Solution for a plane strain rough‐walled hydraulic fracture driven by turbulent fluid through impermeable rock

The impact of turbulent flow on plane strain fluid‐driven crack propagation is an important but still poorly understood consideration in hydraulic fracture modeling. The changes that hydraulic fracturing has experienced over the past decade, especially in the area of fracturing fluids, have played a major role in the transition of the typical fluid regime from laminar to turbulent flow. Motivated by the increasing preponderance of high‐rate, water‐driven hydraulic fractures with high Reynolds number, we present a semianalytical solution for the propagation of a plane strain hydraulic fracture driven by a turbulent fluid in an impermeable formation. The formulation uses a power law relationship between the Darcy‐Weisbach friction factor and the scale of the fracture roughness, where one specific manifestation of this generalized friction factor is the classical Gauckler‐Manning‐Strickler approximation for turbulent flow in a rough‐walled channel. Conservation of mass, elasticity, and crack propagation are also solved simultaneously. We obtain a semianalytical solution using an orthogonal polynomial series. An approximate closed‐form solution is enabled by a choice of orthogonal polynomials embedding the near‐tip asymptotic behavior and thus giving very rapid convergence; a precise solution is obtained with 2 terms of the series. By comparison with numerical simulations, we show that the transition region between the laminar and turbulent regimes can be relatively small so that full solutions can often be well approximated by either a fully laminar or fully turbulent solution.     

Analysis of Manning coefficient for small‐depth flows on vegetated beds

The limitations of Manning's formula are analysed when it is in extreme conditions, and more specifically with small‐depth flows on natural‐vegetation beds. A thorough analysis is made of research carried out on macro‐rough beds, placing particular emphasis on vegetated beds. Research carried out to date on the roughness of vegetated beds and macro‐roughness is commented on, including that carried out at the Laboratory of Hydraulics and Hydrology of the Forestry Engineering Faculty (Polytechnic University of Madrid). The work was done in two phases, the first in a laboratory channel with artificial vegetation and the second in natural beds. The results of the experimental research allow the development of a new approximate method of determining Manning coefficient according to the Froude number. This method may be applied in extreme conditions, both in small depths and steep slopes. It was proved that the Manning coefficient depends not only on roughness height, but also on depth and slope values; thus, it is advisable to choose the appropriate method for its calculation. Copyright © 2005 John Wiley & Sons, Ltd.     

Evaluation of grain shear stresses required to initiate movement of particles in natural rivers

Shear stresses were evaluated at different sites on two rivers. The first (the Rulles) is characterized by a pebbly bedload and a meandering bed with riffles and pools. The second (the Rouge Eau) has mainly a sandy rippled bed where meandering is well developed but also flat gravelly sectors without meandering system. Shear stresses calculated from friction velocities (τ*) using a redefined y₁ roughness height parameter were compared with total shear stresses calculated from the energy grade line and the hydraulic radius (τ), Divergence between these shear stresses seems to increase in the presence of bedforms and large-scale irregularities of the channel. The τ*/τ ratio is close to 0·5 in the gravelly sector of the Rouge Eau and reaches 0·65 in the riffles of the Rulles (generally located at the inflexion point of the meanders), while it is less than 0·3 in the pools of the same river (located in the loops) and only 0·2 in the sandy rippled sector of the Rouge Eau. Grain and bedform shear stresses were evaluated at these same sites by different methods. The grain shear stress (τ') represents on average 30 per cent of the total shear stress in the riffles of the Rulles and the gravelly sector of the Rouge Eau, but less than 15 per cent in the pools in the Rulles and the sandy sectors of the Rouge Eau. However, it emerges from experiments conducted with marked pebbles and in situ observations of erosion and transport of sandy and gravelly particles, that the grain shear stresses are underestimated and cannot explain the movements and modifications actually observed. Conversely, shear stresses calculated from friction velocities at the sites where erosion actually occurred (or failed to occur despite very high velocities) provide a better explanation of the observed movements.     

A hydro‐economic modelling framework for flood damage estimation and the role of riparian vegetation

A modelling framework for the quick estimate of flood inundation and the resultant damages is developed in this paper. The model, called the flood economic impact analysis system (FEIAS), can be applied to a river reach of any hydrogeological river basin. For the development of the integrated modelling framework, three models were employed: (1) a modelling scheme based on the Hydrological Simulation Program FORTRAN model that was developed for any geomorphological river basin, (2) a river flow/floodplain model, and (3) a flood loss estimation model. The first sub‐model of the flood economic impact analysis system simulates the hydrological processes for extended periods of time, and its output is used as input to a second component, the river/floodplain model. The hydraulic model MIKE 11 (quasi‐2D) is the river/floodplain model employed in this study. The simulated flood parameters from the hydraulic model MIKE 11 (quasi‐2D) are passed, at the end of each time step, to a third component, the flood loss model for the estimation of flood damage. In the present work, emphasis was given to the seasonal variation of Manning's coefficient (n), which is an important parameter for the determination of the flood inundation in hydraulic modelling. High values of Manning's coefficient for a channel indicate high flow resistance. The riparian vegetation can have a large impact on channel resistance. The modelling framework developed in this paper was used to investigate the role of riparian vegetation in reducing flood damage. Moreover, it was used to investigate the influence of cutting riparian vegetation scenarios on the flow characteristics. The proposed framework was applied to the downstream part of the Koiliaris River basin in Crete, Greece, and was tested and validated with historical data. Copyright © 2012 John Wiley & Sons, Ltd.     

长江口动量系数分布特征研究

基于长江口1996年3月和9月共23个测点实测水流资料,计算了动量系数的时空变化,并应用线性回归法,计算了特征时间段内的平均动量系数,获得了长江口动量系数时空分布的基本特征:时间上,涨潮大于落潮,洪季大于枯季,而大、中、小潮则依次递增;空间上,自口外向口内,北支呈逐渐增大,而南支呈先增大后减小、口门附近最大的基本特征.由动量系数分析了潮流的摩阻特性,为数值模拟合理选取曼宁系数提供参考.     

Early Permian strike-slip basin formation and felsic volcanism in the Manning Group,southern New England Orogen,eastern Australia

The Manning Group is characterised by rapidly filled strike-slip basins that developed during the early Permian along the Peel--Manning Fault System in the southern New England Orogen. Typically, the Manning Group has been difficult to date owing to the lack of fossiliferous units or igneous rocks. Thus, the timing of transition from an accretionary convergent margin in the late Carboniferous to dominantly strike-slip tectonic regimes that involved development and emplacement of the Great Serpentinite Belt (Weraerai terrane) is not well constrained. One exception are rhyolites of the Ramleh Volcanics that were erupted into the Echo Hills Formation. These developed along the dextral Monkey Creek Fault splay east of the Peel--Manning Fault System. Zircons extracted from the Ramleh Volcanics yield a U–Pb (SHRIMP) age of 295.6?±?4.6?Ma that constrains the minimum age of deposition in this basin to earliest Permian. Whole-rock geochemistry indicates these are peraluminous felsic melts enriched in LREE and incompatible elements with strong depletions in U, Nb, Sr and Ti. These are similar in age and composition to the nearby S-type Bundarra and Hillgrove plutonic supersuites. We suggest that extensive movement along the east-dipping Peel--Manning Fault System was responsible, not only for strike-slip basin development at the surface (Manning Group), but was also the locus for crustal melting that was responsible for generating S-type felsic melts that utilised hanging-wall fault splays as conduits to the surface or to coalesce in the crust as batholiths exclusively to the east of the Peel--Manning Fault System.     

Implication of the flow resistance formulae on the prediction of flood wave propagation

ABSTRACT

This study examines the difference in the predictions of flood wave propagation in open channels depending on the flow resistance formulae, such as the Chézy and Manning’s equation. The celerity and diffusion coefficient are functions of the channel geometry, slope, roughness as well as the resistance formulae. The results suggest that substituting the Chézy equation with Manning’s equation results in different characteristics of flood propagation, which are consistent regardless of the cross-sectional geometry except for a circular cross-section: increasing celerity and decreasing diffusion coefficient. The celerity is more sensitive to the selection of resistance formulae than the diffusion coefficient. Geometry has a greater effect on the celerity and diffusion coefficient, and consequently on the resulting hydrographs. Manning’s equation results in a larger difference in celerity and diffusion coefficient compared to Chézy equation regardless of the water depth. Overall, this study shows that the selection of resistance formulae is important in terms of the resulting hydrographs and peak flow.

EDITOR Z.W. Kundzewicz ASSOCIATE EDITOR not assigned     

一种自适应时间步长的场地地表污染扩散元胞自动机仿真模型

针对传统扩散模型难以动态模拟地表污染物时空不均匀扩散过程的问题,本文提出一种基于元胞自动机模型的污染物地表扩散仿真模型,在综合考虑地表高差及粗糙度对污染物扩散过程影响的基础上,确定了不规则污染场地的元胞边界条件、划分了元胞空间、提出了一种降雨和非降雨条件下污染物扩散流速计算方法,基于分子扩散建立了地表污染扩散模型演变规则。为更好模拟地表污染物扩散情况,本文提出了一种污染物随坡度和质量衰减的元胞自适应时间步长调整算法,该算法能够动态调整元胞自动机的时间步长,防止固定时间步长在污染物快速扩散时错过细节,而缓慢扩散时消耗计算资源。实验设计了降雨和非降雨两种情形对污染物随时间扩散的过程进行仿真与分析。实验结果表明,不同下垫面对污染物扩散速度有很大的影响,污染物在糙率为0.012的水泥地表上的扩散速度约为其在糙率为0.035的一般性土壤地表上的2.7倍;降雨强度和时长能够加快污染物的扩散,且扩散速度随着降雨曲线变化而改变,并在雨强峰值附近达到最大;污染物扩散服从坡度分布特征,且随着时间变化,高污染区域范围和污染物浓度差异渐渐变小,并在一段时间后,浓度变化渐渐趋于平稳;自适应时间步长演变算法能够较好地体现一次演变过程中污染物扩散在不同邻域元胞方向上的细微时间差异,提高污染物时空分布的计算精度。     

确定坡面径流过程曼宁糙率系数的实验方法研究

曼宁糙率系数是用水动力学方法进行流速计算的关键参数。坡面流曼宁糙率系数与明渠流的不同。为确定坡面径流过程的曼宁糙率系数,自行研发了一种包括供水系统、实验水槽和数据观测记录系统的室内可变糙率坡面实验系统。通过87场预实验验证了供水系统的稳定性和准确性。以坡度、实测流量、实测水深、不同糙率板上河砂的平均直径和地表粗糙度为自变量,以曼宁糙率系数为因变量,选用均方根误差(RMSE)和决定系数(R ²)为评价指标,对166种实验场景进行了支持向量机(Support Vector Machines, SVM)训练与预测,发现：① 紊流的训练结果难以预测层流和过渡流的曼宁糙率系数,说明流态不同时,实验因素对水流的影响机制不同;② 若要较为准确地预测曼宁糙率系数,至少需要包括实测水深在内的3种因素;③ 当同时考虑4种及更多种因素时,紊流状态下均可对曼宁糙率系数进行较为准确的预测。