Effects of Principal Stress Directions and Mean Normal Stress on Failure Criterion for Cross-Anisotropic Sand

2013 ◽  
Vol 139 (11) ◽  
pp. 1592-1601 ◽  
Author(s):  
Nina M. Rodriguez ◽  
Poul V. Lade
1995 ◽  
Vol 85 (5) ◽  
pp. 1513-1517
Author(s):  
Z.-M. Yin ◽  
G. C. Rogers

Abstract Earthquake faulting results in stress drop over the rupture area. Because the stress drop is only in the shear stress and there is no or little stress drop in the normal stress on the fault, the principal stress directions must rotate to adapt such a change of the state of stress. Using two constraints, i.e., the normal stress on the fault and the vertical stress (the overburden pressure), which do not change before and after the earthquake, we derive simple expressions for the rotation angle in the σ1 axis. For a dip-slip earthquake, the rotation angle is only a function of the stress-drop ratio (defined as the ratio of the stress drop to the initial shear stress) and the angle between the σ1 axis and the fault plane, but for a strike-slip earthquake the rotation angle is also a function of the stress ratio. Depending on the faulting regimes, the σ1 axis can either rotate toward the direction of fault normal or rotate away from the direction of fault normal. The rotation of the stress field has several important seismological implications. It may play a significant role in the generation of heterogeneous stresses and in the occurrence and distribution of aftershocks. The rotation angle can be used to estimate the stress-drop ratio, which has been a long-lasting topic of debate in seismology.


2018 ◽  
Vol 12 (10) ◽  
pp. 3333-3353 ◽  
Author(s):  
Philipp Mamot ◽  
Samuel Weber ◽  
Tanja Schröder ◽  
Michael Krautblatter

Abstract. Instability and failure of high mountain rock slopes have significantly increased since the 1990s coincident with climatic warming and are expected to rise further. Most of the observed failures in permafrost-affected rock walls are likely triggered by the mechanical destabilisation of warming bedrock permafrost including ice-filled joints. The failure of ice-filled rock joints has only been observed in a small number of experiments, often using concrete as a rock analogue. Here, we present a systematic study of the brittle shear failure of ice and rock–ice interfaces, simulating the accelerating phase of rock slope failure. For this, we performed 141 shearing experiments with rock–ice–rock “sandwich”' samples at constant strain rates (10−3 s−1) provoking ice fracturing, under normal stress conditions ranging from 100 to 800 kPa, representing 4–30 m of rock overburden, and at temperatures from −10 to −0.5 ∘C, typical for recent observed rock slope failures in alpine permafrost. To create close to natural but reproducible conditions, limestone sample surfaces were ground to international rock mechanical standard roughness. Acoustic emission (AE) was successfully applied to describe the fracturing behaviour, anticipating rock–ice failure as all failures are predated by an AE hit increase with peaks immediately prior to failure. We demonstrate that both the warming and unloading (i.e. reduced overburden) of ice-filled rock joints lead to a significant drop in shear resistance. With a temperature increase from −10 to −0.5 ∘C, the shear stress at failure reduces by 64 %–78 % for normal stresses of 100–400 kPa. At a given temperature, the shear resistance of rock–ice interfaces decreases with decreasing normal stress. This can lead to a self-enforced rock slope failure propagation: as soon as a first slab has detached, further slabs become unstable through progressive thermal propagation and possibly even faster by unloading. Here, we introduce a new Mohr–Coulomb failure criterion for ice-filled rock joints that is valid for joint surfaces, which we assume similar for all rock types, and which applies to temperatures from −8 to −0.5 ∘C and normal stresses from 100 to 400 kPa. It contains temperature-dependent friction and cohesion, which decrease by 12 % ∘C−1 and 10 % ∘C−1 respectively due to warming and it applies to temperature and stress conditions of more than 90 % of the recently documented accelerating failure phases in permafrost rock walls.


2009 ◽  
pp. 516-516-25 ◽  
Author(s):  
JRF Arthur ◽  
S Bekenstein ◽  
JT Germaine ◽  
CC Ladd

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Jin-feng Zou ◽  
Jia-min Du

This paper focuses on a novel approach for the quasi-plane strain-softening problem of the cylindrical cavity expansion based on generalized Hoek-Brown failure criterion. Because the intermediate principal stress is deformation-dependent, the quasi-plane strain problem is defined to implement the numerical solution of the intermediate principal stress. This approach assumes that the initial total strain in axial direction is a nonzero constant (ε0) and the plastic strain in axial direction is not zero. Based on 3D failure criterion, the numerical solution of plastic strain is given. Solution of the intermediate principal stress can be derived by Hooke’s law. The radial and circumferential stress and strain considering the intermediate principal stress are obtained by the proposed approach of the intermediate principal stress, stress equilibrium equation, and generalized H-B failure criterion. The numerical results can be used for the solution of strain-softening surrounding rock. In additional, the validity and accuracy of the proposed approach are verified with the published results. At last, parametric studies are carried out using MATLAB programming to highlight the influences of the out-of-plane stress on the stress and displacement of surrounding rock.


2003 ◽  
Vol 38 (6) ◽  
pp. 507-517 ◽  
Author(s):  
S. N Akour ◽  
J. F Nayfeh ◽  
D. W Nicholson

Stress concentrations associated with circular holes in pure shear-loaded plates can be reduced by up to 13.5 per cent by introducing elliptical auxiliary holes along the principal stress directions. These holes are introduced in the areas of low stresses near the main circular hole in order to smooth the principal stress trajectories. A systematic study based on univariate search optimization method is undertaken by using finite element analysis (FEA) to determine the optimum size and location for an auxiliary defence hole system. The results are validated using RGB (red-green-blue) photoelasticity.


2018 ◽  
Vol 82 ◽  
pp. 394-405 ◽  
Author(s):  
Osvaldo P.M. Vitali ◽  
Tarcisio B. Celestino ◽  
Antonio Bobet

2020 ◽  
Vol 223 (2) ◽  
pp. 851-861 ◽  
Author(s):  
G S Reuber ◽  
L Holbach ◽  
A A Popov ◽  
M Hanke ◽  
B J P Kaus

SUMMARY Imaging subsurface structures, such as salt domes, magma reservoirs or subducting plates, is a major challenge in geophysics. Seismic imaging methods are, so far, the most precise methods to open a window into the Earth. However, the methods may not yield the exact depth or size of the imaged feature and may become distorted by phenomena such as seismic anisotropy, fluid flow, or compositional variations. A useful complementary method is therefore to simulate the mechanical behaviour of rocks on large timescales, and compare model predictions with observations. Recent studies have used the (non-linear) Stokes equations and geometries from seismic studies in combination with an adjoint-based approach to invert for rheological parameters that are consistent with surface observations such as GPS velocities. Nevertheless, it would be useful to use other surface observations, such as principal stress directions, as constraints as well. Here, we derive the adjoint formulation for the case that principal stress directions are used as observables with respect to rheological parameters. Both an algebraic and a discretized derivation of the adjoint equations are described. This thus enables the usage of two data fields - surface velocities and stress directions - as a misfit for the inversion. We test the performance of the inversion for principal stress directions on simplified 3-D test cases. Finally, we demonstrate how the adjoint approach can be used to compute 3-D geodynamic sensitivity kernels, which highlight the areas in the model domain that have the largest impact on the misfit value of a particular point. This provides a simple, yet powerful, way to visualize which parts of the model domain are of key importance if changing rheological constants.


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