Abstract
It is proposed that the growth of fractures is the basic process for generating and maintaining permeability in solid rock (bedrock). Many extension fractures grow as hydrofractures, whereas many shear (and extension) fractures grow through the formation of transverse fractures that connect the adjacent tips of existing fractures. In a boundary-element analysis, the hydrofractures are modeled as being driven open by a fluid overpressure that varies linearly from 10 MPa at the fracture centre to 0 MPa at the fracture tip. The host rock has a uniform Young's modulus of 10 GPa, a Poisson's ratio of 0.25, and is dissected by vertical joints and horizontal contacts, each of which is modeled as an internal spring of stiffness 6 MPa m−1. The number of joints and contacts, and their location with respect to the hydrofracture tip are varied in different model runs. The results of the analyses indicate that the tensile stresses generated by overpressured hydrofractures open up joints and contacts out to considerable distances from the fracture tip, so that they tend to link up to form a hydraulic pathway. Using the same Young's modulus, Poisson's ratio, and internal spring constant for joints as in the hydrofracture models, boundary-element models were made to study the interaction stresses that cause neighbouring joints to become interconnected through the growth of linking transverse fractures that, ultimately, may evolve into shear fractures. The models were subjected to tensile stress of 6 MPa acting normal to the joint planes as the only loading. The offset (horizontal distance) and underlap (vertical distance) between the adjacent tips of the joints were varied between model runs. The results show a concentration of tensile and shear stresses in the regions between the neighbouring tips of the joints, but these regions become smaller when the underlap of the joints decreases and changes to overlap. These stress-concentration regions favour the development of transverse (mostly shear) fractures that link up the nearby tips of the joints, so as to form a segmented shear or extension fracture. Analytical results on aperture variation of a hydrofracture in a homogeneous, isotropic rock are compared with boundary-element results for a hydrofracture dissecting layered rocks. The aperture is larger where the hydrofracture dissects soft (low Young's modulus) layers than where it dissects stiff layers. Aperture variation may encourage subsequent groundwater-flow channeling along a pathway generated by a hydrofracture in layered rocks.
Résumé
Nous proposons que le développement des fractures est le processus de base qui génère et maintient la perméabilité des roches indurées de socle. De nombreuses fractures en extension se forment en tant qu'hydrofractures, tandis que de nombreuses fractures de cisaillement (et en extension) se développent par la formation de fractures transverses qui mettent en connexion les parois adjacentes de fractures existantes. Dans une analyse des éléments aux limites, les hydrofractures sont modélisées comme si elles étaient maintenues ouvertes par une surpression de fluide qui varie linéairement de 10 MPa dans la fracture à 0 MPa sur sa paroi. La roche magasin possède un module de Young uniforme de 10 GPa, un rapport de Poisson de 0.25, et est recoupée par des fractures verticales et des joints horizontaux, chacun étant modélisé comme une source interne avec une rigidité de 6 MPa m−1. Le nombre de fractures et de joints et leur localisation par rapport aux parois de l'hydrofracture varient dans les différents traitements de modélisation. Les résultats des analyses indiquent que les contraintes de tension générées par les hydrofractures en surpression ouvrent les fractures et les joints sur des distances considérables à partir des parois de la fracture, de telle sorte qu'elles tendent à se connecter pour former un cheminement hydraulique. En utilisant le même module de Young, le même rapport de Poisson et la même constante de source interne pour les fractures que dans les modèles d'hydrofracture, des modèles d'éléments aux limites ont été élaborés pour étudier les contraintes d'interaction qui provoquent l'interconnexion de fractures voisines grâce à l'extension de fractures transverses qui, finalement, peuvent évoluer en fractures de cisaillement. Les modèles ont été soumis à un effort de traction de 6 MPa appliqué normalement aux plans de fracture comme unique charge. Le déplacement (en distance horizontale) et l'écartement (en distance verticale) entre les parois des fractures ont varié selon les différents traitements. Les résultats montrent une concentration de contraintes de tension et de cisaillement dans les secteurs entre les parois des fractures, mais ces secteurs se réduisent lorsque l'écartement des fractures diminue et devient un recouvrement. Ces zones de concentration des contraintes favorisent le développement de fractures transverses (principalement de cisaillement) qui mettent en relation les parois voisines des fractures de manière à former une fracture segmentée de cisaillement ou d'extension. Les résultats analytiques sur la variation de l'ouverture d'une hydrofracture dans une roche homogène et isotrope sont comparés aux résultats des éléments aux limites pour une hydrofracture recoupant des roches litées. L'ouverture est plus large lorsque l'hydrofracture recoupe des couches tendres (module de Young faible) que lorsqu'elle recoupe des couches rigides. La variation de l'ouverture peut favoriser la chenalisation pour un écoulement souterrain subséquent le long d'un cheminement généré par une hydrofracture dans des roches litées.
Resumen
Se propone que el crecimiento de fracturas es el proceso básico de generación y mantenimiento de la permeabilidad en rocas sólidas (roca madre). Muchas fracturas extensivas crecen por fracturación hidráulica, mientras que muchas fracturas de cizalla (y extensivas) lo hacen mediante la formación de fracturas transversales que conectan los extremos adyacentes de fracturas existentes. Por medio de un análisis de elementos de contorno, se ha modelado el crecimiento de las fracturas hidráulicas por un exceso de presión, la cual varía linealmente entre 10 Mpa en el centro de la fractura y 0 Mpa en el extremo. La roca madre tiene un módulo de Young uniforme de 10 Gpa, un coeficiente de Poisson de 0.25, y está diseccionada por diaclasas verticales y contactos horizontales que son modelados, cada uno de ellos, como fuente interna de rigidez igual a 6 MPa m−1. El número de diaclasas y de contactos, así como su situación respecto al extremo de las fracturas hidráulicas, han sido modificados en diferentes pasadas del modelo. Los resultados de los análisis indican que las tensiones generadas por fracturas hidráulicas sobrepresionadas abren las diaclasas y contactos a distancias considerables del extremo de la fractura, de manera que tienden a unirse y a formar caminos o vías de flujo. Utilizando para las diaclasas el mismo módulo de Young, coeficiente de Poisson y manantial interno constante que se empleó en los modelos de fracturas hidráulicas, se ha elaborado modelos de elementos de contorno para estudiar las tensiones de interacción que causan la interconexión de diaclasas vecinas por medio del crecimiento de fracturas transversales de enlace, y que pueden llegar a convertirse en fracturas de cizalla. Los modelos fueron sometidos a tensiones de 6 Mpa normales a los planos de diaclasas como única carga. Se ha modificado el acomodo o distancia horizontal ("offset") y la distancia vertical ("underlap") entre extremos adyacentes de las diaclasas en las diversas pasadas del modelo. Los resultados muestran una concentración de tensiones y cizallas en las regiones situadas entre extremos vecinos de las diaclasas, pero estas regiones son menores conforme la distancia vertical de las diaclasas decrece y cambia a solapamiento de techo ("overlap"). Estas regiones de concentración de esfuerzos favorecen el desarrollo de fracturas transversales (mayoritariamente de cizalla) que enlazan los extremos vecinos de las diaclasas para formar una fractura segmentada de cizalla o extensiva. Se compara los resultados analíticos de la variación de la apertura de una fractura hidráulica en una roca homogénea e isótropa con los resultados del modelo de elementos de contorno en fracturas hidráulicas que diseccionan rocas estratificadas. La apertura es mayor si la fractura hidráulica disecciona capas deleznables (módulo de Young pequeño) que cuando lo hace en capas rígidas. La variación de la apertura puede favorecer el acanalamiento del flujo de aguas subterráneas a lo largo de caminos generados por una fractura hidráulica en rocas estratificadas.
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Acknowledgements
We thank the Hydrogeology Journal referees for helpful comments. This work was supported by a grant from the European Commission (contract EVR1-CT-1999-40002), several grants from the Norway Research Council, and a PhD grant from Statoil (to Agust Gudmundsson) for Sonja L. Brenner.
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Gudmundsson, A., Gjesdal, O., Brenner, S.L. et al. Effects of linking up of discontinuities on fracture growth and groundwater transport. Hydrogeology Journal 11, 84–99 (2003). https://doi.org/10.1007/s10040-002-0238-0
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DOI: https://doi.org/10.1007/s10040-002-0238-0