of the ratio of the probability distribution function based on grain size (ln R _f) in fall deposits at two localities from the vent (r ₁ and r ₂, respectively) has a linear relationship with the particle-settling velocity, v, as: where Q is the volumetric flow rate of the umbrella cloud and A is a constant for a given pair of localities. The volumetric flow rate of the umbrella cloud can be estimated from granulometric data using this formula. Generally, the thickness–distance relationship of tephra-fall deposits depends on the initial grain-size distribution and the volumetric flow rate of the umbrella cloud. The empirical relationship of the exponential thinning behaviour can be extrapolated towards infinite distance only for a specific initial grain size which is similar to a log-normal distribution with σ _φ=2.5, otherwise it holds only in a limited range of distances. In applying these results to the 1991 eruption of Mt. Pinatubo, it is shown that the volumetric flow rate of the umbrella cloud during the climactic phase of 15 June was approximately 5×10¹⁰ m³/s, which is fairly consistent with the expansion rate of the umbrella cloud observed in the satellite images. Received March 20, 1993/Accepted September 11, 1993