Stochastic partial differential equations in groundwater hydrology

Many problems in hydraulics and hydrology are described by linear, time dependent partial differential equations, linearity being, of course, an assumption based on necessity.Solutions to such equations have been obtained in the past based purely on deterministic consideration. The derivation of such a solution requires that the initial conditions, the boundary conditions, and the parameters contained within the equations be stipulated in exact terms. It is obvious that the solution so derived is a function of these specified, values.There are at least four ways in which randomness enters the problem. i) the random initial value problem; ii) the random boundary value problem; iii) the random forcing problem when the non-homogeneous part becomes random and iv) the random parameter problem.Such randomness is inherent in the environment surrounding the system, the environment being endowed with a large number of degrees of freedom.This paper considers the problem of groundwater flow in a phreatic aquifer fed by rainfall. The goveming equations are linear second order partial differential equations. Explicit form solutions to this randomly forced equation have been derived in well defined regular boundaries. The paper also provides a derivation of low order moment equations. It contains a discussion on the parameter estimation problem for stochastic partial differential equations.     

Some results comparing Monte Carlo simulation and first order Taylor series approximation for steady groundwater flow

The expected head and standard deviation of the head from the first order Taylor series approximation is compared to Monte Carlo simulation, for steady flow in a confined aquifer with transmissivity as a random variable. Emphasis is on the effect of changes in the covariance structure of the transmissivity, and pumping rates, on the errors in the first order Taylor series approximation. The accuracy of the first order Taylor series approximation is found to be particularly sensitive to pumping rates. With significant pumping the approximation is found to under estimate both the expected drawdown and head variance, and the error increases as the pumping rate increases. This can lead to large errors in probability constraints based on moments from the first order Taylor series approximation.     

Hydraulic geometry and changes in flow velocity at a river confluence with coarse bed material

A survey of flows was conducted at a river confluence with coarse bed material. Bridges were installed on both tributaries, at the confluence and farther downstream on the receiving stream. At these stations, flow velocities were measured over a dense grid for seven conditions ranging from very low flows to the bankfull stage. Hydraulic geometry relationships established at all four stations revealed that flow is accelerated through the confluence as stage rises. At bankfull discharge, average velocity is 1.6 times higher at the confluence than on either tributary. Flow acceleration occurs at and above intermediate flow stages and is concentrated at the centre of a linear pool located at the confluence. The development of a zone of high shear stress is also associated with the cell of high flow velocity. Flow acceleration is dissipated at the exit of the pool where water surges over boulder ribs. The acceleration is not related to the development of flow separation zones as observed by Best and Reid (1984) for wide junction angles, nor is it explained by the reduction of the friction exerted by the banks. Acceleration is associated with the plan geometry of the confluence, with the lateral slopes which permit water to converge, and with a reduction in grain roughness at the confluence. Owing to the curvature of the tributary and to the acute angle of entry, relative power losses through the confluence decrease with increasing stages.     

最大峰值加速度与有效峰值加速度的大小比例关系及影响因素探讨

分别以最大峰值加速度(以下简称PGA)和有效峰值加速度(以下简称EPA)为参数,对金沙江流域上12个工程场点进行了地震危险性分析,得到了各个场点在不同的年超越概率下的基岩PGA和EPA值。通过对PGA、EPA值比较分析认为:PGA与EPA值的大小比例关系主要受年超越概率大小的影响,当年超越概率较大时,表现为PGA>EPA;当年超越概率较小时,PGA与EPA的比例关系还与场点周围的潜源分布形式及潜源的震级上限的大小有关,不同的年超越概率、不同的潜源分布形式和震级上限,可使PGA>EPA,也可使PGA相似文献   

基于灰关联与人工神经网络综合评价模型的多层砖房震害预测

结合几次大地震中多层砖房的实际震害资料,基于灰关联识别方法,解析了各影响因子对多层砖房抗震性能的影响程度。以反映结构抗震性能的各类物理参数作为输入数据,以给定地震动峰值加速度下建筑物破坏状态的概率作为输出数据,采用8-6-5层结构,建立了基于BP人工神经网络的非线性模型,并对震害样本进行了训练。结果表明:利用灰关联分析,可得出各因子对多层砖房抗震性能影响程度的大小排序,有利于实际的工程抗震设计;基于BP人工神经网络模型的多层砖房的震害预测结果与震害实例的实际情况比较吻合,其思路和方法可推广于其他不同类型的建筑结构的震害预测。     

A correlation for permanent earthquake-induced deformation of earth embankments

Seismic design of earth dams and embankments is mainly controlled by the permanent deformation that may be induced directly or indirectly because of the design earthquake. Simple design charts, such as those developed by Yegian et al. [Yegian, M.K., Marciano, E.A., and Ghahraman, V.G. 1991. Earthquake-induced permanent deformations: Probabilistic approach. J. Geotech. Eng., 117, 35–50.], Hynes-Griffin and Franklin [Hynes-Griffin, M.E., and Franklin, A.G. 1984. Rationalizing the Seismic Coefficient Method. Miscellaneous Paper GL-84-13, US Army Corps of Engineers Waterways Experiment Station, Vicksburg, Mississippi.], Makdisi and Seed [Makdisi, F.I., and Seed, H.B. 1978. Simplified procedure for estimating dam and embankment earthquake-induced deformations. J. Geotech. Eng., 104, 849–867.], and Sarma [Sarma, S.K. 1975. Seismic stability of earth dams and embankments. Géotechnique, 25, 743–761.], are often used to obtain a preliminary estimate of the permanent, earthquake-induced deformation of earth dams and embankments. Comparison of permanent deformations estimated from these procedures with observations from 122 published case histories on performance of earth dams and embankments during past earthquakes indicate that the estimated permanent earthquake-induced deformations were, in general, smaller than the observed deformations. However, the observed permanent deformation, D_avg, was found to relate to the ratio of yield acceleration, a_y, and the peak horizontal ground acceleration, a_max. The scatter in the observational data, upon which the D_avg–a_y/a_max relationship is based, can be partly explained by the variations in the ratio of the fundamental (elastic) period of the earth structure, T_D, and the predominant period of the earthquake ground motion, T_p, and the magnitude of the earthquake, M_W.     

Groundwater flow modelling of the regional aquifer of the Pampa del Tamarugal,northern Chile

The Pampa del Tamarugal Aquifer (PTA) is an important source of groundwater in northern Chile. In this study, a groundwater flow model of this aquifer is developed and calibrated for the period 1983–2004. The model reproduces the observed flow-field and the water balance components reasonably well. Five scenarios are defined to evaluate the response to different pumping situations. These scenarios show that groundwater heads will continue to decrease with the present pumping discharge rates. To account for variations in the model results due to uncertainties in average recharge rates, randomly generated recharge realizations with different levels of uncertainty are simulated. Evaporation flow rates and groundwater flowing out of the modelled area seem unaffected by the recharge uncertainty, whereas the storage terms can vary considerably. For the most intensive pumping scenario under the generated random recharge rates, it is unlikely that the cumulative discharged volume from the aquifer, at the end of the simulation period, will be larger than 12% of the estimated groundwater reserve. Fluctuations in simulated groundwater heads due to uncertainties in the average recharge values are more noticeable in certain areas. These fluctuations could explain unusual behaviour in the observed groundwater heads in these areas.

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Resumen El Acuífero de la Pampa del Tamarugal (PTA) es una fuente importante de agua subterránea en el norte de Chile. En este estudio se desarrolla y calibra un modelo de flujo de agua subterránea para el periodo 1983–2004. El modelo reproduce razonablemente bien el campo de flujo observado y los componentes del balance hídrico. Se definen cinco escenarios para evaluar la respuesta a diferentes situaciones de bombeo. Estos escenarios muestran que con las tasas de descarga de bombeo actuales las presiones de agua subterránea continuarán en descenso. Para explicar las variaciones en los resultados del modelo debidas a incertidumbres en tasas de recarga promedio se han simulado realizaciones de recarga generadas aleatoriamente con diferentes niveles de incertidumbre. Las tasa de flujo por evaporación y el agua subterránea que fluye fuera del área modelizada parecen no haber sido afectadas por la incertidumbre en recarga mientras que los términos de almacenamiento pueden variar considerablemente. Para el escenario de bombeo más intenso, bajo las tasas de recarga generadas aleatoriamente, no es probable que el volumen descargado acumulado del acuífero al final del periodo de simulación sea mayor del 12% de la reserva de agua subterránea estimada. Las fluctuaciones en las presiones simuladas de agua subterránea debido a las incertidumbres en los valores de recarga promedio son más notorios en ciertas áreas. Las fluctuaciones podrían explicar el comportamiento inusual en las presiones de agua subterránea observadas en estas áreas.

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Résumé L’aquifère de la Pampa del Tamarugal (PTA) représente une importante source d’eau souterraine dans le Nord du Chili. Dans cette étude, un modèle d’écoulement souterrain de cet aquifère est réalisé et calibré pour la période 1983–2004. Celui-ci reproduit le champs d’écoulement observé et les composantes du bilan d’eau raisonnablement bien. Cinq scénarios sont définis pour évaluer la réponse du système à des conditions de pompage différentes. D’après ces scénarios, les niveaux piézomètriques vont continuer à baisser sous l’effet des taux de pompage actuels. Pour tenir compte de la variabilité des résultats du modèle due aux incertitudes sur les taux de recharge moyens, des épisodes de recharge, générés aléatoirement et présentant différents niveaux d’incertitude sont simulés. Les taux d’évaporation et l’eau souterraine s’écoulant hors de la zone modélisée semblent non affectés par l’incertitude sur la recharge, les termes d’emmagasinement en revanche peuvent varier considérablement. Dans le cas du scénario avec le pompage le plus important et des taux de recharge aléatoires, il est peu probable que le volume cumulé pompé hors de l’aquifère à la fin de la simulation atteigne une valeur supérieure à 12% de la réserve d’eau souterraine estimée. Les fluctuations des niveaux piézomètriques simulés liées aux incertitudes sur les recharges moyennes sont plus perceptibles dans certaines zones. Ces fluctuations pourraient expliquer un comportement inhabituel des niveaux piézomètriques observés dans ces zones.

     

Tectonic stress,seismicity, and seismic hazard in the southeastern Carpathians

Intermediate-depth earthquakes in the Vrancea region occur in response to stress generation due to descending lithosphere beneath the southeastern Carpathians. In this article, tectonic stress and seismicity are analyzed in the region on the basis of a vast body of observations. We show a correlation between the location of intermediate-depth earthquakes and the predicted localization of maximum shear stress in the lithosphere. A probabilistic seismic hazard assessment (PSHA) for the region is presented in terms of various ground motion parameters on the utilization of Fourier amplitude spectra used in engineering practice and risk assessment (peak ground acceleration, response spectra amplitude, and seismic intensity). We review the PSHA carried out in the region, and present new PSHA results for the eastern and southern parts of Romania. Our seismic hazard assessment is based on the information about the features of earthquake ground motion excitation, seismic wave propagation (attenuation), and site effect in the region. Spectral models and characteristics of site-response on earthquake ground motions are obtained from the regional ground motion data including several hundred records of small and large earthquakes. Results of the probabilistic seismic hazard assessment are consistent with the features of observed earthquake effects in the southeastern Carpathians and show that geological factors play an important part in the distribution of the earthquake ground motion parameters.     

强余震和主震地面运动分布比较研究

应用地震动衰减关系计算了1966年邢台地震以来中国大陆及近海发生的21次MSge;7地震序列的主震和强余震产生的有效峰值加速度，并对计算结果进行了比较分析， 发现76.2%地震序列的强余震产生的有效峰值加速度超过主震，其中50%多的强余震产生的有效峰值加速度在大范围内大幅度地超过主震. 本研究表明在强余震震中区附近，强余震往往会造成比主震更严重的破坏， 因此在地震危险性分析中要充分考虑强余震的影响场，才能为抗震设防提供科学、安全、可靠的依据.      

Two-stage decision-making under uncertainty and stochasticity: Bayesian Programming

This paper develops a new method for decision-making under uncertainty. The method, Bayesian Programming (BP), addresses a class of two-stage decision problems with features that are common in environmental and water resources. BP is applicable to two-stage combinatorial problems characterized by uncertainty in unobservable parameters, only some of which is resolved upon observation of the outcome of the first-stage decision. The framework also naturally accommodates stochastic behavior, which has the effect of impeding uncertainty resolution. With the incorporation of systematic methods for decision search and Monte Carlo methods for Bayesian analysis, BP addresses limitations of other decision-analytic approaches for this class of problems, including conventional decision tree analysis and stochastic programming. The methodology is demonstrated with an illustrative problem of water quality pollution control. Its effectiveness for this problem is compared to alternative approaches, including a single-stage model in which expected costs are minimized and a deterministic model in which uncertain parameters are replaced by their mean values. A new term, the expected value of including uncertainty resolution, or EVIUR, is introduced and evaluated for the illustrative problem. It is a measure of the worth of incorporating the experimental value of decisions into an optimal decision-making framework. For the illustrative problem, the two-stage adaptive management framework extracted up to approximately 50% of the gains of perfect information. The strength and limitations of the method are discussed and conclusions are presented.