Exact solution for horizontal displacement at center of the surface of an elastic half space under horizontal impulsive punch loading

The exact analytical solution for the horizontal displacement at the center of the surface of an elastic half space under an impulsive loading having the same spatial distribution as the contact stresses that arise underneath a rigid disk when subjected to a static, horizontal load, is obtained using the Cagniard–De Hoop method. The solution can be used to study the dynamical interaction between soil and structures, and can also be used to assess numerical computations with a finite element or a boundary element program.     

Vertical vibration of an embedded rigid foundation in a poroelastic soil

This paper considers time-harmonic vertical vibration of an axisymmetric rigid foundation embedded in a homogeneous poroelastic soil. The soil domain is represented by a homogeneous poroelastic half space that is governed by Biot's theory of poroelastodynamics. The foundation is subjected to a time-harmonic vertical load and is perfectly bonded to the surrounding half space. The contact surface can be either fully permeable or impermeable. The dynamic interaction problem is solved by employing an indirect boundary integral equation method. The kernel functions of the integral equation are the influence functions corresponding to vertical and radial ring loads, and a ring fluid source applied in the interior of a homogeneous poroelastic half space. Analytical techniques are used to derive the solution for influence functions. The indirect boundary integral equation is solved by using numerical quadrature. Selected numerical results for vertical impedance of rigid foundations are presented to demonstrate the influence of poroelastic effect, foundation geometry, hydraulic boundary condition along the contact surface and frequency of excitation.     

Analytical and numerical solutions for wave propagation in water-saturated porous layered half-space

A fluid-saturated one-layer continuum underlain by a rigid half-space is considered. An exact solution is developed in frequency domain for analyzing disturbance induced by a strip footing located at the surface with vertical harmonic excitation. Since the analytical solution can be used only for very simple conditions, a finite element model has been developed also and compared with the exact solution. It is shown that finite element results are in close agreement with the results which have been obtained by a transformation technique. The proposed finite element scheme can take into account the complex geometry and inhomogeneity for practical problems. Besides this, the analytical results exhibit the overall characteristic of wave propagation in porous media and will provide a representative test problem which can be used for a quantitative evaluation of the accuracy of various numerical solution methods.     

Magnetotelluric response of a two-dimensional sloping contact by the finite element method

Summary The finite element method, with triangular elements, is used to study the effect of a two-dimensional sloping contact on the surface electromagnetic fields. It is found in the case ofH-polarization and small slopes that the electric field and the apparent resistivity near the contact, on the conductive side, are higher than their asymptotic values. In the case ofE-polarization the apparent resistivity and phase values on the conductive side fall off less rapidly to their asymptotic values with decreasing slope resulting in higher apparent resistivity and phase values on the conductive side, than those expected for a vertical contact. The peak in the amplitude and phase of the normalized vertical magnetic field shifts from the resistive side for a vertical contact to the conductive side for a sloping contact. Far from the sloping contact, on the conductive side, higher values are observed for the normalized vertical magnetic field than in the case of a vertical contact.     

竖向地震动对滑动摩擦隔震桥梁结构地震反应的影响

利用接触摩擦单元建立了滑动摩擦隔震桥梁支座在竖向地震动作用下的有限元模型,通过算例讨论了竖向地震动对不同支座摩擦系数和不同刚度(墩径)滑动摩擦隔震桥梁地震反应的影响,初步探讨了竖向地震动的激励方向对分析结果的影响,分析结果表明,竖向地震动对滑动摩擦隔震桥梁结构的地震反应有较大的影响,在竖向地震动较为明显地区的滑动摩擦隔震桥梁结构设计时,应予以考虑。     

基于Lamb问题的谱元法和有限元法模拟精度比较

在地震动数值模拟方法中,谱元法和有限元法是应用较广泛的两种方法。基于经典的Lamb问题模型,首先推导给出地表竖向位移的解析解答。然后分别利用常用的四阶谱元法和线性有限元法,模拟了地表脉冲力源作用下模型的位移响应。考虑有意义的最短波长内的采样点个数及单元高宽比的变化,对比了两种方法的模拟精度;结果表明:对于谱元法,观测点与波源之间需至少包含两个网格,在此条件下,最短波长内包含一个网格（最短波长内5个采样点）时,数值解与解析解的误差小于1%,已达很高的精度;对于有限元法,最短波长内需包含10个网格时才能达到这一精度。此外,在满足网格尺寸要求的前提下,单元水平向与垂直向尺寸的比值在1∶1到5∶1的范围内时,谱元法和有限元法的模拟精度均变化不大。因此,单位波长内采样点个数相同时,谱元法的模拟精度比有限元法高的多,同时,在一定范围内两种方法的模拟结果对于宽高比的变化不敏感。     

Modelling of pile wave barriers by effective trenches and their screening effectiveness

The three-dimensional problem of isolation of vibration by a row of piles is studied numerically on the basis of a model replacing the row of piles by an effective trench in order to reduce the modelling complexity. The analysis is accomplished with the aid of an advanced frequency domain boundary element method, which is used for both the infilled trench and the soil medium in conjunction with a coupling procedure based on enforcement of equilibrium and compatibility at the trench–soil interface. Linear elastic or viscoelastic material behaviour is assumed for both the piles and the soil. The piles can be tubular or solid and have circular or square cross-section. The vibration source is a vertical force, harmonically varying with time, and the row of piles acts as a passive wave barrier. The effective trench model is constructed by invoking well known homogenization techniques used in the mechanics of fibre-reinforced composite materials, and its accuracy is compared against a rigorous boundary element analysis modelling each pile separately in full contact with the soil medium. On the basis of the effective trench model, the screening effectiveness of a row of piles is studied through parametric studies.     

Dynamic plate-soil interaction - finite and infinite, flexible and rigid plates on homogeneous, layered or Winkler soil

An integral method to calculate the solution of a homogeneous or layered soil due to a harmonic point load is described. An infinite plate at the surface of the soil can be introduced in this integration in wavenumber domain, too. Finite structures on the soil are calculated by a combined finite element and boundary element method, which makes use of the point load solution of the soil. The compliance functions for a vertical point load and some vibration modes are calculated for realistic parameters of the plate and the soil and for a wide range of frequencies. The influence of the stiffness of the soil and the foundation is investigated, showing that the soil mainly affects the low-frequent response whereas the structural properties are more important at higher frequencies. A rigid approximation of flexible plates is only found at low frequencies, if the elastic length is used as the radius of a rigid disk. At higher frequencies, a characteristic behaviour of the flexible plate of approximately is observed, what is in clear contrast to the compliance of rigid foundations. A plate on a visco-elastic support (Winkler soil) shows similar displacements as a plate on a homogeneous half-space, but the maximal stresses between the plate and the soil are considerably smaller which is found to be more realistic for a plate on a layered soil. For practical applications, a normalized diagram and some explicit formulas of the exact and the approximate solutions of an infinite plate on a homogeneous half-space are given, which is a useful model to represent the soil-structure interaction of flexible foundations.     

Effects of vertical excitation on the seismic performance of a seismically isolated bridge with sliding friction bearings

A finite element model is constructed for a sliding friction bearing in a seismically isolated bridge under vertical excitation with contact/friction elements. The effects of vertical excitation on the seismic performance of a seismically isolated bridge with sliding friction bearings and different bearing friction coefficients and different stiffness levels (pier diameter) are discussed using example calculations, and the effects of excitation direction for vertical excitation on the analysis results are explored. The analysis results shows that vertical excitation has a relatively large impact on seismic performance for a seismically isolated bridge with sliding friction bearings, which should be considered when designing a seismically isolated bridge with sliding friction bearings where vertical excitation dominates.     

A local model for analysis of pump and treat systems with vertical barrier walls

We present a mathematical model of local, steady groundwater flow near a vertical barrier wall. Flow features represented in the model include an impermeable arc-shaped barrier wall and multiple wells; distant boundary conditions are not included explicitly, but their effects on the local flow field are modelled by specifying a uniform flow at infinity and a constant areal recharge within a local domain. We develop an explicit closed-form solution to the boundary-value problem using the analytic element method. The solution is an extension of a harmonic solution presented by Anderson and Mesa [Anderson EI, Mesa E. The effects of vertical barrier walls on the hydraulic control of contaminated groundwater. Adv Water Resourc 2006;29(1):89–98] which does not include the effects of recharge. We demonstrate that the general solution with recharge consists of the harmonic solution superposed on a special case of the harmonic solution along with two elementary one-dimensional flow solutions. The results are used to investigate the effects of areal recharge on the capture zone envelopes of the pumping wells and on the reduction in discharge that can be achieved by including a barrier wall in a pump and treat design. We find that the benefits of including an open barrier wall in a design, measured as a reduction in the pumping rate required to contain a plume, increase for higher recharge rates. Dimensionless plots of capture zone envelopes are presented for a practical well and barrier wall configuration.     

磁赤道处化极方法

化向地磁极(化极)是最基本的磁测资料处理方法之一,化极能消除或减少斜磁化影响,提高对磁测资料的认识程度和解释水平,对研究地壳产生的磁异常具有重要意义.但低纬度地区特别是磁赤道处,化极处理很不稳定甚至奇异,一直是位场研究的难点.针对地磁纬度较低特别是磁赤道地区磁异常化极的困难,利用从磁北极处垂直磁化向低纬度地区水平磁化方向转换稳定的特点,提出"狭义化赤"概念,并将其与低纬度磁异常"倒相"解释方法结合,提出专门用于磁赤道处化极的方法.该方法扩展了现有的化极理论,实现了磁赤道处的稳定化极.区别于目前任何方法,专门用于(近)水平磁化条件下的化极计算,具有原理简单,实现方便,收敛速度快等特点.对理论模型和实际资料计算表明这种针对磁赤道地区磁异常的化极处理方法是稳定、可靠的.     

Asymptotic formulae for correcting finite element predicted natural frequencies of gravity and embankment dams

Extraction of natural frequencies of a gravity dam or an embankment dam plays an important role in the seismic design of the dam because the seismic response of a dam is dependent largely on the dynamic characteristics of the dam. Owing to the lack of exact solutions and the geometry of a dam, numerical methods such as finite element methods have been often used to extract the natural frequencies of the dam. Since the finite element method is an approximate one, the resulting finite element solution to the natural frequency of a dam cannot be safely used unless its accuracy is evaluated within the acceptable range for the seismic design of the dam. To solve this problem, some asymptotic formulae for correcting the finite element predicted natural frequencies of a gravity dam and an embankment dam have been developed in this paper. Since the present asymptotic formulae are derived from the fact that the finite element solution tends to the exact one if the finite element size used approaches zero, they provide a corrected solution of higher accuracy for the natural frequency of a dam so that the accuracy of a finite element solution can be evaluated against this corrected solution. After the correctness and usefulness of the present formulae are assessed, two practical examples have been given to show how the asymptotic formulae can be used to correct and evaluate the discretization error for the finite element predicted natural frequencies of gravity dams and embankment dams.     

三维陆地可控源电磁法有限元模型降阶快速正演

三维陆地可控源电磁法有限元快速正演的主要瓶颈在于多频率大型稀疏方程组求解问题.本文引入一种基于模型降阶的Krylov子空间投影算法,推导了有限元刚度矩阵的模型降阶形式,构建了频率域传递函数;采用标准正交向量序列,构建一个远远小于有限元刚度矩阵维度的矩阵,该矩阵与频率无关,通过一次模型降阶即可实现多频点有限元方程快速求解.采用基于电场的变分方程,加入散度校正条件,以消除伪解;引入伪δ函数,消除了源点的奇异性,可适用于复杂背景模型三维有限元数值模拟,并为多源的求解奠定了基础;以层状介质模型解析解为标准,通过和基于Pardiso直接求解器的有限元算法（3DFEM）进行比较,模型降阶法计算时间小于前者的1/10,平均相对误差在1.72%,在满足精度要求下,实现了高效率三维有限元数值求解;分别设计了横向高低阻模型和纵向高低阻模型,分析了从近区到远区电场和卡尼亚视电阻率的变化规律,假极值的表现特征,阴影效应的影响等,从而也验证了该算法的正确性.最后,建立了一个地层陷落柱模型,通过模型降阶有限元正演模拟,发现视电阻率断面图在陷落柱上方出现"凹陷",与模型设计吻合,表明该算法对复杂地层模拟具有同样的适用性.     

Geoelectrical and hydrochemical investigations for characterizing the salt water intrusion in the Khanasser valley, northern Syria

An integrated approach of geoelectrical and hydrochemical investigation surveys was proposed for indicating contact regions between saline and fresh groundwater in the Khanasser valley region, northern Syria. The qualitative and quantitative interpretations of 34 vertical electrical soundings (VES) enable to characterize the salt water intrusion laterally and vertically. The established iso-apparent resistivity maps for different AB/2 spacings obviously indicate the presence of a lowresistivity (less than 4 Ohm·m) zone related to the salt water intrusion in the Quaternary and Paleogene deposits. The different hydrochemical and geophysical parameters, such as electrical resistivity, total dissolved solids (TDS) and major ions concentrations used to characterize the salt water intrusion gave almost similar results in locating and mapping the different boundaries of the groundwater salinity. The proposed approach is useful for mapping the interface between different groundwater qualities, and can be therefore used to successfully characterize the salt water intrusion phenomenon in other semi-arid regions. The application of such an approach is a powerful tool and can be used for water resource management in the water scarce areas.     

Cyclic hysteretic flow in porous medium column: model, experiment, and simulations

A periodic vertical movement of the groundwater table results in a subsequent cyclic response of the water content and pressure profiles in the vadose zone. The sequence of periodic wetting and drying processes can be affected by hysteresis effects in this zone. A one-dimensional saturated/unsaturated flow model based on Richards’ equation and the Mualem (Soil Sci. 137 (1984) 283) hysteresis model is formulated which can take into account multi-cycle hysteresis effects in the relation between capillary pressure and water content. The numerical integration of the unsaturated flow equation is based on a Galerkin-type finite element method. The flow domain is discretised by finite elements with linear shape functions. Simulations start with static water content and pressure profiles, which correspond to either a boundary drying or wetting retention curve. To facilitate the numerical solution of the hysteretic case an implicit non-iterative procedure was chosen for the solution of the nonlinear differential equation. Laboratory experiments were performed with a vertical sand column by imposing a high frequency periodic pressure head at the lower end of the column. The total water volume in the column, and the periodic water content profile averaged over time were measured. The boundary drying and wetting curves of the relation between water content and capillary pressure were determined by independent experiments. The simulations of the experimental conditions show a clear effect of the hysteresis phenomenon on the water content profile. The simulations with hysteresis agree well with the measurements. Computed dimensionless water content profiles are presented for different oscillation frequencies with and without consideration of hysteresis.     

High-resolution Givetian-Frasnian boundary recognition from conodont-chemo-stratigraphic correlation at Liujing, Guangxi, South China

The Givetian-Frasnian boundary at Liujing, Guangxi, South China is for the first time recognized and correlated in high resolution using characteristic chemocycles of element abundance fluctuation integrated with conodont biostratignphy. The first appearance of Ancyrodella rotundiloba early form is as a biomarker, and the boundary of lowering fluctuation of element abundance followed by a sequence of characteristic chemocycles with a sequence of cmodonts is as an abiotic auxiliary marker. The error is not more than 0.10 Ma. The study indicates that in a quiet interval, characteristic chemocycles integrated with biomarkers can be used for boundary recognition and regional cormlation in high resolution, and this method has potential for intercontinental correlation     

Improved tilt-depth method for fast estimation of top and bottom depths of magnetic bodies

The tilt-depth method can be used to make fast estimation of the top depth of magnetic bodies. However, it is unable to estimate bottom depths and its every inversion point only has a single solution. In order to resolve such weaknesses, this paper presents an improved tilt-depth method based on the magnetic anomaly expression of vertical contact with a finite depth extent, which can simultaneously estimate top and bottom depths of magnetic bodies. In addition, multiple characteristic points are selected on the tilt angle map for joint computation to improve reliability of inversion solutions. Two- and threedimensional model tests show that this improved tilt-depth method is effective in inverting buried depths of top and bottom bodies, and has a higher inversion precision for top depths than the conventional method. The improved method is then used to process aeromagnetic data over the Changling Fault Depression in the Songliao Basin, and inversion results of top depths are found to be more accurate for actual top depths of volcanic rocks in two nearby drilled wells than those using the conventional tilt-depth method.     

砖墙体抗震承载力仿真分析与试验对比

为研究竖向压应力和高宽比对砖墙体抗震性能的影响,以砖墙体抗震承载力典型试验试件为基础,利用有限元分析软件ANSYS建立适当的空间模型。根据砖墙体的破坏模式和材料性能把墙体划分成块体单元、灰缝单元以及接触单元,为各部分材料选用不同的本构关系模型与破坏准则。并将计算结果与试验结果进行对比,验证文中模型的可适用性。选用经验证后的模型,变换竖向压应力和高宽比,得出相应的结论:墙体的开裂荷载和抗侧承载力随着高宽比的增大明显呈降低的趋势;不同高宽比的墙体,竖向压应力的影响规律不尽相同。     

Magnetic methods in tracing soil erosion,Kharkov Region,Ukraine

Magnetic measurements of soils are an effective research tool in assessing soil erosion. This approach is based on detecting layers showing different magnetic properties in vertical soil profiles and lateral catenas. The objective of this research is to compile data on magnetic susceptibility (MS) of soils in Eastern Ukraine to assess the soil erosion rates. The chernozems of Tcherkascy Tishki (Kharkov Region, Ukraine) have undergone a field crop rotation without proper soil conservation technologies being applied. We conducted an intrinsic element grouping of the magnetic susceptibility values and demonstrated that they can be used as MS cartograms in soil erosion mapping. The study showed a strong correlation between the MS values and the erosion index. MS and the erosion index were found to correlate with the humus content. Magnetic mineralogical analyses suggest the presence of highly magnetic minerals (magnetite and maghemite) as well as weakly magnetic goethite, ferrihydrite, and hematite. Stable pseudosingle-domain (PSD), single-domain (SD), and superparamagnetic (SP) grains of pedogenic origin dominate in the studied chernozems. Being an effective, quick and low cost alternative, magnetic methods can be successfully used in the soil erosion investigations.     

SV波在饱和土体自由表面的反射

基于饱和两相介质弹性波动方程分析SV波在饱和土体自由表面的反射问题,引入波动方程的势函数解答,求解出二维问题中SV波入射情况下饱和土体自由场的位移、速度、加速度和应力响应。在饱和土体自由场响应解析解基础上,建立SV波入射下饱和土体自由场静、动力有限元模型。建模中考虑了如下几方面因素:(1)在不同分析步,对土体单元赋予不同材料本构。通过*model change命令进行单元生死设定,从而实现在初始应力场平衡的静力状态下采用DuncanChang本构模型,而地震波动输入时采用Davidenkov动力本构模型;(2)采用多孔介质黏弹性人工边界条件,在人工边界上分别施加固相和液相介质的弹簧和阻尼来模拟饱和土体中能量的传播;(3)将地震波转化为作用在人工边界上的等效地震荷载,施加到人工边界节点上;(4)土体单元采用4结点平面应变孔压单元(CPE4P)。有限元计算与解析解比较结果表明:SV波在垂直入射和掠入射时,竖向位移响应为零;在45°左右入射时,水平位移响应最大;60°左右入射时,竖向位移响应最大。这些结论与解析解吻合较好,本文模型为建立土-结构动力相互作用模型打下良好的基础。