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Hydrogeology Journal

, Volume 26, Issue 3, pp 755–769 | Cite as

Nonlinear consolidation in randomly heterogeneous highly compressible aquitards

  • Berenice Zapata-Norberto
  • Eric Morales-CasiqueEmail author
  • Graciela S. Herrera
Paper

Abstract

Severe land subsidence due to groundwater extraction may occur in multiaquifer systems where highly compressible aquitards are present. The highly compressible nature of the aquitards leads to nonlinear consolidation where the groundwater flow parameters are stress-dependent. The case is further complicated by the heterogeneity of the hydrogeologic and geotechnical properties of the aquitards. The effect of realistic vertical heterogeneity of hydrogeologic and geotechnical parameters on the consolidation of highly compressible aquitards is investigated by means of one-dimensional Monte Carlo numerical simulations where the lower boundary represents the effect of an instant drop in hydraulic head due to groundwater pumping. Two thousand realizations are generated for each of the following parameters: hydraulic conductivity (K), compression index (C c), void ratio (e) and m (an empirical parameter relating hydraulic conductivity and void ratio). The correlation structure, the mean and the variance for each parameter were obtained from a literature review about field studies in the lacustrine sediments of Mexico City. The results indicate that among the parameters considered, random K has the largest effect on the ensemble average behavior of the system when compared to a nonlinear consolidation model with deterministic initial parameters. The deterministic solution underestimates the ensemble average of total settlement when initial K is random. In addition, random K leads to the largest variance (and therefore largest uncertainty) of total settlement, groundwater flux and time to reach steady-state conditions.

Keywords

Nonlinear consolidation Groundwater flow Heterogeneity Monte Carlo Stochastic modeling 

Consolidation non linéaire dans des semi-perméables (aquitards) aléatoirement hétérogènes très compressibles

Résumé

Une importante subsidence due à l’exploitation d’eau souterraine peut se produire dans des systèmes aquifères multi-couches où sont présents des semi-perméables (aquitards) très compressibles. La nature fortement compressible des semi-perméables conduit à une consolidation non linéaire où les paramètres d’écoulement de l’eau souterraine dépendent des contraintes. Ce cas est. encore compliqué par l’hétérogénéité des propriétés hydrodynamiques et géotechniques des semi-perméables. L’effet de l’hétérogénéité verticale réelle des paramètres hydrodynamiques et géotechniques sur la consolidation des formations semi-perméables très compressibles est. étudié au moyen de simulations de Monte Carlo 1D où la limite inférieure représente l’effet d’une baisse instantanée de la charge hydraulique due à un pompage. Deux mille simulations sont générées pour chacun des paramètres suivants: conductivité hydraulique (K), coefficient de compressibilité (C c), indice de vide (e) et m (un paramètre empirique reliant K et e). La structure de corrélation, la moyenne et la variance de chaque paramètre ont été obtenues à partir d’une synthèse bibliographique sur des études de terrain dans les sédiments lacustres de la ville de Mexico. Les résultats indiquent que, parmi les paramètres considérés, la K aléatoire a l’effet le plus important sur le comportement moyen d’ensemble du système, par comparaison à un modèle de consolidation non linéaire avec des paramètres initiaux déterministes. La solution déterministe sous-estime la moyenne d’ensemble du tassement total lorsque la K initiale est. aléatoire. De plus, la K aléatoire conduit à la plus forte variance (et par conséquent à la plus forte incertitude) du tassement total, du flux d’eau souterraine et du temps nécessaire pour atteindre un régime permanent.

Consolidación no lineal en acuitardos de alta compresibilidad heterogéneos aleatoriamente

Resumen

Una severa subsidencia del terreno debido a la explotación de agua subterránea puede ocurrir en sistemas multiacuíferos donde están presentes acuitardos altamente compresibles. La naturaleza altamente compresible de los acuitardos conduce a una consolidación no lineal donde los parámetros de flujo del agua subterránea dependen del esfuerzo. El caso se complica aún más por la heterogeneidad de las propiedades hidrogeológicas y geotécnicas de los acuitardos. El efecto de la heterogeneidad vertical de los parámetros hidrogeológicos y geotécnicos en la consolidación de acuitardos altamente compresibles se investiga mediante simulaciones numéricas unidimensionales de Monte Carlo donde el límite inferior representa el efecto de una caída instantánea en la carga hidráulica debido al bombeo del agua subterránea. Se generaron dos mil realizaciones para cada uno de los siguientes parámetros: conductividad hidráulica (K), índice de compresión (C c), relación de vacíos (e) y m (un parámetro empírico que relaciona la conductividad hidráulica y la relación de vacíos). La estructura de correlación, la media y la varianza para cada parámetro se obtuvieron de una revisión de la literatura sobre los estudios de campo en los sedimentos lacustres de la Ciudad de México. Los resultados indican que, entre los parámetros considerados, l a K aleatoria tiene el mayor efecto sobre el comportamiento promedio del conjunto del sistema en comparación con un modelo de consolidación no lineal con parámetros iniciales determinísticos. La solución determinista subestima el promedio de conjunto del asentamiento total cuando la K inicial es aleatoria. Además, el valor aleatorio de K conduce a una mayor varianza (y, por lo tanto, mayor incertidumbre) de asentamiento total, del flujo de agua subterránea y del tiempo para alcanzar las condiciones en estado estacionario.

随意挑选的异质、可高度压缩弱透水层中的非线性固结

摘要

抽取地下水引起的严重地面沉降可出现在具有可高度压缩的弱透水层的多重含水层系统中,弱透水层的可高度压缩特性导致非线性固结,发生固结地方的地下水流参数与应力相关。弱透水层的水文地质和岩土特性异质性会使情况更加复杂。通过在下部边界水头由于抽水展示出瞬间下降的地方开展一维Monte Carlo数值模拟调查了水文地质和岩土参数的现实垂直异质性对可高度压缩的弱透水层固结的影响。以下参数中每个参数产生了2000个认识结果:水力传导率(K),压缩指数(Cc),孔隙比(e)及 m(与水力传导率好人孔隙比有关的经验参数)。通过查阅墨西哥城湖湘沉积野外研究的文献获取了每个参数的相关结构、平均值和方差。结果表明,在所考虑的参数中,与采用确定性初始参数的非线性固结模型相比时,随机K对系统的整体平均行为影响最大。当初始K为随机时,确定性解决方案低估了整个沉降中整体的平均值。另外,随机K导致整个沉降、地下水通量和时间的最大方差(所以最大不确定性)而达到稳态条件。

Consolidação não-linear em aquitardes aleatoriamente heterogêneos e altamente compressíveis

Resumo

A subsidência da terra severa devida à extração de águas subterrâneas pode acontecer em sistemas multi-aquíferos onde existem aquitardos altamente compressíveis. A natureza altamente compressível dos aquitardes leva a uma consolidação não-linear quando parâmetros de fluxo de águas subterrâneas são dependentes do estresse. O caso é ainda mais complicado pela heterogeneidade das propriedades hidrogeológicas e geotécnicas dos aquitardos. O efeito realístico da heterogeneidade vertical dos parâmetros hidrogeológicos e geotécnicos na consolidação de aquitardos altamente compressíveis é investigado por meio de simulações numéricas unidimensionais de Monte Carlo, onde o limite inferior representa o efeito de uma queda instantânea na carga hidráulica devido ao bombeamento das águas subterrâneas. São geradas duas mil realizações para cada um dos seguintes parâmetros: condutividade hidráulica (K), índice de compressão (C c), razão de vazios (e) e m (parâmetro empírico relacionando à condutividade hidráulica e razão de vazios). A estrutura de correlação, a média e a variância para cada parâmetro foram obtidas a partir de uma revisão da literatura sobre estudos de campo nos sedimentos lacustres da Cidade do México. Os resultados indicam que, entre os parâmetros considerados, o K aleatório tem o maior efeito no comportamento médio do sistema quando comparado a um modelo de consolidação não-linear com parâmetros iniciais determinísticos. A solução determinística subestima a média do conjunto da resolução total quando o K inicial é aleatório. Além disso, o K aleatório leva à maior variação (e, portanto, maior incerteza) da resolução total, do fluxo das águas subterrâneas e do tempo para atingir condições de estado estacionário.

Notes

Funding Information

This research was funded by grant IN113717 from UNAM-DGAPA-PAPIIT and by a doctoral scholarship from CONACYT to the leading author.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  • Berenice Zapata-Norberto
    • 1
  • Eric Morales-Casique
    • 2
    Email author
  • Graciela S. Herrera
    • 3
  1. 1.Posgrado en Ciencias de la TierraUniversidad Nacional Autónoma de MéxicoCiudad de MéxicoMexico
  2. 2.Instituto de GeologíaUniversidad Nacional Autónoma de MéxicoCiudad de MéxicoMexico
  3. 3.Instituto de GeofísicaUniversidad Nacional Autónoma de MéxicoCiudad de MéxicoMexico

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