Numerical simulation of a discontinuous gallery lining's behavior,and its interaction with rock

Deep excavation in some geological media needs lining of the gallery. This could limit the extent of the so‐called excavation damaged zone and the resulting convergence of the material due to tunneling. Boom clay, the reference potential host rock in Belgium for disposal of high‐level radioactive waste, is one of these media for which lining of the gallery walls is essential. A correct simulation of the lining behavior in the course of the excavation process, where the rock comes into contact with the lining, and in the long term, remains a significant challenge in analysis of the whole coupled phenomena of rock in interaction with the lining. This study aims to numerically model the lining behavior. The main objective is to develop a model that could realistically simulate the behavior of a discontinuous lining made of concrete segments. We propose to numerically analyze the response of the blocks in contact with each other and in interaction with rock, with the use of zero‐thickness interface elements. To validate the developed model and a proposed approach, a particular analysis compares the obtained results with the available in situ measurements. This study then discusses the deficiency of the simplistic model that considers a continuous lining. In addition, regarding the contact mechanism on the interface between the rock and the lining, the obtained results demonstrate an interesting relation between the contact phenomena and the shear banding within the rock around the gallery. Copyright © 2017 John Wiley & Sons, Ltd.     

At‐a‐station hydraulic geometry relations, 2: calibration and testing

Using a large number of data sets obtained from various sources, the geometric relations derived in Part 1 are calibrated and verified using the split sampling approach. The calibration of parameters shows that the change in stream power is not shared equally among hydraulic variables and that the unevenness depends on the boundary conditions to be satisfied by the channel under consideration. The agreement between the observed values of the hydraulic variables and those predicted by the derived relations is close for the verification data set and lends credence to the hypotheses employed in this study. Copyright © 2007 John Wiley & Sons, Ltd.     

考虑降雨入渗的非连续性岩体边坡稳定分析

由于断层和节理切割,边坡岩体一般具有非连续特性,降雨入渗是影响其稳定的重要因素之一。应用饱和与非饱和渗流理论建立了岩体边坡的非稳定饱和与非饱和渗流分析模型,并采用块体系统的非连续变形分析建立了降雨入渗非饱和渗流场影响的岩体边坡稳定分析和评价模型。作为应用实例,对某高速公路岩体边坡在降雨入渗条件下的非稳定饱和与非饱和渗流场及其对边坡稳定性的影响进行详细分析,并对边坡的稳定性进行评价。     

Propagation of oblique waves over small bottom undulation in an ice-covered two-layer fluid

Scattering of oblique incident waves by small bottom undulation in a two-layer fluid, where the upper layer has a thin ice-cover while the lower one has the undulation, is investigated within the framework of linearized water wave theory. The ice-cover is being modeled as an elastic plate of very small thickness. There exist two modes of time-harmonic waves–one with lower wave number propagating along the ice-cover (ice-cover mode) and the other with higher wave number along the interface (interfacial mode). A perturbation analysis is employed to solve the corresponding boundary value problem governed by modified Helmholtz equation and thereby evaluating the reflection and transmission coefficients approximately up to first order for both modes. A patch of sinusoidal ripples, having two different wave numbers over two consecutive stretches, is considered as an example and the related coefficients are determined. It is observed that when the wave is incident on the ice-cover surface we always find energy transfer to the interface, but for interfacial incident waves there are parameter ranges for which no energy transfer to the ice-cover surface is possible. Also it is observed that for small angles of incidence, the reflected energy is more as compared to the other angles of incidence. These results are demonstrated in graphical form. From the derived results, the solutions for problems with free surface can be obtained as particular cases.     

Oblique surface wave propagation over a small undulation on the bottom of an ocean

The problem of oblique water wave diffraction by small undulation of the bottom of a laterally unbounded ocean is considered using linear water wave theory. A perturbation analysis is employed to obtain the velocity potential, the reflection and the transmission coefficients up to the first order in terms of integrals involving the shape functions c(x) representing the bottom undulation. Finite cosine transform is used to find the first order potential, and this potential is utilised in obtaining the first order reflection and transmission coefficients. Some particular forms of the shape function representing an exponentially damped undulation, a single hump and a patch of sinusoidal ripples are considered and the integrals for the reflection and transmission coefficients are evaluated. For the exponentially damped undulation, it is observed that the reflection ceases much before transmission while for the single hump, reflection and transmission go hand in hand up to a certain value of the wavenumber, after which they vanish. For the patch of sinusoidal ripples having the same wavenumber, the reflection coefficient up to the first order is found to be an oscillatory function in the quotient of twice the component of the wavenumber along x-axis and the ripple wavenumber. When this quotient becomes one, the theory predicts a resonant interaction between the bed and free surface, and the reflection coefficient becomes a multiple of the number of ripples. High reflection of the incident wave energy occurs if this number is large. Also, when a patch of ripples having different wavenumbers is considered the same result follows. Known results for the normal incidence are recovered as special cases for the patch of sinusoidal ripples. The theoretical observations are shown computationally.     

Response of shear wave from a corrugated interface between elastic solid/viscoelastic half‐spaces

The propagation of plane shear wave at a corrugation interface between elastic solid and viscoelastic liquid half‐spaces has been investigated. Adopting Rayleigh's method of approximation, the reflection and refraction coefficients corresponding to reflected and refracted SH‐waves have been derived for the first order of approximation of the corrugated interface. These coefficients are derived in the closed form for a periodic interface. Numerical computation has been performed for a particular model and the results are depicted graphically. The results of Asano (Bull. Earthquake Res. Inst. 1960; 38 (2):177–197) and Kielczynski and Pajewski (J. Acoust. Soc. Am. 1987; 81 (3):599–605) are recovered from this study. Copyright © 2010 John Wiley & Sons, Ltd.     

非连续子母块体理论模型研究(Ⅱ):实例分析

依据第Ⅰ部分所提出的非连续子母块体理论模型,应用Visual C++语言开发了基于Windows的面向对象的非连续子母块体计算分析模块。通过斜面滑块、两块体相互作用、悬臂梁端部受力等算例验证了所提出的非连续子母块体理论模型及所开发的计算分析模块的可行性与有效性。将开发的计算分析模块应用于石拱桥受极限荷载发生破坏失稳的工程实例中,通过与其他算法的计算结果进行对比讨论,证明了非连续子母块体理论模型在处理材料破坏问题方面的优越性。     

Note on the Generalized Hansen and Laplace Coefficients

Recently, Breiter et al. [Celest. Mech. Dyn. Astron., 2004, 88, 153–161] reported the computation of Hansen coefficients X _k ^{γ ,m} for non-integer values of γ. In fact, the Hansen coefficients are closely related to the Laplace b _s ^(m), and generalized Laplace coefficients b _s,r ^(m) [Laskar and Robutel, 1995, Celest. Mech. Dyn. Astron., 62, 193–217] that do not require s,r to be integers. In particular, the coefficients X ₀ ^{γ ,m} have very simple expressions in terms of the usual Laplace coefficients b _{γ +2} ^(m), and all their properties derive easily from the known properties of the Laplace coefficients.     

Some Recurrence Relations Between Hansen Coefficients

A new system of recurrence relations for Hansen coefficients is obtained. This system gives a connection between only those coefficients which are included in the disturbing function of planetary or satellite motion and allows to compute efficiently the Hansen coefficients for perturbations both from internal and external bodies. The recurrence process can be realized both from high to low and from low to high harmonical terms of the disturbing function. The corresponding algorithms of evaluation of Hansen coefficients are presented. The efficiency of the obtained system of recurrence relations is discussed.     

地下水埋深对作物产量与水分利用效率的影响及作物系数变化

采用排水式蒸渗仪试验,研究不同地下水埋深对冬小麦和春玉米产量和水分利用效率的影响及其作物系数的变化,表明冬小麦和春玉米生育期的地下水位分别控制在1.5 m和1.0 m以下时产量和水分利用效率最为适宜,作物系数随地下水埋深的变化而变化,幅度可达到0.5～0.6,作物系数最大值处于1.2 m埋深处。研究结果可为地下水埋深较...