Quasi-steady two-equation models for diffusive transport in fractured porous media: large-scale properties for densely fractured systems

When dealing with the macroscopic behavior of a fractured porous medium, one is faced with the problem of computing the large-scale parameters from the fracture network properties. In particular, when the retained model is the quasi-steady two-equation model, three effective coefficients have to be estimated. This upscaling problem has been reviewed using a volume averaging method by Quintard and Whitaker. As a result, a closed form of the macroscopic model was obtained with associate closure problems that can be used for the determination of the required parameters. In this paper, we use the corresponding problems to study and discuss the behavior of the effective properties of 2D densely fractured systems. First, the emphasis is put on the large-scale fracture permeability tensor, which is related to the degree of interconnection of the fractures combined to the effect of matrix diffusion. Secondly, the exchange coefficient is considered, in particular, its dependence on the matrix blocks geometry. Finally, we compare our approach with numerous techniques currently proposed in the literature.     

New statistical methods for the comparison and characterization of particle shape

This paper presents novel methods for robust statistical testing of particle shape data. Shape (the relative lengths of three orthogonal axes) is a key property of sedimentary particles, providing information on provenance, transport history and depositional environment. However, the usefulness of shape data, including the ability to make robust comparisons between samples, has been constrained by the absence of a satisfactory definition of the mean shape for a sample of particles. Such a definition is proposed and used to develop confidence regions for the population mean shape using both parametric (theoretical) and computational (bootstrap) methods. These techniques are based on a transform that permits multivariate statistical methods for the analysis of compositional data to be extended to shape. These techniques are validated with reference to a dataset of 169 clast samples and found to perform well. A statistical test on the mean – using the multivariate extension of Student's t-test, Hotelling's T² – is presented. The benefits of the methods presented are demonstrated with reference to a case study. © 2019 John Wiley & Sons, Ltd.     

A comparison of cross-hole electrical and seismic data in fractured rock

Cross‐hole anisotropic electrical and seismic tomograms of fractured metamorphic rock have been obtained at a test site where extensive hydrological data were available. A strong correlation between electrical resistivity anisotropy and seismic compressional‐wave velocity anisotropy has been observed. Analysis of core samples from the site reveal that the shale‐rich rocks have fabric‐related average velocity anisotropy of between 10% and 30%. The cross‐hole seismic data are consistent with these values, indicating that observed anisotropy might be principally due to the inherent rock fabric rather than to the aligned sets of open fractures. One region with velocity anisotropy greater than 30% has been modelled as aligned open fractures within an anisotropic rock matrix and this model is consistent with available fracture density and hydraulic transmissivity data from the boreholes and the cross‐hole resistivity tomography data. However, in general the study highlights the uncertainties that can arise, due to the relative influence of rock fabric and fluid‐filled fractures, when using geophysical techniques for hydrological investigations.     

Discontinuous Galerkin methods for advective transport in single-continuum models of fractured media

Accurate simulation of flow and transport processes in fractured rocks requires that flow in fractures and shear zones to be coupled with flow in the porous rock matrix. To this end, we will herein consider a single-continuum approach in which both fractures and the porous rock are represented as volumetric objects, i.e., as cells in an unstructured triangular grid with a permeability and a porosity value associated with each cell. Hence, from a numerical point of view, there is no distinction between flow in the fractures and the rock matrix. This enables modelling of realistic cases with very complex structures. To compute single-phase advective transport in such a model, we propose to use a family of higher-order discontinuous Galerkin methods. Single-phase transport equations are hyperbolic and have an inherent causality in the sense that information propagates along streamlines. This causality is preserved in our discontinuous Galerkin discretization. We can therefore use a simple topological sort of the graph of discrete fluxes to reorder the degrees-of-freedom such that the discretized linear system gets a lower block-triangular form, from which the solution can be computed very efficiently using a single-pass forward block substitution. The accuracy and utility of the resulting transport solver is illustrated through several numerical experiments.     

Anisotropic effective conductivity in fractured rocks by explicit effective medium methods

In this work, we assess the use of explicit methods for estimating the effective conductivity of anisotropic fractured media. Explicit methods are faster and simpler to use than implicit methods but may have a more limited range of validity. Five explicit methods are considered: the Maxwell approximation, the T‐matrix method, the symmetric and asymmetric weakly self‐consistent methods, and the weakly differential method, where the two latter methods are novelly constructed in this paper. For each method, we develop simplified expressions applicable to flat spheroidal “penny‐shaped” inclusions. The simplified expressions are accurate to the first order in the ratio of fracture thickness to fracture diameter. Our analysis shows that the conductivity predictions of the methods fall within known upper and lower bounds, except for the T‐matrix method at high fracture densities and the symmetric weakly self‐consistent method when applied to very thin fractures. Comparisons with numerical results show that all the methods give reliable estimates for small fracture densities. For high fracture densities, the weakly differential method is the most accurate if the fracture geometry is non‐percolating or the fracture/matrix conductivity contrast is small. For percolating conductive fracture networks, we have developed a scaling relation that can be applied to the weakly self‐consistent methods to give conductivity estimates that are close to the results from numerical simulations.     

Site characterization by seismic noise in Istanbul,Turkey

Single station seismic noise measurements were carried out at 192 sites in the western part of Istanbul, Turkey. This extensive survey allowed the fundamental resonance frequency of the sedimentary cover to be mapped, and identify areas prone to site amplification. The results are in good agreement with the geological distribution of sedimentary units, indicating a progressive decrease of the fundamental resonance frequencies from the northeastern part, where the bedrock outcrops, towards the southwestern side, where a thickness of some hundreds meters for the sedimentary cover is estimated. The particular distribution of fundamental resonance frequencies indicates that local amplification of the ground motion might play a significative role in explaining the anomalous damage distribution after the 17 August 1999 Kocaeli Earthquake.     

Flow dimension as an indicator of hydraulic behavior in site characterization of fractured rock

We examine the possibility of using the flow dimension identified from constant pressure injection tests as a tool for characterizing the hydraulic conditions of fractured media. The data comes from a low-conductivity crystalline rock site, from depths of up to 450 m, and is obtained with 2 m and 10 m measurement scales. In the analysis, the general solution for n-dimensional flow by Barker (1988) is applied. The results show that the most prominent characteristics of the medium can be identified; that is, linear and sublinear flow dimensions as distinguished from dimensions higher than two. In many cases, however, there is significant difficulty in distinguishing the dimensions n = 2, 2.5, and 3 from each other. This is usually because of the experimental difficulties in achieving the ideal conditions required by the theory during the early part of the experiment. In such cases, a full flow curve is not available for the type-curve fitting. In the nonunique cases the higher dimensions typically correspond to higher, sometimes unrealistically high, values of specific storage and to the less reliable and less representative early part of the experiment. Therefore, most of the dimensions in categories n = 3 can be excluded, thus leaving the majority observations in the categories of n = 2 and n = 2-2.5. The dominance of dimension n = 2 is more pronounced for data related to fracture zones in comparison to that related to "average" rock, in particular in the 2 m scale data. The proportion of low (n < 1.5) flow dimensions is small, but for the 10 m scale data it is relatively higher at greater depths and corresponds to lower conductivities. For the smaller 2 m scale data, the low dimensions are not linked to greater depths or systematically smaller conductivities, giving preliminary indication of different flow dimension behavior for the two different scales.     

The fractal properties of topography: A comparison of methods

In this study the fractal characteristics of fifty-five digital elevation models from seven different United States physiographic provinces are determined using seven methods. The self-similar fractal model tested in this analysis is found to provide a very good fit for some landscapes, but an imperfect fit for others. Thus, outright rejection of this model does not appear to be warranted, but neither does a blind application. The three implementations of the dividers methods considered in this study consistently produce lower dimensions than those produced by the other methods, and those dimensions consistently do not vary much between surfaces. Although the dimensions produced by the cell counting method (applied to the digital elevation model itself) display consistent intersurface variation, the dimensions are generally lower than those produced by the variogram-based methods. Among the variogram-based methods, the dimensions of the quarter-sections of the digital elevation models are generally greater than the dimensions obtained from the other variogram-based methods. The dimensions produced by the variogram method which considered the surfaces on a directional basis are very similar, on average, to the dimensions produced by the entire-surface variogram.     

Measurement system for systematic hydrological characterization of unsaturated fractured welded tuff in a mined underground tunnel

A field investigation of unsaturated flow through a lithophysal unit of fractured welded tuff containing lithophysal cavities has been initiated. To characterize flow in this spatially heterogeneous medium, a systematic approach has been developed to perform tests in boreholes drilled at regular intervals in an underground tunnel (drift). The purpose of the testing is to quantify the amounts of water seeping into the drift versus the amount of water moving around the drift when released into boreholes at many equidistant locations along the drift. In this paper, we describe the test equipment system that has been built for this purpose. Because the field-scale measurements--of liquid flow in the unsaturated, fractured rocks--require continuous testing for periods of days to weeks, the control of test equipment has been fully automated, allowing operation with no human presence at the field site. Preliminary results from the first set of tests indicate that, while the effects of evaporation on characterization of hydrological properties of the rock can be significant, these effects can be controlled and quantified. These tests give insight into the role of the cavities as potential storage during the initial transient flow prior to the breakthrough of water at the drift crown, as well as the role of connected fractures that provide the subsequent quasi-steady flow. In addition to the stated purpose of realizing the flow partitioning, the results yield values for the effective porosity in the pathways for liquid flow in the regions tested thus far.     

Site response implications associated with using non-unique Vs profiles from surface wave inversion in comparison with other commonly used methods of accounting for Vs uncertainty

This paper discusses variability and accuracy of site response predictions performed using shear wave velocity (Vs) profiles derived from non-unique surface wave inversions and other commonly used statistical methods of accounting for epistemic uncertainty and aleatory variability in Vs. Specifically, linear and equivalent linear site response analyses were performed on the following three classes of Vs profiles: (1) 350 Vs profiles developed by performing multiple surface wave inversions, each with a unique set of layering parameters, on a common dispersion dataset, (2) two upper/lower range base-case Vs profiles developed by systematically increasing or decreasing the solution Vs profile by 20%, and (3) 100 Vs profiles developed using the Vs randomization procedure proposed by Toro (1995) [26]. Vs profiles derived from surface wave inversions generally yielded accurate site response estimates with minimal variability, so long as their theoretical dispersion data fit the experimental dispersion data well. On the other hand, the upper/lower range and randomized Vs profiles generally produced inaccurate and highly variable site response predictions, although the inclusion of site-specific parameters in the randomization model improved the results. At real sites where substantial aleatory variability is anticipated and/or the epistemic uncertainty is quite high, the site response estimates associated with the randomized and/or upper/lower range Vs profiles may be deemed acceptable. However, if the experimental dispersion data and horizontal-to-vertical spectral ratios are shown to be consistent over the footprint of a site, it may be possible to significantly reduce the uncertainty associated with the input Vs profile and the resulting uncertainty in the site response.     

几种时频分析方法比较

地震信号由于各种原因,往往是一种非线性、非平稳信号,基于平稳信号理论的常规傅立叶变化方法不能刻画任一时刻的频率成分.时频分析能同时保留时间与频率信息,目前已经出现了很多时频分析方法.本文介绍了Hilbert变换、Hilbert-Huang变换、正弦曲线拟合、雷克子波匹配、短时傅立叶变换、小波变换、S变换以及Cohen类这八种方法,并从时间分辨率、频率分辨率,以及对多频率成份信号适应能力等各方面阐述了各种方法的优缺点,对其中的一些方法结合了理论记录进行了试算,进一步阐述了这些方法的长处和不足之处.     

Site amplification of S-waves in Bursa City and its vicinity, Northwestern Turkey: comparison of different approaches

Microearthquake recordings of local events have been used to quantify the site effects in the vicinity of Bursa City, northwest Turkey. Since the city is located near the southwest branch of the western extension of the North Anatolian Fault (NAF) zone, the importance of the seismic hazard in the region becomes progressively more important. The accelerograms of 69 earthquakes that were recorded on different geologic units, massive limestone, slope deposit and Quaternary sediment were analyzed to estimate the response of the recording sites. Site amplification functions were obtained by using three different approaches (standard spectral ratio, SSR; horizontal to vertical, H/V ratio and generalized inversion method, GIM) and the differences between the methods were also evaluated. We found large discrepancies between the SSR and H/V ratio methods, specifically; the former yields almost three times higher amplitudes than those obtained in the latter approach. Station located within the Bursa Quaternary basin (SCKR) is characterized by the largest estimates of the amplification amplitudes (8.0, 4.5 and 4.0 for SSR, H/V ratio and GIM, respectively) in all the three methods. On the other hand, stations located on deep limestone geological unit (SIGD and SKAY) show the least amplification level, ranging between 1.0 and 1.6. Three methods are able to identify resonant frequencies of the sites, although the absolute amplitudes of the amplification function are obtained different from each method.     

The use of damage functionals in earthquake engineering: A comparison between different methods

The behaviour of the EPP-SDOF model under seismic actions is analysed herein by different ‘damage functionals’ to define collapse under cyclic loading. In particular, the damage functionals based on the concept of maximum ductility and dissipated plastic energy are first compared. Afterwards the methods of Banon and Veneziano, Park and Ang and the linear cumulative law of plastic fatigue are reviewed and extensively analysed. Comparisons in the case of simple cyclic histories and in terms of acceleration collapse spectra are carried out with reference to significant earthquake records. In particular, it is shown in which cases the damage functionals of Banon and Veneziano, Park and Ang and the linear cumulative law of plastic fatigue, completely defined by the value of a single parameter, degenerate in the limit methods of ductility or dissipated energy and in which cases they provide similar results.     

A review of inverse methods in seismic site characterization

Journal of Seismology - Seismic site characterization attempts to quantify seismic wave behavior at a specific location based on near-surface geophysical properties, for the purpose of mitigating...     

Synthetic design hydrographs for ungauged catchments: a comparison of regionalization methods

Design flood estimates for a given return period are required in both gauged and ungauged catchments for hydraulic design and risk assessments. Contrary to classical design estimates, synthetic design hydrographs provide not only information on the peak magnitude of events but also on the corresponding hydrograph volumes together with the hydrograph shapes. In this study, we tested different regionalization approaches to transfer parameters of synthetic design hydrographs from gauged to ungauged catchments. These approaches include classical regionalization methods such as linear regression techniques, spatial methods, and methods based on the formation of homogeneous regions. In addition to these classical approaches, we tested nonlinear regression models not commonly used in hydrological regionalization studies, such as random forest, bagging, and boosting. We found that parameters related to the magnitude of the design event can be regionalized well using both linear and nonlinear regression techniques using catchment area, length of the main channel, maximum precipitation intensity, and relief energy as explanatory variables. The hydrograph shape, however, was found to be more difficult to regionalize due to its high variability within a catchment. Such variability might be better represented by looking at flood-type specific synthetic design hydrographs.     

几种push-over分析方法对比研究

Push-over方法是一种静力非线性计算方法，是近年来在国内外得到广泛研究应用的用于评价结构抗震能力的新方法。采用这种方法计算结构的弹塑性地震反应将会逐渐为广大的工程设计人员所接受，但目前对于这种用静力的方法去预测结构的动力反应，其可靠性如何一直是许多学者所关注的，而且对于现有的几种方法的优劣也没有给出综合的评价。本文在国内外有关理论和方法的基础上，对几种push-over分析方法进行了简要评述，并通过分析计算对其中有代表性的能力谱方法、位移影响系数法和适应谱push-over方法进行了详细的对比研究。指出了其中存在的问题，试图寻找并推荐一种比较好的方法。结果能够实现这一目标，对于push-over方法的发展将会有一定的推动作用。     

Delineating floodplain and upland areas for hydrologic models: a comparison of methods

A spatially distributed representation of basin hydrology and transport processes in hydrologic models facilitates the identification of critical source areas and the placement of management and conservation measures. Floodplains are critical landscape features that differ from neighbouring uplands in terms of their hydrological processes and functions. Accordingly, an important step in watershed modelling is the representation of floodplain and upland areas within a watershed. The aim of this study is (1) to evaluate four floodplain–upland delineation methods that use readily available topographic data (topographic wetness index, slope position, uniform flood stage, and variable flood stage) with regard to their suitability for hydrological models and (2) to introduce an evaluation scheme for the delineated landscape units. The methods are tested in three U.S. watersheds ranging in size from 334 to 629 km² with different climatic, hydrological, and geomorphological characteristics. Evaluation of the landscape delineation methods includes visual comparisons, error matrices (i.e. cross‐tabulations of delineated vs reference data), and geometric accuracy metrics. Reference data were obtained from the Soil Survey Geographic (SSURGO) database and Federal Emergency Management Agency (FEMA) flood maps. Results suggest that the slope position and the variable flood stage method work very well in all three watersheds. Overall percentages of floodplain and upland areas allocated correctly were obtained by comparing delineated and reference data. Values range from 83 to 93% for the slope position and from 80 to 95% for the variable flood stage method. Future studies will incorporate these two floodplain–upland delineation methods into the subwatershed‐based hydrologic model Soil and Water Assessment Tool (SWAT) to improve the representation of hydrological processes within floodplain and upland areas. Copyright © 2016 John Wiley & Sons, Ltd.     

Field study of hydrogeologic characterization methods in a heterogeneous aquifer

Hydraulic conductivity (K) and specific storage (S(s)) are required parameters when designing transient groundwater flow models. The purpose of this study was to evaluate the ability of commonly used hydrogeologic characterization approaches to accurately delineate the distribution of hydraulic properties in a highly heterogeneous glaciofluvial deposit. The metric used to compare the various approaches was the prediction of drawdown responses from three separate pumping tests. The study was conducted at a field site, where a 15 m × 15 m area was instrumented with four 18-m deep Continuous Multichannel Tubing (CMT) wells. Each CMT well contained seven 17 cm × 1.9 cm monitoring ports equally spaced every 2 m down each CMT system. An 18-m deep pumping well with eight separate 1-m long screens spaced every 2 m was also placed in the center of the square pattern. In each of these boreholes, cores were collected and characterized using the Unified Soil Classification System, grain size analysis, and permeameter tests. To date, 471 K estimates have been obtained through permeameter analyses and 270 K estimates from empirical relationships. Geostatistical analysis of the small-scale K data yielded strongly heterogeneous K fields in three-dimensions. Additional K estimates were obtained through slug tests in 28 ports of the four CMT wells. Several pumping tests were conducted using the multiscreen and CMT wells to obtain larger scale estimates of both K and S(s). The various K and S(s) estimates were then quantitatively evaluated by simulating transient drawdown data from three pumping tests using a 3D forward numerical model constructed using HydroGeoSphere (Therrien et al. 2005). Results showed that, while drawdown predictions generally improved as more complexity was introduced into the model, the ability to make accurate drawdown predictions at all CMT ports was inconsistent.