Feasibility of Seismic Characterization of Multiple Fracture Sets
Estimation of parameters of multiple fracture sets is often required for successful exploration and development of naturally fractured reservoirs. The goal of this paper is to determine the maximum number of fracture sets of a certain rheological type which, in principle, can be resolved from seismic data. The main underlying assumption is that an estimate of the complete effective stiffness tensor has been obtained, for example, from multiazimuth, multicomponent surface seismic and vertical seismic profiling (VSP) data. Although typically only a subset of the stiffness elements (or some of their combinations) may be available, this study helps to establish the limits of seismic fracture-detection algorithms. The number of uniquely resolvable fracture systems depends on the anisotropy of the host rock and the rheology and orientation of the fractures. Somewhat surprisingly, it is possible to characterize fewer vertical fracture sets than dipping ones, even though in the latter case the fracture dip has to be found from the data. For the simplest, rotationally invariant fractures embedded in either isotropic or transversely isotropic with a vertical symmetry axis (VTI) host rock, the stiffness tensor can be inverted for up to two vertical or four dipping fracture sets. In contrast, only one fracture set of the most general (microcorrugated) type, regardless of its orientation, is constrained by the effective stiffnesses. These results can be used to guide the development of seismic fracture-characterization algorithms that should address important practical issues of data acquisition, processing, and inversion for particular fracture models.
Seismic Characterization of Dipping Fractures In Transversely Isotropic Background
Although it is believed that natural fracture sets predominantly have near-vertical orientation, oblique stresses and other mechanisms may tilt fractures away from the vertical. Here, we examine an effective medium produced by a single system of obliquely dipping, rotationally invariant fractures embedded in a VTI (transversely isotropic with a vertical symmetry axis) background rock. This model is monoclinic with a vertical symmetry plane that coincides with the dip plane of the fractures.
On the use of the Hardening Soil Small Strain model in geotechnical practice
This article highlights the importance of using advanced constitutive soil models in numerical modelling as daily geotechnical practice. In this context, the Hardening Soil (HS) model is presented as the most advanced soil model implemented in the ZSoil finite element code. The article recalls the basic features of the HS model and it explains their role in numerical simulations. The role of pre-failure non-linear behaviour of soils is also discussed. An application of the HS model is illustrated on typical geotechnical problems such as retaining wall excavation, tunnel excavation and undrained loading followed by consolidation.