A numerical model for the dynamic analysis of inclined pile groups

The paper presents a numerical model for the dynamic analysis of pile groups with inclined piles in horizontally layered soil deposits. Piles are modelled with Euler–Bernoulli beams, while the soil is supposed to be constituted by independent infinite viscoelastic horizontal layers. The pile–soil–pile interaction as well as the hysteretic and geometric damping is taken into account by means of two‐dimensional elastodynamic Green's functions. Piles cap is considered by introducing a rigid constraint; the condensation of the problem permits a consistent derivation of both the dynamic impedance matrix of the soil–foundation system and the foundation input motion. These quantities are those used to perform inertial soil–structure interaction analyses in the framework of the substructure approach. Furthermore, the model allows evaluating the kinematic stress resultants in piles resulting from waves propagating in the soil deposit, taking into account the pile–soil–pile interactions. The model validation is carried out by performing accuracy analyses and comparing results in terms of dynamic impedance functions, kinematic response parameters and pile stress resultants, with those furnished by 3D refined finite element models. To this purpose, classical elastodynamic solutions are adopted to define the soil–pile interaction problem. The model results in low computational demands without significant loss of precision, compared with more rigorous approaches or refined finite element models. Copyright © 2015 John Wiley & Sons, Ltd.     

Resistance of soil to a horizontally vibrating pile

The resistance of a soil layer to steady horizontal vibration of an elastic pile is theoretically investigated. The pile is assumed to be vertical and of circular cross-section. The soil is modelled as a linear viscoelastic layer with hysteretic material damping. A closed form solution is obtained for the resistance of the soil layer to the motion. This resistance depends on shear modulus of soil, frequency, pile slenderness, material damping and Poisson's ratio. A parametric study of the effect of these parameters is included. The soil layer resistance is expressed in a form which can be used directly in the solution of the soil-pile interaction problem which is treated in a subsequent paper. The approach also applies for rigid deeply embedded footings.     

A model for the 3D kinematic interaction analysis of pile groups in layered soils

The paper presents a numerical model for the analysis of the soil–structure kinematic interaction of single piles and pile groups embedded in layered soil deposits during seismic actions. A finite element model is considered for the pile group and the soil is assumed to be a Winkler‐type medium. The pile–soil–pile interaction and the radiation problem are accounted for by means of elastodynamic Green's functions. Condensation of the problem permits a consistent and straightforward derivation of both the impedance functions and the foundation input motion, which are necessary to perform the inertial soil–structure interaction analyses. The model proposed allows calculating the internal forces induced by soil–pile and pile‐to‐pile interactions. Comparisons with data available in literature are made to study the convergence and validate the model. An application to a realistic pile foundation is given to demonstrate the potential of the model to catch the dynamic behaviour of the soil–foundation system and the stress resultants in each pile. Copyright © 2009 John Wiley & Sons, Ltd.     

Time-domain solution for transient dynamic response of a large-diameter thin-walled pipe pile

The propagation of stress waves in a large-diameter pipe pile for low strain dynamic testing cannot be explained properly by traditional 1D wave theories. A new computational model is established to obtain a wave equation that can describe the dynamic response of a large-diameter thin-walled pipe pile to a transient point load during a low strain integrity test. An analytical solution in the time domain is deduced using the separation of variables and variation of constant methods. The validity of this new solution is verifi ed by an existing analytical solution under free boundary conditions. The results of this time domain solution are also compared with the results of a frequency domain solution and fi eld test data. The comparisons indicate that the new solution agrees well with the results of previous solutions. Parametric studies using the new solution with reference to a case study are also carried out. The results show that the mode number affects the accuracy of the dynamic response. A mode number greater than 10 is required to enable the calculated dynamic responses to be independent of the mode number. The dynamic response is also greatly affected by soil properties. The larger the side resistance, the smaller the displacement response and the smaller the refl ected velocity wave crest. The displacement increases as the stress waves propagate along the pile when the pile shaft is free. The incident waves of displacement and velocity responses of the pile are not the same among different points in the circumferential direction on the pile top. However, the arrival time and peak value of the pile tip refl ected waves are almost the same among different points on the pile top.     

Dynamic pile response using two pile-driving techniques

Because of disadvantages caused by pile top driving, a new pile driving technique by which the hammer is inside the pile has been developed by contractors. The so called “down-the hole” piling system is used to drive a tubular pile in an experimental set-up in the laboratory. This new technique is tested and compared with pile top driving using similar hammer energy. A reduction of noise and the opportunity to save steel are confirmed during a field test program. Also, a reduction in driving time and a higher bearing capacity have been observed. Some similar conclusions are arrived at in the laboratory study, specially the low level of stresses in the pile and the shaft friction.     

Green's function for three-dimensional elastic wave equation with a moving point source on the free surface with applications

High-speed train seismology has come into being recently. This new kind of seismology uses a high-speed train as a repeatable moving seismic source. Therefore, Green's function for a moving source is needed to make theoretical studies of the high-speed train seismology. Green's function for three-dimensional elastic wave equation with a moving point source on the free surface is derived. It involves a line integral of the Green's function for a fixed point source with different positions and corresponding time delays. We give a rigorous mathematical proof of this Green's function. According to the principle of linear superposition, we have also obtained the Green's function for a group of moving sources which can be regarded as a model of a traveling high-speed train. Based on a temporal convolution, an analytical formula for other moving sources is also given. In terms of a moving Gaussian source, we deal with the issue of numerical calculations of the analytical formula. Applications to modelling of a traveling high-speed train are presented. We have considered both the land case and the bridge case for a traveling high-speed train. The theoretical seismograms show different waveform features for these two cases.     

Dynamic behaviour of pile foundations in homogeneous and non-homogeneous media

A three-dimensional formulation based on Green's functions of cylindrical loads in layered semi-infinite media is employed to investigate the dynamic behaviour of piles in homogeneous and non-homogeneous half spaces. The pile-soil-pile interaction taking place in pile groups is incorporated in the model. The results presented in this paper include the dynamic stiffnesses and dampings of single piles as well as those of representative 2 × 2 and 4 × 4 square pile groups in the soil media considered in this study. In addition, the distribution of forces applied on the pile cap among the individual piles in a group is investigated.     

A FAST FOURIER TRANSFORM METHOD FOR RAPID COMPUTATION OF GRAVITY AND MAGNETIC ANOMALIES DUE TO ARBITRARY BODIES*

The spectrum of a magnetic or a gravity anomaly due to a body of a given shape with either homogeneous magnetization or uniform density distribution can be expressed as a product of the Fourier transforms of the source geometry and the Green's function. The transform of the source geometry for any irregularly-shaped body can be accurately determined by representing the body as closely as possible by a number of prismatic bodies. The Green's function is not dependent upon the source geometry. So the analytical expression for its transform remains the same for all causative bodies. It is, therefore, not difficult to obtain the spectrum of an anomaly by multiplying the transform of the source geometry by that of the Green's function. Then the inverse of this spectrum, which yields the anomaly in the space domain, is calculated by using the Fast Fourier Transform algorithm. Many examples show the reliability and accuracy of the method for calculating potential field anomalies.     

桩身轴向应变的连续监测法

静力试桩中桩身轴向应变是分析荷载传递机理的基础。滑动测微计可连续地测定桩身每米内的平均应变,通过荷载-应变关系曲线可较准确地计算轴向力、摩阻力、端阻力、负摩阻力;水平试桩时安装二条测管可准确地推算挠度曲线、最大弯矩点,临界荷载、极限荷载等桩基设计的主要参数,还可全面地评价桩身质量。该仪器不仅可用于各类试桩,还可用于各类岩土工程的现场位移监测。     

钢管桩单桩复合地基加固隧道软土地基试验研究

为了对宝兰客运专线王家沟隧道软弱地基进行加固处理,并了解加固后的桩基受力状态,通过现场试验及数值模拟,研究钢管桩单桩复合地基的荷载沉降特性及钢管桩轴力、桩侧摩阻力以及桩身弯矩的变化规律。研究结果表明:由现场试验所得的P-s(荷载-位移)、s-lgt(位移-时间的对数)以及s-lgp(位移-荷载的对数)曲线没有明显可以确定极限承载力的特征点,根据规范采取控制沉降的方式给出极限承载力特征值为200 kPa,并可以此作为设计依据。根据数值模拟中钢管桩的总沉降量以及荷载沉降"归一化曲线",数值模拟可以作为现场试验的必要补充。数值模拟结果显示:桩身轴力呈"D"状分布,最大值为59.8 kN;在距桩顶2 m桩长范围内有负摩阻力产生,其余部位均为正摩阻力,负摩阻力最大值约为130 kPa,正摩阻力最大值约为50 kPa,且桩身中性点并不唯一;桩身上部有弯矩产生,但数值很小,对钢管桩稳定性的影响可以忽略。     

Dynamics of resilient-friction base isolator (R-FBI)

The Resilient-Friction Base Isolator (R-FBI) is composed of a set of flat rings which can slide on each other with a central rubber core and/or peripheral rubber cores. In this base isolator the interfacial friction force acts in parallel with the elastic force in the rubber. It combines the beneficial effect of friction damping with that of the resiliency of rubber. The rubber cores distribute the sliding displacement and velocity along the height of the R-FBI. They do not carry any vertical loads and are not vulcanized to the sliding rings. The system's analytical model and the computer experimental results for both horizontal and vertical components of recorded ground motions and various levels of friction and damping are presented. These results clearly demonstrate the R-FBI's potential as an effective aseismic base isolator.     

The influence of a coastal headland on oceanic boundary currents

Abstract

The steady state circulation of a constant barotropic current around a coastal headland, bay, or combination of the two, located on a flat bottom, mid-latitude β-plane is considered. The maximum displacement of the coastal features from the mean straight coastline is assumed to be small compared to the longshore variation of the coastline. Under this slowly varying coastline approximation, a linearised vorticity equation is derived for the perturbation stream function. An analytical solution for the perturbation stream function is obtained using a Green's function technique. For a specified coastline the effects of coastal orientation, linear friction and the strength of the mean flow are investigated. The model predicts that the flow field will adopt the pattern of the coastline. The question of whether a coastal feature is likely to induce linear flow dynamics within the coastal boundary layer is also addressed. In the case when a single Gaussian headland or bay violates the slowly varying longshore condition the model predicts that flow stagnation will not occur. However for multiple headlands and bays, flow stagnation is possible when the slowly varying longshore condition is sufficiently violated.

Cape Mendocino and Point Conception along the California coast can be modelled using either a single Gaussian headland coastline or a multiple headland and bay coastline. In either case the model coastline does not vary slowly alongshore and nonlinear flow in the coastal region is likely. A permanent eddy to the south of Point Conception is likely to testify to the non-linear flow regime induced by the headland.     

Experimental investigation on seismic behavior of scoured bridge pier with pile foundation

This study investigated the seismic performance and soil‐structure interaction of a scoured bridge models with pile foundation by shaking table tests using a biaxial laminar shear box. The bridge pier model with pile foundation comprised a lumped mass representing the superstructure, a steel pier, and a footing supported by a single aluminum pile within dry silica sand. End of the pile was fixed at the bottom of the shear box to simulate the scenario that the pile was embedded in a firm stratum of rock. The bridge pier model was subjected to one‐directional shakes, including white noise and earthquake records. The performance of the bridge pier model with pile foundation was discussed for different scoured conditions. It is found that the moment demand of pile increases with the increase of scoured depth whereas the moment demand of the bridge pier decreases, and this transition may induce the bridge failure mechanism transform from pier to pile. The seismic demand on scoured pile foundations may be underestimated and misinterpreted to a certain degree. When evaluating the system damping ratio with SSI, the system response may not be significantly changed even if the soil viscous damping contribution is varied. Copyright © 2014 John Wiley & Sons, Ltd.     

Dynamic-stiffness matrix of soil by the boundary-element method: Conceptual aspects

Starting from a weighted-residual formulation, the various boundary-element methods, i.e. the weighted-residual technique, the indirect boundary-element method and the direct boundary-element method, are systematically developed for the calculation of the dynamic-stiffness matrix of an embedded foundation. In all three methods, loads whose analytical response in the unbounded domain can be determined are introduced acting on the continuous soil towards the region to be excavated. In the weighted-residual technique and in the indirect boundary-element method, a weighting function is used; in the latter case, it is selected as the Green's function for the surface traction. In the direct boundary-element method, the surface traction along the structure-soil interface is interpolated. The same type of boundary matrices which have a clear physical interpretation are identified in the three formulations, each of which is illustrated with a simple static example. The indirect boundary-element method leads to the most accurate results. The guaranteed symmetry and the fact that the displacement arising from the applied loads can easily be calculated and compared to the prescribed displacement makes the indirect boundary-element method especially attractive for calculating the dynamic-stiffness matrix of the soil. Instead of calculating the dynamic-stiffness matrix of the embedded foundation with the boundary-element method, it can be determined as the difference of those of the regular free field and of the excavated part. The calculation of the former does not require the Green's function for the surface traction. The dynamic stiffness of the excavated part can be calculated by the finite-element method.     

Soil reaction to lateral harmonic pile motion

The analytical representation of dynamic soil reaction to a laterally-loaded pile using 3D continuum modeling is revisited. The governing elastodynamic Navier equations are simplified by setting the dynamic vertical normal stresses in the soil equal to zero, which uncouples the equilibrium in vertical and horizontal directions and allows a closed-form solution to be obtained. This physically motivated approximation, correctly conforming to the existence of a free surface, was not exploited in earlier studies by Tajimi, Nogami and Novak and leads to a weaker dependence of soil response to Poisson's ratio which is in agreement with numerical solutions found in literature. The stress and displacement fields in the soil and the associated reaction to an arbitrary harmonic pile displacement are derived analytically using pertinent displacement potentials and eigenvalue expansions over the vertical coordinate. Both infinitely long piles and piles of finite length are considered. Results are presented in terms of dimensionless parameters and graphs that highlight salient aspects of the problem. A detailed discussion on wave propagation and cutoff frequencies based on the analytical findings is provided. A new dimensionless frequency parameter is introduced to demonstrate that the popular plane-strain model yields realistic values for soil reaction only at high frequencies and low Poisson's ratios.     

Horizontal dynamic response of a large-diameter pipe pile considering the second-order effect of axial force

The second-order effect of axial force on horizontal vibrating characteristics of a large-diameter pipe pile is theoretically investigated. Governing equations of the pile-soil system are established based on elastodynamics. Three-dimensional wave equations of soil are decoupled through differential transformation and variable separation. Consequently, expressions of soil displacements and horizontal resistances can be obtained. An analytical solution of the pile is derived based on continuity conditions between the pile and soil, subsequently from which expressions of the complex impedances are deduced. Analyses are carried out to examine the second-order effect of axial force on the horizontal vibrating behavior of the pipe pile. Some conclusions can be summarized as follows: stiffness and damping factors are decreased with the application of axial force on the pile head; distributions of the pile horizontal displacement and rotation angle are regenerated due to the second-order effect of the applied axial force; and redistributions of the bending moment and shearing force occur due to the second-order effect of the applied axial force.     

打桩引起的地面振动的研究

为了对打桩引起的地面振动进行研究,应用一维应力波理论建立了粘弹性成层土中等截面弹性桩的力学模型,得到了桩中任意一点处位移的半解析解。利用桩与土的相互作用将桩对土的作用力简化到各土层面上。在复阻尼理论和纳维方程的基础上,利用分层法得到了任意荷载作用下土的位移、速度和加速度的解。从而得到了打桩引起的地面振动的衰减特性。通过实测结果和计算结果的比较说明了该方法的可行性。     

Geophysical experiments to image the shallow internal structure and the moisture distribution of a mine waste rock pile

Several field surveys of a waste rock pile were carried out during the summers of 2002 and 2003 using ground-penetrating radar, electromagnetic conductivity and DC resistivity imaging. The waste rock deposit is prone to generate acid mine drainage (AMD) due to the oxidation of sulphidic minerals. One of the most critical factors that lead to the production of AMD is unsaturated water flow and the ensuing moisture distribution in the waste rock. This geophysical characterization study, performed over a 30 m × 30 m test zone, was designed to image the internal structure controlling the water flux at shallow depth. The subsurface was found to consist of three zones for the first 6 m of the pile, mainly based on electrical resistivities: a thin superficial conductive material, an intermediate 2 to 3 m thick highly resistive zone, and a lower, more conductive medium. With the help of hydrogeological tests, chemical analyses and two 2.5 m-deep trenches, it is shown that the two conductive zones are correlated with fine-grained waste rock and the resistive zone correlates with a coarser material. In the two deeper zones, the contact between the two types of waste rock is typically highlighted by a sharp resistive/conductive boundary. An increase of conductance in the relatively thin upper layer towards the edge of the pile appears to be caused by an increase in thickness of the fine-grained material. Additional geophysical surveys carried out on a profile along the flank of the upper bench of the pile show that the main features of the internal structure are sub-parallel to the slope, at least for the first 3 m in depth. The data also show an increase in resistivity from the top to bottom of the slope, in accordance with expected particle segregation, from fine-grained material at the top to coarser material at the bottom. Wide-angle reflection GPR monitoring during large scale infiltration tests seems to indicate preferential flow paths towards the direction of coarser, more pervious material (which also appears to be less oxidized). Water preferentially flows through the coarse-grained material, but it is stored by capillary forces in the fine-grained material. Apart from the deposition methods, the results strongly suggest that factors such as machinery-induced mechanical alteration, construction history of the pile, and increased oxidization near the edges could explain the resistivity model. The model interpreted from geophysical imaging agrees well with the conceptual model of the rock pile. The resistivity and GPR methods appear to be efficient geophysical methods to characterize the internal structure and preferential flow patterns within unsaturated waste rock piles.     

Seismic response of bridge piers on pile groups for different soil damping models and lumped parameter representations of the foundation

This paper presents a wide parametric study aimed at elucidating the influence, on the computed seismic response of bridge piers, of two related aspects of the model: (1) the adoption of the classical hysteretic or the causal Biot's damping models for the soil and (2) the use of two different lumped parameter models of different complexity and accuracy to approximate the impedances of the pile foundation. A total of 2072 cases, including different superstructures, pile foundations, soil deposits, and seismic input signals, are studied. The results are presented so that the influence of the different parameters involved in the analysis can be assessed. From an engineering point of view, both lumped parameter models provide, in general, sufficiently low errors. The choice of the most adequate model for each case will depend not only on the configuration of the structure and the soil-foundation system but also on the assumed soil damping model, whose influence on the computed seismic responses is relevant in many cases. The nonphysical behaviour provided by the classical hysteretic damping model for the soil at zero frequency generates issues in the process of fitting the impedance functions. It is also found that larger deck displacements are predicted by Biot's model due to the higher damping at low frequencies provided by the classical hysteretic damping model.