Far-zone contributions to the gravity field quantities by means of Molodensky’s truncation coefficients

To reduce the numerical complexity of inverse solutions to large systems of discretised integral equations in gravimetric geoid/quasigeoid modelling, the surface domain of Green’s integrals is subdivided into the near-zone and far-zone integration sub-domains. The inversion is performed for the near zone using regional detailed gravity data. The farzone contributions to the gravity field quantities are estimated from an available global geopotential model using techniques for a spherical harmonic analysis of the gravity field. For computing the far-zone contributions by means of Green’s integrals, truncation coefficients are applied. Different forms of truncation coefficients have been derived depending on a type of integrals in solving various geodetic boundary-value problems. In this study, we utilise Molodensky’s truncation coefficients to Green’s integrals for computing the far-zone contributions to the disturbing potential, the gravity disturbance, and the gravity anomaly. We also demonstrate that Molodensky’s truncation coefficients can be uniformly applied to all types of Green’s integrals used in solving the boundaryvalue problems. The numerical example of the far-zone contributions to the gravity field quantities is given over the area of study which comprises the Canadian Rocky Mountains. The coefficients of a global geopotential model and a detailed digital terrain model are used as input data.     

气煤弹性各向异性系数实验测试

气煤裂隙丰富,具有弹性各向异性,确定气煤弹性各向异性类型与大小,对煤田各向异性研究具有重要意义. 本文在对气煤煤样孔隙率测试的基础上,测量了顺煤层面、垂直于煤层面、与煤层面成45°三个方向上纵波速度（V_P）和横波速度（V_SH、V_SV）,计算弹性常数. 对于具有垂向对称轴横向各向同性模型,各向异性系数平均值|ε|≤0.2、|δ|≤0.2和|γ|≤0.2,表明气煤是弱各向异性介质;对于横向对称轴横向各向异性模型,各向异性系数平均值ε(V)≈δ(V),按照Thomsen观点气煤各向异性是由椭圆裂隙引起弹性各向异性.本文还讨论了各向异性系数与孔隙率的关系,表明各向异性的大小与孔隙率之间有一定的关系. 因此当煤层厚度与其顶底板岩性不变或变化很小,可以认为气煤各向异性主要由裂隙引起的,气煤各向异性大小和方向能够反映煤的裂缝密度和方位.     

扩展有限元法的数值方面

扩展有限元法是一种在常规有限元框架内求解强和弱不连续问题的新型数值方法,其原理是在裂尖附近用一些奇异函数和沿裂纹面用阶跃函数加强传统有限元的基,以考虑跨过裂纹的位移场的不连续,该加强策略允许计算网格独立于不连续体几何。讨论了扩展有限元法的一些数值方面,主要包括：水平集法确定界面和加强节点与加强方式、裂尖加强范围的选择、J积分区域的确定和积分方案等。     

交错网格任意阶导数有限差分格式及差分系数推导

交错网格有限差分算法以其高效、精确、实用等优点在地震波数值模拟中得到广泛应用。目前交错网格有限差分的精度已达到时间4阶、空间2N阶;然而在求空间三次导数时,差分格式实际上并未达到所谓的2N阶精度,而是采用了低阶的差分格式及差分系数,这样有利于提高大尺度空间正演时的计算效率;但从计算精度的角度考虑,有必要推导出准确的满足2N阶精度的交错网格有限差分格式及差分系数,以得到更高精度的正演结果。笔者利用Taylor公式展开首次推导出了可导函数任意次导数的任意偶数阶精度的差分近似式及相应的差分系数,从而完善了常规高精度交错网格有限差分算法。采用新推导的交错网格有限差分格式得到的正演波形与解析解进行了对比,证明了新推导的差分格式的正确性,并与常规差分格式的正演波形进行了比较,结果显示,新推导出的交错网格有限差分格式模拟结果稳定性好,精度更高。     

Wave force coefficients for horizontally submerged rectangular cylinders

The results of wave force measurements carried out on a section of horizontally submerged rectangular cylinders, which are used as pontoons in many offshore structures, are reported in this paper. Two rectangular cylinders with aspect (depth–breadth) ratios equal to $\frac{1}{2}$ and $\frac{3}{4}$ and a square section (aspect ratio=1.0) cylinder are chosen for this study. Experiments are carried out in a wave tank at a water depth of 2.2 m at low Keulegan–Carpenter (KC) numbers to measure the horizontal and vertical wave forces acting on a 100 mm section, located at mid-length of the cylinders. For each cylinder, tests are carried out for two relative depths of submergence of 2.68 and 4.68. Measured wave forces in regular and irregular waves are then used to derive drag (C_D) and inertia coefficients (C_M). The analysis show that at very low KC numbers the inertia coefficients for all cylinders approached the potential flow values for both horizontal and vertical forces. The drag coefficients at low KC numbers exhibited large values and they decreased sharply with increase in KC number. For the square cylinder, where relatively a large KC number is obtained compared to other cylinders, inertia coefficients reached minimum values in the range of KC of about 3–4 and increased thereafter. In this range, C_M values are about 50% or so, smaller than the same at KC close to zero. The results of the experiments reveal that aspect ratio has large influence on hydrodynamic coefficients.     

298.15K下LiCl-Li_2B_4O_7-H_2O体系中LiCl的活度系数和离解平衡研究

用锂离子选择电极和经典 Ag- Ag Cl电极测定了 2 98.15K下 L i Cl- Li2 B4 O7- H2 O体系中离子强度范围为 0 .0 1～ 2 .50 mol· kg-1,不同 Li2 B4 O7离子强度分数的 L i Cl的平均活度系数。由实验数据 ,用迭代法及多元线性回归法 ,求取了 L i2 B4 O7的化学计量离解平衡常数 Km,热力学离解平衡常数 K及 Pitzer离子作用参数 ,并与实验值比较标准偏差为 0 .0 50 0。同时该实验结果在 0 .0 1- 0 .50 mol·kg-1离子强度范围内与 2 98.15K下 L i Cl- L i2 SO4 - H2 O体系 L i Cl平均活度系数的变化趋势进行了比较 ,得到 L i Cl在 Li2 B4 O7介质中平均活度系数随 Yb的增大而增大 ,而在 L i2 SO4 介质中则减小     

卫生填埋场复合边坡地震稳定性和永久变形分析

采用非连续变形分析方法,对卫生填埋场复合型边坡的地震稳定性和永久变形进行了详细地计算分析,探讨了边坡倾角、土与土工膜之间的摩擦系数、边坡的长度、覆盖土层的厚度以及地震加速度对边坡的稳定性和永久变形的影响。由边坡的破坏形式,讨论了复合型边坡的破坏机理,指出了文献[1]给出的计算公式的适用条件以及局限性,为卫生填埋场复合型衬垫层的稳定设计提供参考。     

海域不同类别场地地震动参数变化规律研究

基于海域场地分类标准,选取南海海域实测钻孔作为计算模型,同时人工构造部分钻孔计算模型,对126条不同特性地震动输入下5种类别场地计算模型开展土层反应分析计算,分析不同地震动输入下不同海域场地峰值加速度和特征周期变化规律.结果表明,场地类别和地震动输入强度显著影响峰值加速度放大系数和特征周期,场地土越软,地震动输入强度越...     

基于DDA和FEM的砌体结构震动分析

运用非连续变形分析（DDA）和有限元方法(FEM)对砌体结构进行震动分析。建模中将砌体结构的砖、柱、过梁以及楼板等视为独立的弹性体分别作有限元划分,弹性体之间运动由接触界面的张开、闭合和滑动控制来实现,通过防止弹性体间的侵入来校正弹性块体系统的位移与应变最小二乘拟合结果。弹性块体间滑动采用库仑摩尔定律控制砂浆的作用与失效,输入相当于地震烈度Ⅸ度的加速度峰值的迁安波对砌体结构模型进行震力分析,研究相应震动过程。算例表明,DDA和FEM组合的方法能很好地模拟砌体结构受地震作用的动力响应过程。在较大地震作用下,砌体结构首先从底层开始开裂破坏并导致结构倒塌,与农村砌体结构震害现象吻合较好。     

Hydrodynamic characteristics of rill flow on steep slopes

Rill erosion is a dominant sediment source on sloping lands. However, the amount of soil loss from rills on steep slopes is vastly more than that on gentle slopes because of differences in rill shape and hydraulic patterns. The aims of this paper are to determine the hydrodynamic characteristics of rills and the friction coefficients in steep slope conditions and to propose modifications of some hydraulic parameters used in soil loss prediction models. A series of inflow experiments was conducted on loess slopes. The results show that the geometric and hydraulic properties of rill on the steep loess slopes, which are characterized by the mean width of cross sections, mean velocity and mean depth of flow, are related to discharge and slope gradient in power functions. However, the related exponents to discharge are 0.26, 0.48 and 0.26, respectively, which are different from the exponents derived in previous studies, which were conducted on gentle slopes. The Manning roughness coefficient ranged from 0.035 to 0.071, with an average of 0.0536, and the Darcy–Weisbach friction coefficients varied from 0.4 to 1.9. The roughness coefficients are closely related to the Reynolds numbers and flow volumes; however, the correlations vary with slope gradient. The roughness coefficients are directly proportional to the Reynolds number and the flow volume on steep slopes, in contrast with the roughness coefficients found on gentle slopes, which decrease as the Reynolds number and flow volume increase. This difference is caused by the interactions among the hydraulics of the flow, the shape of the rills and the sediment concentrations on steep slopes. The results indicate that parameters used in models to predict rill erosion have to be modified according to slope gradient. Copyright © 2015 John Wiley & Sons, Ltd.