SH波对浅埋圆柱形弹性夹杂附近多个半圆形凸起的散射

利用复变函数及移动坐标法建立了多个半圆形凸起及附近浅埋弹性夹杂对SH波散射问题的解析方法.求解时将整个求解模型进行分区,区域I为包括多个半圆形凸起在内的多个圆形区域;区域II包括多个半圆形凹陷和1个圆柱形弹性夹杂.然后在两个区域内分别构造满足边界条件的位移解.最后,根据连接面的契合条件,利用移动坐标法将两个区域在公共边界上装配起来,同时考虑弹性夹杂的边界条件,建立起求解该问题的无穷代数方程组.通过算例,讨论了凸起间距,夹杂埋深等参数对地表位移幅值的影响.     

SH波在含圆形孔洞的半圆形凸起处的散射

采用复变函数法研究了含有圆形孔洞的半圆形凸起地形对SH波的散射问题。第一步将所研究的域分为两个域，相应地构造出了所论问题的两组解：一组是在凸起边界上满足应力为零、而其余边界应力待定的圆环域中的级数解，另一个组为含有半圆形凹陷的半空间的解。第二步，通过上述两个域(两组解)在“公共边界”上实施“契合”，建立起求解该问题的无穷代数方程组。第三步，对有限个方程进行数值求解，给出了地表位移幅值和圆形孔洞的表面位移及周边上的动应力集中的数值结果，并讨论了波数及凸起和圆孔半径比等的影响。     

半无限空间界面附近SH波对圆形衬砌的散射

建立了求解半无限空间中SH波对浅埋圆形衬砌结构的散射与动应力集中问题的解析方法。利用SH波散射的对称性和多极坐标的方法，在复平面上构造出了一个可以预先满足半空间自由表面上应力自由的边界条件的浅埋圆形衬砌对稳态SH波散射的波函数，并构造出衬砌内的散射波函数。然后根据衬砌周围的边界条件，将该问题转化为对一组无穷代数方程组的求解。最后给出了具体算例，并讨论了其数值结果。     

SH波入射时半圆形凸起地形附近浅埋圆形衬砌结构的动应力分析

本文给出了地下圆形衬砌结构与地面上的半圆形凸起地形对垂直于地面入射的SH波散射问题的解答。方法是将求解区域分割成两部分。其一为包含半圆形凸起地形在内的圆形区域Ⅰ，其二为带有一个半圆形凹陷和一个圆形衬砌结构的弹性半空间Ⅱ，半圆形凹陷部分为其公共边界，在区域Ⅰ和Ⅱ中分别构造其位移解，然后再通过移动坐标，使其满足“公共边界”上的条件和地下衬砌的边界条件，建立起求解该问题的无穷代数方程组。最后，本文给出了算例，并讨论了数值结果，给出了圆形衬砌结构周边上的动应力集中系数变化规律。     

半无限空间中圆形孔洞周围SH波的散射

建立了求解在含有圆形孔洞的弹性半空间中SH波散射与圆形孔洞附近动应力集中问题的解析方法。利用SH波散射的对称性和多极坐标的方法，构造了一个可以预先满足半空间自由表面上应力自由边界条件的圆形孔洞对SH波散射的波函数。利用这一波函数，则可将该问题转化成对一个圆形孔洞散射的求解问题。该问题的解答最终又可归结为对一组无究代数方程组的求解问题，并可利用截断有限项的方法对其进行计算，最后给出了有关圆形也洞附近动应力集中问题的算例和数值结果，并讨论了波数与圆孔至自由边界距离变化对动应力集中的影响。     

SH波入射时等腰三角形与半圆形凸起地形的地震动

利用复变函数和移动坐标研究了等腰三角形凸起和半圆形凸起地形对SH波的散射.首先将求解区域分为三个部分,区域I为一个带有半圆形弧线的等腰三角形区域,区域II为含有两个半圆形凹陷的弹性半空间,区域III为包括半圆形凸起在内的圆形区域.在区域I中构造满足在腰三角形斜边上应力自由的驻波函数WA,在区域II中分别构造两个半圆形凹陷的散射波WB和WC,且两者均预先满足水平界面上应力为零的边界条件,在区域III构造一个上半部边界应力为零,而其余部分位移、应力任意的驻波函数.将所研究的问题转换成一个求解满足在"公共边界"上位移应力连续的问题.可利用坐标移动方法,通过傅立叶级数展开,建立该问题代数方程组,并采用截断有限项的方法对其进行求解.最后,给出了一个算例.     

SH波入射时多个半圆形沉积谷地附近浅埋圆形孔洞的动力分析

本文采用辅助函数的思想,利用复变函数和多级坐标的方法给出了SH波入射条件下多个半圆形沉积谷地附近浅埋圆形孔洞动力分析问题的解答。将整个求解区域分割成两部分来处理,区域I为多个半圆形沉积谷地,区域II为浅埋圆形孔洞附近带半圆形凹陷的半无限弹性空间。在区域I和II中分别构造位移解,并在二个区域的“公共边界”上实施位移应力的连续条件,建立求解该问题的无穷代数方程组。最后,本文给出了算例和数值结果,并对其进行了讨论。     

SH波在浅埋可移动圆柱形刚性夹杂处的散射与地震动

采用复函数、多极坐标法研究了含有可移动圆柱形刚性夹杂的弹性半空间对SH波的散射问题。构造一个能自动满足含可移动刚性圆柱的弹性半空间自由表面上应力为零的边界条件的散射波,应用可移动圆柱形刚性夹杂的运动条件来确定该散射波。最终则可将求解问题归结为求解一个无穷代数方程组,采用截断有限项的方法对其进行求解。给出了地表位移幅值的数值结果,并讨论了各种参数对它的影响。     

SH波入射时半圆形凸起与凹陷地形的地震动

研究了弹性半空间中半圆形凸起与凹陷相连地形对SH波的散射问题。将整个求解区域分割为2部分,在其中分别构造满足边界条件的位移解,通过移动坐标使之满足“公共边界”以及半圆形凹陷表面上的边界条件,从而建立起求解该问题的无穷代数方程组。最后,给出了地表位移幅值的数值结果以及凸起地形顶点和凹陷地形最低点处位移幅值的反应谱并进行了讨论。     

双相介质半空间中椭圆形夹杂及直线裂纹对SH波的散射

采用Green函数法和保角映射法研究了双相介质半空间中位于界面两侧的浅埋椭圆形夹杂和直线裂纹对SH的散射问题。首先,将研究模型沿垂直界面剖分为两个直角平面进行研究:含有椭圆形夹杂的区域I和含有直线裂纹的区域II。利用保角映射法和镜像叠加原理构造区域I内的散射波场,利用裂纹"切割"技术和Green函数法构造区域II中直线裂纹。其次,利用界面"契合"技术在契合面上施加未知外力系使契合模型满足界面上的应力和位移连续性条件,建立求解附加未知外力系的无穷代数方程组,并通过傅里叶级数展开和有限项截断求解;最后,通过具体算例讨论了入射角度、入射波数和直线裂纹等因数对椭圆形夹杂的动应力集中系数的影响。     

Analysis of a guided wave along a conducting structure in a borehole

A guided wave along a borehole is often observed in borehole radar measurements. These guided waves deform the antenna pattern and can cause artefacts in radar measurements. A water-filled borehole or a conducting logging cable can function as a waveguide for electromagnetic waves under some conditions. We describe the theoretical characteristics of such a guided wave in a borehole and compare them with our experiments. The measured signal discussed was obtained with a directional borehole radar. This radar uses a cylindrical conformal array antenna as receiver and is a model of a conducting structure in a borehole. The induced field around the borehole was compared with the theory. The most fundamental symmetrical and asymmetrical modes were TM₀₁ and HE₁₁, and they were identified in the measured signals using time–frequency distribution analysis and by observation of the azimuthal field distribution of the magnetic field.     

Steady flow to a well near a stream with a leaky bed

We present an explicit analytic solution for steady, two-dimensional ground water flow to a well near a leaky streambed that penetrates the aquifer partially. Leakage from the stream is approximated as occurring along the centerline of the stream. The problem domain is infinite and pumping on one side of the stream induces flow on the other side. The solution includes the effects of uniform flow in the far field and a sloping hydraulic head in the stream. We use the solution to investigate the interaction between ground water and surface water in the stream, the effects of pumping on the opposite side of the stream, and the effects of the leaky streambed on the capture zone envelope of the well. We develop a relationship between parameters such that the pumping well will not capture water from the stream, or from the opposite side of the stream. When the discharge of the well is large enough to capture water from the stream, the shape of the capture zone envelope depends on flow conditions on the side of the stream opposite the well.     

The safety distance of a tunnel under-traversing a slope body with a landslide-prone zone

At present, substantial scientific research achievements have been made in the research on landslide occurrence, movement mechanism, mitigation measures, and structural stability during tunnel excavation. However, the interaction mechanism of a tunnel under-traversing a slope body with potential landslides is still not well understood. Based on the field data provided by previous investigations in the study area, six sets of 1:100 laboratory experiment model tests were conducted to study the stability of the landslide-prone zone of the slope body with an under-traversing tunnel. The selected distances between the tunnel and the sliding surface are 1.5, 3, and 5 times of the tunnel diameter, respectively. The experiment results show the interaction between the landslide-prone zone and the tunnel, elucidating the effect of potential landslides during the tunnel excavation process and the reaction of the landslide slip on the tunnel structure. Several conclusions are obtained: ① During the process of tunnel excavation, the vertical displacement of the tunnel vault decreases with the increase of the buried depth. ② The vertical displacement of the sliding surface increases with the increase of the buried depth of the tunnel. The horizontal displacement of sliding surface decreases with the increase of the buried depth. ③ After the occurrence of a rainfall-induced landslide, the vertical displacement of the tunnel vault in the 1.5-diameter-distance case is 57.29% greater than that in the 3.0-dismeter-distance case.④ For a two-cave tunnel, it is suggested that the cave farther from the landslide toe should be firstly excavated since it may generate less structural deformation.     

Compared performance of a conceptual and a mechanistic hydrologic models of a green roof

In order to investigate the hydrologic response of a green roof system within the urban environment, a monitoring campaign is carried out at the green roof site of the University of Genova (Italy). Experimental data confirm that the green roof is able to significantly mitigate the generation of runoff with median values of retained volume and peak reduction, respectively, equal to 94 and 98%. A conceptual linear reservoir and a simple mechanistic (Hydrus‐1D) models are implemented to simulate the hydrologic behaviour of the system; each model is calibrated and validated based on experimental data collected at the green roof site. The hydrographs simulated with both hydrologic models reproduce with acceptable matching capabilities the experimental measurements, as confirmed by the Nash‐Sutcliffe Efficiency index generally greater than 0·60. Although the relative percentage differences evaluated for the selected hydrograph variables (the total effluent volume, the peak flow rate and the hydrograph centroid) demonstrate that the mechanistic model is more accurate, prediction errors of the conceptual model are generally limited when compared with the observed hydrologic performance. Results of the present comparison are useful in supporting conceptual model selection in case the hydrologic response is addressed for hydrologic performance assessment. Copyright © 2011 John Wiley & Sons, Ltd.     

Diffraction of a compressional wave by a rigid barrier in a liquid half-space

Summary The problem of diffraction of compressional waves by a rigid barrier of finite height fixed in a liquid half space has been studied. Wiener-Hopf technique forms the basis of the methods used to solve the problem. Exact solutions have been obtained in terms of Fourier integrals whose evaluation along an appropriate contour gives the transmitted, reflected and diffracted waves. The diffracted waves decay rapidly away from the barrier.     

Fault detection on a sewer network by a combination of a Kalman filter and a binary sequential probability ratio test

One of the aims of sewer networks is the protection of population against floods and the reduction of pollution rejected to the receiving water during rainy events. To meet these goals, managers have to equip the sewer networks with and to set up real-time control systems. Unfortunately, a component fault (leading to intolerable behaviour of the system) or sensor fault (deteriorating the process view and disturbing the local automatism) makes the sewer network supervision delicate. In order to ensure an adequate flow management during rainy events it is essential to set up procedures capable of detecting and diagnosing these anomalies.

This article introduces a real-time fault detection method, applicable to sewer networks, for the follow-up of rainy events. This method consists in comparing the sensor response with a forecast of this response. This forecast is provided by a model and more precisely by a state estimator: a Kalman filter. This Kalman filter provides not only a flow estimate but also an entity called ‘innovation’. In order to detect abnormal operations within the network, this innovation is analysed with the binary sequential probability ratio test of Wald. Moreover, by crossing available information on several nodes of the network, a diagnosis of the detected anomalies is carried out. This method provided encouraging results during the analysis of several rains, on the sewer network of Seine-Saint-Denis County, France.     

Choosing a specification for a field precision thermostat

Provisions are determined for matching the thermostating temperature with the heater temperature as well as for installing a sensor depending on the position of the heater. The results of theoretical analysis and comparative assessment of three specifications of thermostats intended for use in geophysical equipment are considered. It is shown that, if the outside temperature changes in a few tens of degrees, two of the three specifications are able to ensure consistent thermostating temperature with an error rate not exceeding 0.010°C. According to the experiment, a “hybrid” two-step thermostat maintains the temperature with an error rate of about 0.002°C on the condition that the outside temperature changes within 10°C.     

Evaporation from a riparian system in a semi-arid environment

Measurements of micrometeorological variables were made for a complete annual cycle using an automatic weather station and two energy budget–Bowen ratio systems at a field site adjacent to the Santa Cruz River in southern Arizona. These data were used to provide the basis of an estimate of the evaporation from a one-mile long losing reach of a riparian corridor in this semi-arid environment. A remotely sensed map of vegetation cover was used to stratify the corridor into five categories of surface cover. The total evaporation was calculated as the area-weighted average of the measured evaporation for sampled areas of the two most common covers, and appropriate estimates of evaporation for the less common covers. Measurements showed a substantial, seasonally dependent evaporation from the taller, deep-rooted riparian cover in the study reach, while the short, sparse vegetation provided little evaporation. In terms of the volume of water evaporated from the study reach, the evaporation from irrigated agriculture accounts for almost half of the total loss, while the majority of the remaining evaporation is from the taller riparian vegetation covers, with about one-quarter of the total loss estimated as coming from obligatory phreatophytes, primarily cottonwood. © 1998 John Wiley & Sons, Ltd.