skip to main content


Title: Topographic stress and rock fracture: a two-dimensional numerical model for arbitrary topography and preliminary comparison with borehole observations: TOPOGRAPHIC STRESS AND ROCK FRACTURE
Award ID(s):
0725019 1239285 1331726
NSF-PAR ID:
10098735
Author(s) / Creator(s):
; ; ;
Date Published:
Journal Name:
Earth Surface Processes and Landforms
Volume:
40
Issue:
4
ISSN:
0197-9337
Page Range / eLocation ID:
512 to 529
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. We present a stochastic bulk damage model for rock fracture. The decomposition of strain or stress tensor to its negative and positive parts is often used to drive damage and evaluate the effective stress tensor. However, they typically fail to correctly model rock fracture in compression. We propose a damage force model based on the Mohr-Coulomb failure criterion and an effective stress relation that remedy this problem. An evolution equation specifies the rate at which damage tends to its quasi-static limit. The relaxation time of the model introduces an intrinsic length scale for dynamic fracture and addresses the mesh sensitivity problem of earlier damage models. The ordinary differential form of the damage equation makes this remedy quite simple and enables capturing the loading rate sensitivity of strain-stress response. The asynchronous Spacetime Discontinuous Galerkin (aSDG) method is used for macroscopic simulations. To study the effect of rock inhomogeneity, the Karhunen-Loeve method is used to realize random fields for rock cohesion. It is shown that inhomogeneity greatly differentiates fracture patterns from those of a homogeneous rock, including the location of zones with maximum damage. Moreover, as the correlation length of the random field decreases, fracture patterns resemble angled-cracks observed in compressive rock fracture. 
    more » « less
  2. null (Ed.)
    Abstract. The continuum of behavior that emerges during fracturenetwork development in crystalline rock may be categorized into threeend-member modes: fracture nucleation, isolated fracture propagation, andfracture coalescence. These different modes of fracture growth producefracture networks with distinctive geometric attributes, such as clusteringand connectivity, that exert important controls on permeability and theextent of fluid–rock interactions. To track how these modes of fracturedevelopment vary in dominance throughout loading toward failure and thushow the geometric attributes of fracture networks may vary under theseconditions, we perform in situ X-ray tomography triaxial compressionexperiments on low-porosity crystalline rock (monzonite) under upper-crustalstress conditions. To examine the influence of pore fluid on the varyingdominance of the three modes of growth, we perform two experiments undernominally dry conditions and one under water-saturated conditions with 5 MPa ofpore fluid pressure. We impose a confining pressure of 20–35 MPa and thenincrease the differential stress in steps until the rock failsmacroscopically. After each stress step of 1–5 MPa we acquire athree-dimensional (3D) X-ray adsorption coefficient field from which weextract the 3D fracture network. We develop a novel method of trackingindividual fractures between subsequent tomographic scans that identifieswhether fractures grow from the coalescence and linkage of several fracturesor from the propagation of a single fracture. Throughout loading in all ofthe experiments, the volume of preexisting fractures is larger than that ofnucleating fractures, indicating that the growth of preexisting fracturesdominates the nucleation of new fractures. Throughout loading until close tomacroscopic failure in all of the experiments, the volume of coalescingfractures is smaller than the volume of propagating fractures, indicatingthat fracture propagation dominates coalescence. Immediately precedingfailure, however, the volume of coalescing fractures is at least double thevolume of propagating fractures in the experiments performed at nominallydry conditions. In the water-saturated sample, in contrast, although thevolume of coalescing fractures increases during the stage preceding failure,the volume of propagating fractures remains dominant. The influence ofstress corrosion cracking associated with hydration reactions at fracturetips and/or dilatant hardening may explain the observed difference infracture development under dry and water-saturated conditions. 
    more » « less
  3. Abstract Topographic form stress (TFS) plays a central role in constraining the transport of the Antarctic Circumpolar Current (ACC), and thus the rate of exchange between the major ocean basins. Topographic form stress generation in the ACC has been linked to the formation of standing Rossby waves, which occur because the current is retrograde (opposing the direction of Rossby wave propagation). However, it is unclear whether TFS similarly retards current systems that are prograde (in the direction of Rossby wave propagation), which cannot arrest Rossby waves. An isopycnal model is used to investigate the momentum balance of wind-driven prograde and retrograde flows in a zonal channel, with bathymetry consisting of either a single ridge or a continental shelf and slope with a meridional excursion. Consistent with previous studies, retrograde flows are almost entirely impeded by TFS, except in the limit of flat bathymetry, whereas prograde flows are typically impeded by a combination of TFS and bottom friction. A barotropic theory for standing waves shows that bottom friction serves to shift the phase of the standing wave’s pressure field from that of the bathymetry, which is necessary to produce TFS. The mechanism is the same in prograde and retrograde flows, but is most efficient when the mean flow arrests a Rossby wave with a wavelength comparable to that of the bathymetry. The asymmetry between prograde and retrograde momentum balances implies that prograde current systems may be more sensitive to changes in wind forcing, for example associated with climate shifts. 
    more » « less