William Z. Savage

Gravitational stresses in anisotropic rock masses

Abstract This paper presents closed-form solutions for the stress field induced by gravity in anisotropic rock masses. These rocks are assumed to be laterally restrained and are modelled as a homogeneous, orthotropic or transversely isotropic, linearly elastic material. The analysis, constrained by the thermodynamic requirement that strain energy be positive definite, gives the following important result: inclusion of anisotropy broadens the range of permissible values of gravity-induced horizontal stresses. In fact, for some ranges of anisotropic rock properties, it is thermodynamically admissible for gravity-induced horizontal stresses to exceed the vertical stress component; this is not possible for the classical isotropic solution. Specific examples are presented to explore the nature of the gravity-induced stress field in anisotropic rocks and its dependence on the type, degree and orientation of anisotropy with respect to the horizontal ground surface.

Gravitational stresses in long symmetric ridges and valleys

The effect of topography on near-surface, gravity-induced stresses has been analysed using an elastic solution similar to one originally given by Akhpatelov and co-workers. The topographic features considered here are isolated symmetric ridges and valleys, and explicit solutions are presented for these particular features. The main results are: (1) non-zero horizontal compressive stresses develop at and near ridge crests and decrease with increasing Poissons ratio, and (2) horizontal tensile stresses develop under the valley, but decrease and become compressive with increasing Poissons ratio. For both geometries, all stresses increase with depth and approach a standard state of stress. The magnitude of the topographically induced stresses is on the order of the characteristic stress ϱgb, where b is the height of the ridge or the depth of the valley.

Probabilistic Assessment of Precipitation-Triggered Landslides Using Historical Records of Landslide Occurrence, Seattle, Washington

Ninety years of historical landslide records were used as input to the Poisson and binomial probability models. Results from these models show that, for precipitation-triggered landslides, approximately 9 percent of the area of Seattle has annual exceedance probabilities of 1 percent or greater. Application of the Poisson model for estimating the future occurrence of individual landslides results in a worst-case scenario map, with a maximum annual exceedance probability of 25 percent on a hillslope near Duwamish Head in West Seattle. Application of the binomial model for estimating the future occurrence of a year with one or more landslides results in a map with a maximum annual exceedance probability of 17 percent (also near Duwamish Head). Slope and geology both play a role in localizing the occurrence of landslides in Seattle. A positive correlation exists between slope and mean exceedance probability, with probability tending to increase as slope increases. Sixty-four percent of all historical landslide locations are within 150 m (500 ft, horizontal distance) of the Esperance Sand/Lawton Clay contact, but within this zone, no positive or negative correlation exists between exceedance probability and distance to the contact.

Gravitational spreading of steep-sided ridges (“sackung”) in Western United States

SummaryLarge-scale gravitational spreading and movement along fractures of steep-sided ridges in the mountainous areas of the western United States are characterized by linear fissures, trenches, and uphill-facing scarps on tops and sides of ridges. Spreading appears to take place by movement along disconnected planes and/or by slow plastic deformation of a rock mass. In some places, valleyward squeezing out of weak shales overlain by rigid rocks causes extensional fracturing and outward movement of the rigid layers, as illustrated by extension of two laccoliths overlying Mancos Shale, one at Dolores Peak and another at Crested Butte in western Colorado. Gravitational forces acting on a ridge of more homogeneous material causes tensional spreading of the ridge parallel to its long axis, for example in fractured granitic rock north of Mt. Massive in central Colorado, where a survey course has been established to monitor the movement. Recognition and understanding of these large-scale gravitational features and the mechanism that causes them are pertinent to site selection and design of engineering structures in high mountains. If fractures extend to considerable depth and if movement is continuing, engineering structures in valleys or tunnels through the spreading ridges could be damaged.RésuméL’étalement à grande échelle causé par la force de gravitation et le mouvement le long de fractures affectant les arêtes à pente accentuée dans les régions montagneuses de l’ouest des Etats-Unis d’Amérique sont caractérisés par des fissures linéaires, des fossés et des escarpements façant l’amont, localisés sur les sommêts et les versants des crêtes. L’étalement semble prendre place par mouvement le long de plans disjoints, et/ou par déformation plastique lente d’une masse rocheuse. Dans quelques localités, l’extrusion vers l’aval d’argiles schisteuses meubles surmontées par des roches rigides cause des fractures d’extension et un mouvement des couches rigides vers l’extérieur, comme le montre l’extension de deux laccolites recouvrant l’argile schisteuse de Mancos (l’un à Dolores Peak et l’autre à Crested Butte, dans l’ouest du Colorado). Les forces de gravitation agissant sur une crête formée dans un matériau plus homogène causent l’étalement de la crête par tension le long de son axe longitudinal; par exemple dans la roche granitique fracturée au nord du Mt. Massive dans le Colorado central, òu des mesures d’arpentage sont faites régulièrement pour contrôler le mouvement. La reconnaissance et la compréhension de ces phénomènes à grande échelle dus à la force de gravitation et de leurs mécanismes sont utiles à la sélection des sites de construction et au calcul des ouvrages d’art en haute montagne. Si les fractures s’étendent à des profondeurs considérables et si le mouvement continue a présent, les ouvrages d’art situés dans les vallées ou les tunnels transversaux aux crêtes qui s’étalent peuvent être endommagés.

Landslide faults and tectonic faults, analogs?: The Slumgullion earthflow, Colorado

Recent geophysical observations of landslide movement support the hypothesis that processes involved in landslide faulting are analogous to those that operate in crustal-scale faulting. Relative to crustal faulting studies, quantitative seismic, geodetic, and creep measurements of landslide deformation may be made in a very short time with readily available instrumentation and at relatively minimal expense. Our results indicate that the displacement of landslide material occurs along discrete faults exhibiting a combination of brittle failure, indicated by slide quakes and creep events, and as stable sliding observed as steady-state creep. Although slide quakes were observed, a more steady-state failure process of relieving accumulating strain is indicated.

Gravity-induced stresses in stratified rock masses

SummaryThis paper presents closed-form solutions for the stress field induced by gravity in anisotropic and stratified rock masses. These rocks are assumed to be laterally restrained. The rock mass consists of finite mechanical units, each unit being modeled as a homogeneous, transversely isotropic or isotropic linearly elastic material. The following results are found. The nature of the gravity induced stress field in a stratified rock mass depends on the elastic properties of each rock unit and how these properties vary with depth. It is thermodynamically admissible for the induced horizontal stress component in a given stratified rock mass to exceed the vertical stress component in certain units and to be smaller in other units; this is not possible for the classical unstratified isotropic solution. Examples are presented to explore the nature of the gravity induced stress field in stratified rock masses. It is found that a decrease in rock mass anisotropy and a stiffening of rock masses with depth can generate stress distributions comparable to empirical hyperbolic distributions previously proposed in the literature.

GRAVITATIONAL AND TECTONIC STRESSES IN ANISOTROPIC ROCK WITH IRREGULAR TOPOGRAPHY

Abstract An analytical method is presented to predict stresses in rock masses with smooth and irregular topographies formed by the superposition of multiple long and symmetric ridges and valleys. The rock masses are subject to gravity, uniaxial tectonic horizontal compression or tension acting normal to the ridge and valley axis, or to combined gravitational and tectonic loadings. The method can be applied to ridges and valleys of realistic shape, in generally anisotropic, orthotropic, transversely isotropic, or nearly isotropic rock masses. Numerical examples are presented to show the nature of the in situ stress field in transversely isotropic rock masses with different symmetric and asymmetric topographies under gravitational loading, uniaxial tectonic horizontal loading, or combined gravitational and tectonic loading. Under gravity alone, it is shown that non-zero horizontal compressive stresses exceeding the vertical stress develop at and near ridge crests, and that horizontal tensile stresses develop under isolated valleys. Addition of a horizontal uniaxial compression to gravity increases slightly the horizontal compression at the crest of ridges and diminishes the horizontal tension in valley bottoms. Addition of the horizontal tectonic stress has little effect on the magnitude of the vertical stress.

Gravitational Stresses in Long Symmetric Ridges and Valleys in Anisotropic Rock

Abstract The effect of topography and rock mass anisotropy on gravitational stresses in long isolated symmetric ridges and valleys is modeled using an analytical method proposed earlier by the first two authors. The rock mass deforms under a condition of plane strain. A parametric study is presented on the effect of (1) topography, (2) orientation of anisotropy and (3) degree of anisotropy on the magnitude and distribution of gravitational stresses in transversely isotropic rock masses with planes of anisotropy striking parallel to the ridge or valley axis. It is found that compressive stresses develop near ridge crests and that tensile stresses develop in valley bottoms and valley walls. The magnitude of the gravitational stresses is of the order of the characteristics stress ϱgβbβ where ϱ is the rock density, g is the gravitational acceleration and βbβ is the height of the ridge or depth of the valley.

On the state of stress in the near-surface of the earth's crust

Five models for near-surface crustal stresses induced by gravity and horizontal deformation and the influence of rock property contrasts, rock strength, and stress relaxation on these stresses are presented. Three of the models—the lateral constraint model, the model for crustal stresses caused by horizontal deformation, and the model for the effects of anisotropy—are linearly elastic. The other two models assume that crustal rocks are brittle or viscoelastic in order to account for the effects of rock strength and time on near-surface stresses. It is shown that the lateral constraint model is simply a special case of the combined gravity-and deformation-induced stress field when horizontal strains vanish and that the inclusion of the effect of rock anisotropy in the solution for crustal stresses caused by gravity and horizontal deformation broadens the range for predicted stresses. It is also shown that when stress levels in the crust reach the limits of brittle rock strength, these stresses become independent of strain rates and that stress relaxation in ductile crustal rocks subject to constant horizontal strain rates causes horizontal stresses to become independent of time in the long term.

A digital photogrammetric method for measuring horizontal surficial movements on the Slumgullion earthflow, Hinsdale County, Colorado

The traditional approach to making aerial photographic measurements uses analog or analytic photogrammetric equipment. We have developed a digital method for making measurements from aerial photographs which uses geographic information system (GIS) software, and primarily DOS-based personal computers. This method, which is based on the concept that a direct visual comparison can be made between images derived from two sets of aerial photographs taken at different times, was applied to the surface of the active portion of the Slumgullion earthflow in Colorado to determine horizontal displacement vectors from the movements of visually identifiable objects, such as trees and large rocks. Using this method, more of the slide surface can be mapped in a shorter period of time than using the standard photogrammetric approach. More than 800 horizontal displacement vectors were determined on the active earthflow surface using images produced by our digital photogrammetric technique and 1985 (1:12,000-scale) and 1990 (1:6,000-scale) aerial photographs. The resulting displacement field shows, with a 2-m measurement error (~10%), that the fastest moving portion of the landslide underwent 15-29 m of horizontal displacement between 1985 and 1990.