http://amasud.web.engr.illinois.edu/Papers/Stabilized_Methods-F-H-M-FEM-Book-2004.pdf

Stabilized Finite Element Methods

Certain geologic media are known to have small permeability; subsurface environments composed of these media and lacking well developed secondary permeability have groundwater flow sytems with many distinctive characteristics. Moreover, groundwater flow in these environments appears to influence the evolution of certain hydrologic, geologic, and geochemical systems, may affect the accumulation of pertroleum and ores, and probably has a role in the structural evolution of parts of the crust. Such environments are also important in the context of waste disposal. This review attempts to synthesize the diverse contributions of various disciplines to the problem of flow in low-permeability environments. Problems hindering analysis are enumerated together with suggested approaches to overcoming them. A common thread running through the discussion is the significance of size- and time-scale limitations of the ability to directly observe flow behavior and make measurements of parameters. These limitations have resulted in rather distinct small- and large-scale approaches to the problem. The first part of the review considers experimental investigations of low-permeability flow, including in situ testing; these are generally conducted on temporal and spatial scales which are relatively small compared with those of interest. Results from this work have provided increasingly detailed information about many aspects of the flow but leave certain questions unanswered. Recent advances in laboratory and in situ testing techniques have permitted measurements of permeability and storage properties in progressively “tighter” media and investigation of transient flow under these conditions. However, very large hydraulic gradients are still required for the tests; an observational gap exists for typical in situ gradients. The applicability of Darcy's law in this range is therefore untested, although claims of observed non-Darcian behavior appear flawed. Two important nonhydraulic flow phenomena, osmosis and ultrafiltration, are experimentally well established in prepared clays but have been incompletely investigated, particularly in undisturbed geologic media. Small-scale experimental results form much of the basis for analyses of flow in low-permeability environments which occurs on scales of time and size too large to permit direct observation. Such large-scale flow behavior is the focus of the second part of the review. Extrapolation of small-scale experimental experience becomes an important and sometimes controversial problem in this context. In large flow systems under steady state conditions the regional permeability can sometimes be determined, but systems with transient flow are more difficult to analyze. The complexity of the problem is enhanced by the sensitivity of large-scale flow to the effects of slow geologic processes. One-dimensional studies have begun to elucidate how simple burial or exhumation can generate transient flow conditions by changing the state of stress and temperature and by burial metamorphism. Investigation of the more complex problem of the interaction of geologic processes and flow in two and three dimensions is just beginning. Because these transient flow analyses have largely been based on flow in experimental scale systems or in relatively permeable systems, deformation in response to effective stress changes is generally treated as linearly elastic; however, this treatment creates difficulties for the long periods of interest because viscoelastic deformation is probably significant. Also, large-scale flow simulations in argillaceous environments generally have neglected osmosis and ultrafiltration, in part because extrapolation of laboratory experience with coupled flow to large scales under in situ conditions is controversial. Nevertheless, the effects are potentially quite important because the coupled flow might cause ultra long lived transient conditions. The difficulties associated with analysis are matched by those of characterizing hydrologic conditions in tight environments; measurements of hydraulic head and sampling of pore fluids have been done only rarely because of the practical difficulties involved. These problems are also discussed in the second part of this paper.

Groundwater Flow in Low‐Permeability Environments

Measurements of pore-fluid pressure and total bed-normal stress at the base of several ~10 m 3 experimental debris flows provide new insight into the process of debris-flow deposition. Pore-fluid pressures nearly sufficient to cause liquefaction were developed and maintained during flow mobilization and acceleration, persisted in debris-flow interiors during flow deceleration and deposition, and dissipated significantly only during postdepositional sediment consolidation. In contrast, leading edges of debris flows exhibited little or no positive pore-fluid pressure. Deposition therefore resulted from grain-contact friction and bed friction concentrated at flow margins. This finding contradicts models that invoke widespread decay of excess pore-fluid pressure, uniform viscoplastic yield strength, or pervasive grain-collision stresses to explain debris-flow deposition. Furthermore, the finding demonstrates that deposit thickness cannot be used to infer the strength of flowing debris.

Debris-flow deposition: Effects of pore-fluid pressure and friction concentrated at flow margins

A critical review on idealization and modeling for interaction among soil–foundation–structure system

Recent advances in the field of sterotactic neurosurgery have made it possible to coregister preoperative computed tomography (CT) and magnetic resonance (MR) images with instrument locations in the operating field. However, accounting for intraoperative movement of brain tissue remains a challenging problem. While intraoperative CT and MR scanners record concurrent tissue motion, there is motivation to develop methodologies which would be significantly lower in cost and more widely available. The approach the authors present is a computational model of brain tissue deformation that could be used in conjunction with a limited amount of concurrently obtained operative data to estimate subsurface tissue motion. Specifically, the authors report on the initial development of a finite element model of brain tissue adapted from consolidation theory. Validations of the computational mathematics in two and three dimensions are shown with errors of 1%-2% for the discretizations used. Experience with the computational strategy for estimating surgically induced brain tissue motion in vivo is also presented. While the predicted tissue displacements differ from measured values by about 15%, they suggest that exploiting a physics-based computational framework for updating preoperative imaging databases during the course of surgery has considerable merit. However, additional model and computational developments are needed before this approach can become a clinical reality.

A computational model for tracking subsurface tissue deformation during stereotactic neurosurgery

This paper analyzes the one-, pseudo three- and three-dimensional theories of consolidation. The particular problem of a strip load on a half-plane is solved for the complete stress field. The Mandel-Cryer effect is noted and analyzed in terms of its physical motivation and influence on failure conditions. Attention is drawn to the lateral distribution of excess pore pressure and maximum shear stress. The effect of pore pressure spreading is noted. Three-dimensional pseudo and three-dimensional theories are compared. The pseudo theory is not a good approximation to three-dimensional consolidation. An analysis of thick clay layers is made using London clay an an example. Predictions of the progress of consolidation by three-dimensional theory are approximately one order of magnitude faster than by conventional theory. It is concluded that three-dimensional theory models the consolidation process better than other comparable theories. It is recommended that field experience by developed to enable appropriate interpretation of this theory.

An Analysis of Consolidation Theories

An analytical solution to the layered consolidation problem for a general set of boundary conditions and an arbitrary load history is presented herein. An example is provided in which the soil profile consists of four compressible layers.

One-dimensional consolidation of layered systems

A study is made of various types of viscoelastic effective stress-strain relations, and their influence on the time-settlement relations in secondary consolidation. This study examines both deviatoric and volumetric components of the effective stress-strain relations. It is shown that the effective stress-strain relationship for a clay layer, is derivable from several combinations of volumetric and deviatoric behavior.

Robert L. Schiffman

Papers

An Analysis of Consolidation Theories

One-dimensional consolidation of layered systems

The Secondary Consolidation of Clay