A new model for the vibration isolation via pile rows consisting of infinite number of piles

In this study, on the basis of the Floquet transform method, a numerical model for the simulation of the vibration isolation via multiple periodic pile rows with infinite number of piles is established. By means of the fictitious pile method due to Muki and Sternberg, the second kind of Fredholm integral equations for the pile rows are developed by using the fundamental solutions for the half‐space and the compatibility conditions between the piles and half‐space. Employing the Floquet transform method, integral equations for the pile rows in the wavenumber domain are then derived. Solution of the integral equations yields the wavenumber domain solution for the pile rows. The space domain solution can then be retrieved by inversion of the Floquet transform. Numerical results show that the proposed model with the Floquet transform method is in a good agreement with those of the conventional direct superposition method. On the basis of the new model, influences of the spacing between neighboring piles, the Young's modulus of the piles, and the pile length on the vibration isolation effect of the pile rows are investigated. Numerical simulations conducted in this study show that compared with the direct superposition method, the efficiency of the proposed model for simulation of the vibration isolation via pile rows is very high. Copyright © 2012 John Wiley & Sons, Ltd.     

Numerical algorithm for the dynamic analysis of base-isolated structures with dry friction

This paper deals with the techniques for solving ordinary differential equations with essential nonlinearity arising from the representation of frictional force by the sign function of the relative velocity. This problem is connected with dynamic behavior studies of base-isolated structures with dry friction devices.Mathematical evidence is presented concerning the inaccuracies of the solution which are connected with the representation of the frictional force by the sign function. An approximation of this sign model is made on the basis of the appropriate linearization of a small part of the frictional force function. A numerical algorithm for the dynamic analysis of base-isolated structures with dry friction is proposed. Numerical tests are carried out for establishing the exactness of the proposed techniques. The obtained results prove the accuracy of the techniques.     

On a power series solution to the Boussinesq equation

For certain initial and boundary conditions the Boussinesq equation, a nonlinear partial differential equation describing the flow of water in unconfined aquifers, can be reduced to a boundary value problem for a nonlinear ordinary differential equation. Using Song et al.'s (2007) [7] approach, we show that for zero head initial condition and power-law flux boundary condition at the inlet boundary, the solution in the form of power series can be obtained with Barenblatt's (1990) [2] rescaling procedure applied to the power series solution obtained in Song et al. (2007) [7] for the power-law head boundary condition. Polynomial approximations can then be obtained by taking terms from the power series. Although for a small number of terms the newly obtained approximations may be worse than polynomial approximations obtained by other techniques, any desired accuracy can be achieved by taking more terms from the power series.     

Hydraulics of runoff and loess loam deposition

On many more or less loamy soils, rill erosion is reported to start on slopes that are equal to or steeper than 2–3°; critical Froude numbers for the start of rill wash on these slopes vary between 2·0 and 3·0. This explains why colluvial deposition often occurs on slopes below 2–3°, when water spreads out at the downslope extremities of the rills. The critical hydraulic conditions for loess loam deposition were tested in the laboratory for slopes of 0·5° and 2°, applying unit-discharges (q) up to 10 cm²/s. It appeared from these experiments that for afterflow, without raindrop impact, deposition starts for critical load concentrations (c_cr) varying between several g/1 and about 60 g/l. Under rain c_cr amounts to a minimum value of 100–125 g/l and it increases when the runoff film becomes thinner. Nevertheless, deposition in pluvial runoff is also possible, as was the case during the Weichselian, according to data from quarries in Belgium and in The Netherlands. A modified Kalinske equation is proposed for c_cr prediction, with the introduction of a typical empirical coefficient C_r and considering such factors as shear stress and mean particle size. Massive sedimentation may occur when it stops raining and afterflow starts, since c_cr values are then much lower. It is shown from the Shields' diagram that loamy suspensions are more sensitive to sedimentation than sands in clear water.     

用内蕴时间理论进行土流变本构方程研究

利用内蕴时间理论对土的流变性进行了理论研究。提出了在准三轴条件下土的流变本构方程 ,并且利用土的三轴流变试验结果对所得土流变本构方程进行了验证。验证结果表明用内蕴时间理论推导的土流变本构方程能很准确地描述土的流变性。     

矿柱稳定性影响因素敏感性分析及其应用研究

为研究矿柱稳定性影响因素的敏感程度,以招金大尹格庄金矿为研究背景,从矿柱载荷、强度、失稳形式及影响因素确定四方面推导出两种矿柱形式的安全系数计算公式,设计采用6因素5水平正交试验对矿柱稳定性影响因素敏感性进行分析,并研究主要影响因素与矿柱安全系数之间的函数关系。研究表明,矿柱宽度、矿体开采深度和矿房宽度3个主要因素对矿柱稳定性影响程度是最为剧烈的;矿柱安全系数随着矿柱宽度地增加呈指数形式递增且递增速率不断加大,随矿体开采深度地增加呈幂函数形式递减且递减速率逐渐变缓,随矿房宽度地增加呈负指数形式递减且降低速率逐渐变慢。利用DPS和Matlab建立的矿柱安全系数回归方程得出保证安全生产的合理矿柱尺寸,矿房宽度应不超过8 m,布置条形矿柱宽度应不小于3.6 m,布置方形矿柱宽度应不小于5.9 m。结合采场矿柱布置实际,应用效果较为理想,可为下中段矿体回采矿块布置提供较好的依据。     

Density estimation of two-phase flow with multiscale and randomly perturbed data

In this paper, we describe an efficient approach for quantifying uncertainty in two-phase flow applications due to perturbations of the permeability in a multiscale heterogeneous porous medium. The method is based on the application of the multiscale finite element method within the framework of Monte Carlo simulation and an efficient preprocessing construction of the multiscale basis functions. The quantities of interest for our applications are the Darcy velocity and breakthrough time and we quantify their uncertainty by constructing the respective cumulative distribution functions. For the Darcy velocity we use the multiscale finite element method, but due to lack of conservation, we apply the multiscale finite volume element method as an alternative for use with the two-phase flow problem. We provide a number of numerical examples to illustrate the performance of the method.     

粒状碎屑溜砂坡运动方程与砂坡土r压力计算（溜砂坡系列研究之三）

在溜砂坡系列研究之二的基础上,对风干砂的运动特征进行了细致观察。将干砂流视为连续介质的流动,对干砂流的运动动力和阻力进行了深入研究,建立了干砂流垂线流速分布方程和干砂流体底面、表面滑动速度方程。结合挡砂工程,将干砂流体视为沿底面（此种砂坡的天然休止角）滑动的三角体,从而导出粒状碎屑溜砂坡水平土压力（或水平推力）计算模型。     

非线性Rossby波所满足的三阶Zakharov方程与低频振荡

本文在基本气流具有水平切变的情况下,利用摄动法导出了非线性Rossby波所满足的三阶Zakharov方程,然后,考虑了基流具有弱切变的情况,通过使用三阶Zakharov方程研究了Rossby波列的第一类不稳定性问题。结果表明:通过非线性作用,大气中的Rossby波列可产生调制不稳定。同时,本文对这种不稳定的区域,增长率和周期进行了详细的计算,并讨论了波振幅、波数、纬度和基流切变对它们的影响,指出Rossby波列的调制不稳定可以激发30～60天的低频振荡。