Mathematical modeling of flooding due to river bank failure

Modeling of flooding events resulting from bank overflooding and levee breaching is of relevant social and environmental interest. Two-dimensional (2D) hydrodynamic models integrating the shallow water equations turn out to be very effective tools for the purpose at hand. Many of the available models also use 1D channel elements, fully coupled to the 2D model, to simulate the flow of small channels dissecting the urban and rural areas, and 1D elements, referred to as 1D-links, to efficiently model the flow over levees, road and rail embankments, bunds, the flow through control gates, either free or submerged, and the operation of other hydraulic structures. In this work we propose a physically-based 1D-link to model breach formation and evolution in fluvial levees, and levee failure due to either piping or overtopping. The proposed 1D-link is then embedded in a 1D–2D hydrodynamic model, thus accounting for critical feedbacks between breach formation and changes in the hydrodynamic flow field. The breach model also includes the possibility of simulating breach closure, an important feature particularly in the view of hydraulic risk assessment and management of the emergency. The model is applied to five different case studies and the results of the numerical simulations compare favorably with field observations displaying a good agreement in terms of urban and rural flooded areas, water levels within the channel, final breach widths, and water volumes flowed through the breach.     

Time patterns of polarization currents generated in measuring the electrical conductivity of rocks

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Modelling of resuspension due to fish activity:Mathematical modeling and annular flume experiments

A spatially averaged numerical model was developed to describe the erosion of cohesive sediment. Together with known empirical relations, the model comprises a new formulation for resuspension due to fish activity. Experiments on erosion of natural sediments in the annular flume at Aachen University are used for model calibration. Empirical coefficients were evaluated with genetic algorithms to achieve the best agreement between the model results and the experimental data. The presented model shows sufficient flexibility to account for various sediment properties, including different sediment sources, natural and artificial contaminants, presence or absence of aquatic organisms, and results in an average coefficient of determination, R2 = 90.5% between the model results and the experimental data. Model validation allows it to be assumed that different contaminants affect bed properties differently. Fish activity plays an essential role in correct resuspension prediction. Further sediment erosion experiments with carefully chosen conditions will allow a more comprehensive model evaluation. The presented model is intended to serve as a building block in the development of a hydraulic-sediment-biota model within the W3-Hydro: Water Quality Event Detection for Urban Water Security and Urban Water Management Based on Hydrotoxicological Investigations project that aims to improve the knowledge concerning bioavailability, transport, fate, and effects of contaminants on the aquatic environment.     

Acoustic emission phenomena due to plasticity of rocks

Acoustic emission patterns arising at the stage of plastic deformation (creep and relaxation) of plastic and brittle rocks are discussed. It is suggested that these patterns are related to the spatial localization of plastic deformation and strain hardening of rocks under loads exceeding the yield strength.     

Low-frequency scaling applied to stochastic finite-fault modeling

Stochastic finite-fault modeling is an important tool for simulating moderate to large earthquakes. It has proven to be useful in applications that require a reliable estimation of ground motions, mostly in the spectral frequency range of 1 to 10 Hz, which is the range of most interest to engineers. However, since there can be little resemblance between the low-frequency spectra of large and small earthquakes, this portion can be difficult to simulate using stochastic finite-fault techniques. This paper introduces two different methods to scale low-frequency spectra for stochastic finite-fault modeling. One method multiplies the subfault source spectrum by an empirical function. This function has three parameters to scale the low-frequency spectra: the level of scaling and the start and end frequencies of the taper. This empirical function adjusts the earthquake spectra only between the desired frequencies, conserving seismic moment in the simulated spectra. The other method is an empirical low-frequency coefficient that is added to the subfault corner frequency. This new parameter changes the ratio between high and low frequencies. For each simulation, the entire earthquake spectra is adjusted, which may result in the seismic moment not being conserved for a simulated earthquake. These low-frequency scaling methods were used to reproduce recorded earthquake spectra from several earthquakes recorded in the Pacific Earthquake Engineering Research Center (PEER) Next Generation Attenuation Models (NGA) database. There were two methods of determining the stochastic parameters of best fit for each earthquake: a general residual analysis and an earthquake-specific residual analysis. Both methods resulted in comparable values for stress drop and the low-frequency scaling parameters; however, the earthquake-specific residual analysis obtained a more accurate distribution of the averaged residuals.     

2维和2.5维起伏地表直流电法有限差分数值模拟

起伏地表直流电场数值模拟现多采用有限元法,主要是因为其有灵活的处理曲边界的能力,然而有限元法比有限差分法要复杂,如果让有限差分法也同样具有较好的处理曲边界的能力,那数值模拟将变得更为简单.本文通过在非正则内点处采用不等距差分,在起伏地表点处直接实现边界条件,克服转移法人为改变地表形状的弊端,使得基于笛卡尔网格的有限差分...     

内部磁场梯度引起的扩散对NMR岩石测量响应的影响

低场NMR岩心分析能够刻度NMR测井响应,对于较为准确地预测储层的渗透率、束缚水体积等与产能密切相关的参数尤其重要.对来自南海东部油田的100%饱和盐水的砂岩岩心进行了变回波间隔的实验室NMR T2测量,随着回波间隔的增大对实验观测到的两种不同的T2 分布的移动进行了理论上的分析和解释.随着回波间隔的增加,T2谱向着长弛豫时间的移动可以用过优化NMR采集参数消除掉,而对另外一种由内部磁场梯度引起的移动即随着回波间隔增加T2谱向短弛豫时间的移动则复杂得多,至今为止也无法做到定量化内部磁场梯度的值,这种移动能够引起错误的NMR测井解释.因此理解内部磁场梯度对T2弛豫时间的影响是很有必要的.文中对由内部磁场梯度扩散引起的扩散弛豫对T2弛豫时间的影响进行了理论上的模拟计算,这有助于理解和解释岩石内部磁场梯度对NMR T2弛豫时间的影响.最后结合压汞毛管压力曲线,解释了具体的岩心实验结果,并且计算了具体的岩心的内部磁场梯度值,计算出的内部磁场梯度值应该被视为内部磁场梯度的几何平均值.     

计算震磁背景场的数学方法

如何计算地磁场 (或地磁剩余场 )及其长期变化的趋势变化 ,是提取震磁异常的关键。文章简要介绍了计算震磁背景场的数学方法 :多项式方法、球冠谐和分析方法、矩谐分析方法和曲面样条函数方法     

Monte Carlo method applied to modeling copper transport in river sediments

Monte Carlo simulation (MCS) methodology has been applied to explain the variability of parameters for pollutant transport and fate modeling. In this study, the MCS method was used to evaluate the transport and fate of copper in the sediment of the Tibagi River sub-basin tributaries, Southern Brazil. The statistical distribution of the variables was described by a dataset obtained for copper concentration using sequential extraction, organic matter (OM) amount, and pH. The proposed stochastic spatial model for the copper transport in the river sediment was discussed and implemented by the MCS technique using the MatLab 7.3? mathematical software tool. In order to test some hypotheses, the sediment and the water column in the river ecosystem were considered as compartments. The proposed stochastic spatial model makes it possible to predict copper mobility and associated risks as a function of the organic matter input into aquatic systems. The metal mobility can increase with the OM posing a rising environmental risk.     

电法填埋场渗漏检测极化噪声的剔除方法

电学填埋场渗漏检测方法是利用漏洞电流引起的感应电势异常来定位防渗膜上的漏洞位置.当漏洞电流较小时,检测电极上的极化电位噪声极易将电势的异常值淹没,导致漏洞定位的失败.基于电极极化电位噪声的特点,提出了采用低频交变方波供电的方式来剔除该类噪声.在小型模拟填埋场中的实验结果表明:当回路电流为70 mA,膜上供电电极接电源正极时,防渗层上的两个漏洞只有一个被检出;膜上供电电极接电源负极时,则两个漏洞皆未被检出;将两次实验数据对应相减,则两个漏洞皆被准确定位.     

Mathematical modeling of PCB bioaccumulation in Perna viridis

In the present work, we built a mathematical model of polychlorinated biphenyl (PCB) bioaccumulation in Perna viridis, namely, a one-compartment model with a time dependent incorporation rate R (μg g⁻¹ lipid per ppb water per day), with positive substrate cooperativity as the underlying physical mechanism. The temporal change of the PCB concentration Q (μg g⁻¹ lipid) in the soft tissues of the mussel depends on the competition of the input rate RW and the output rate kQ, where W is the concentration of PCB in water (ppb water) and k is the elimination rate (per day). From our experimental data, k=0.181±0.017 d⁻¹. The critical concentration in water W_c for positive substrate cooperativity was found to be 2.4 ppb. Below W_c, R is a constant. For a water concentration of 0.5 ppb Aroclor 1254, R=24.0±2.4 μg g⁻¹ lipid ppb⁻¹ d⁻¹. Above W_c, positive substrate cooperativity comes into effect and R becomes a function of time and dependent on the concentration Q in a form R=γQ/(Q+δ). This is the case for a water concentration of 5 ppb Aroclor 1254, where γ=15.1 μg g⁻¹ lipid ppb⁻¹ d¹ and δ≈200 μg g⁻¹ lipid. From this model, the uptake is exponentially increasing when the PCB concentration in the mussel is small compared to 200 μg g⁻¹ lipid, and hyperbolically increasing when the concentration is large compared to 200 μg g⁻¹ lipid, which are consistent with the experimental data. The model is useful for understanding the true processes taking place during the bioaccumulation and for risk assessment with higher confidence. Future experimental data which challenge the present model are anticipated and in fact desirable for improvement and perfection of the model.     

Monitoring of relative changes in the electrical conductivity of rocks from observations of the magnetotelluric apparent resistivity (numerical modeling)

A method for direct conversion of observed variations in the magnetotelluric (MT) apparent resistivity ρ_a into relative variations in the resistivity of elements of a well-studied geoelectric structure is proposed. The method is tested on a 1-D model structure consisting of seven horizontal layers in three of which the conductivity can vary within certain limits. It is inferred that the frequency range and the accuracy of methods of magnetotelluric sounding presently applied to the construction of transfer operators are sufficient for determining relative changes in the resistivity of rocks; the latter, as distinct from ρ_a, can serve as an effective prognostic parameter. The method can be extended to more complex geoelectric structures.     

New model of polarization of rocks: Theory and application

Mathematical modeling of a little known model of induced polarization (IP) referred to as “induced polarization caused by constrictivity of pores” was developed. Polarization occurs in all types of rocks if surface areas and transfer numbers are different for connected pores. During the polarization process, all contacts between pores of different transfer numbers will be blocked and the electrical current will flow through the remaining channels. Diffusion equations with different specified boundary conditions for time-on and time-off have been used to develop the base of this model. The new algorithm was tested on laboratory measurements. Several samples were selected: shale, mudstone, tillite, hematite, lava, and manganese ore. Each theoretical model includes pores of more than 40 different sizes sporadically distributed in the sample. The obtained data show good agreement with theory and provide new information about pore size distribution in samples, prevalent pore radius, and effect of anisotropy.     

Small-scale electrical resistivity tomography of wet fractured rocks

This paper describes a series of experiments that tested the ability of the electrical resistivity tomography (ERT) method to locate correctly wet and dry fractures in a meso-scale model. The goal was to develop a method of monitoring the flow of water through a fractured rock matrix. The model was a four by six array of limestone blocks equipped with 28 stainless steel electrodes. Dry fractures were created by placing pieces of vinyl between one or more blocks. Wet fractures were created by injecting tap water into a joint between blocks. In electrical terms, the dry fractures are resistive and the wet fractures are conductive. The quantities measured by the ERT system are current and voltage around the outside edge of the model. The raw ERT data were translated to resistivity values inside the model using a three-dimensional Occam's inversion routine. This routine was one of the key components of ERT being tested. The model presented several challenges. First, the resistivity of both the blocks and the joints was highly variable. Second, the resistive targets introduced extreme changes the software could not precisely quantify. Third, the abrupt changes inherent in a fracture system were contrary to the smoothly varying changes expected by the Occam's inversion routine. Fourth, the response of the conductive fractures was small compared to the background variability. In general, ERT was able to locate correctly resistive fractures. Problems occurred, however, when the resistive fracture was near the edges of the model or when multiple fractures were close together. In particular, ERT tended to position the fracture closer to the model center than its true location. Conductive fractures yielded much smaller responses than the resistive case. A difference-inversion method was able to correctly locate these targets.     

A contribution to the measurement of frequency dependence of electrical conductivity of rocks

Summary Some errors of method occurring in A. C. measurements of the electrical conductivity of rocks are discussed. It is demonstrated that the difference between A.C. and D.C. conductivities, at given frequency, depends mostly on the magnitude of the D.C. conductivity and magnitude of the dielectric constant.     

Velocity variations in carbonate rocks due to dual porosity and wave-induced fluid flow

Stiffness variations in carbonates may be described as resulting from different concentrations of flat compliant pores or cracks, which can have a significant effect on the effective stiffness and acoustic properties (e.g., velocities and attenuations) of dry as well as saturated carbonates, although they carry extremely little porosity. As shown in this paper, the effects of dual porosity and wave-induced fluid flow or pore pressure communication may also play a significant role. On the basis of a previously published T-matrix approach to model the effective viscoelastic properties of cracked porous media, we illustrate the (frequency-dependent) effects of wave-induced fluid flow (mainly squirt flow) or pore pressure communication for a model structure consisting of a mixture of fluid-saturated porous grains and fluid-saturated cavities (vugs, etc.) that are embedded in a solid matrix associated with carbonates. We assume that the pores within the porous grains are decoupled from the pores in the solid matrix (and possibly saturated with different fluids) but that each pore system at the micro and/or mesoscale may or may not be connected. For each of four different connectivity models, we present numerical results for four different cases of microstructure (that emphasize the importance of cracks and flat compliant pores). Our numerical results indicate that the velocity and attenuation spectra of carbonates vary significantly, even when the crack density and all other volume concentrations are constant.     

Laboratory measurements of electrical properties of rocks and minerals

In this paper all important results on laboratory measurements of electrical properties of rocks and minerals for the last four years are presented. Although basic results from all over world are reviewed, East European and U.S.S.R. works are described more extensively. Only D.C. conductivity results are considered, however all principal conclusions hold in similar form for both D.C. and A.C. conductivities. At the end the most important areas of further study and measurement are depicted and the main problems of the future are outlined.     

Two dimensional transient fundamental solution due to suddenly applied load in a half-space

A transient Green function due to suddenly applied line loads in an isotropic and homogeneous half-space is reported in this paper. The derivation of the half-space Green function in the Laplace and the Fourier transform spaces is first reviewed. Following an explicit inversion of the Fourier transform, the inverse Laplace transform is implemented along the contour integral on the p-complex plane in an integral form. The half-space Green function consists of full-space Green functions and a singularity-free complementary term. It can be easily incorporated into current transient boundary elements using the transient full-space Green function. Combined with finite elements, the half-space Green function can be used in a hybrid procedure to solve transient half-space problems without discretization of the free surface. Numerical results are presented to illustrate transient wave propagation in a half-space.