Showing papers on "Slip line field published in 1979"

Modeling of rock friction: 1. Experimental results and constitutive equations

Abstract: Direct shear experiments on ground surfaces of a granodiorite from Raymond, California, at normal stresses of ∼6 MPa demonstrate that competing time, displacement, and velocity effects control rock friction. It is proposed that the strength of the population of points of contacts between sliding surfaces determines frictional strength and that the population of contacts changes continuously with displacements. Previous experiments demonstrate that the strength of the contacts increases with the age of the contacts. The present experiments establish that a characteristic displacement, proportional to surface roughness, is required to change the population of contacts. Hence during slip the average age of the points of contact and therefore frictional strength decrease as slip velocity increases. Displacement weakening and consequently the potential for unstable slip occur whenever displacement reduces the average age of the contacts. In addition to this velocity dependency, which arises from displacement dependency and time dependency, the experiments also show a competing but transient increase in friction whenever slip velocity increases. Creep of the sliding surface at stresses below that for steady state slip is also observed. Constitutive relationships are developed that permit quantitative simulation of the friction versus displacement data as a function of surface roughness and for different time and velocity histories. Unstable slip in experiments is controlled by these constitutive effects and by the stiffness of the experimental system. It is argued that analogous properties control earthquake instability.

Modeling of rock friction: 2. Simulation of preseismic slip

Abstract: The constitutive relations developed in the companion paper are used to model detailed observations of preseismic slip and the onset of unstable slip in biaxial laboratory experiments. The simulations employ a deterministic plane strain finite element model to represent the interactions both within the sliding blocks and between the blocks and the loading apparatus. Both experiments and simulations show that preseismic slip is controlled by initial inhomogeneity of shear stress along the sliding surface relative to the frictional strength. As a consequence of the inhomogeneity, stable slip begins at a point on the surface and the area of slip slowly expands as the external loading increases. A previously proposed correlation between accelerating rates of stable slip and growth of the area of slip is supported by the simulations. In the simulations and in the experiments, unstable slip occurs shortly after a propagating slip event traverses the sliding surface and breaks out at the ends of the sample. In the model the breakout of stable slip causes a sudden acceleration of slip rates. Because of velocity dependency of the constitutive relationship for friction, the rapid acceleration of slip causes a decrease in frictional strength. Instability occurs when the frictional strength decreases with displacement at a rate that exceeds the intrinsic unloading characteristics of the sample and test machine. A simple slider-spring model that does not consider preseismic slip appears to approximate the transition adequately from stable sliding to unstable slip as a function of normal stress, machine stiffness, and surface roughness for small samples. However, for large samples and for natural faults the simulations suggest that the simple model may be inaccurate because it does not take into account potentially large preseismic displacements that will alter the friction parameters prior to instability.

A model for the earthquake cycle in underthrust zones

Abstract: The time-dependent surface deformation due to thrust faulting in an elastic plate overlying a viscoelastic half space is examined and compared with geodetic measurements of earthquake-related crustal movements from Japan. The model fault is two-dimensional, and the half-space rheology is that of a Maxwell solid whose instantaneous response to applied loads is purely elastic but which subsequently flows to relieve imposed shear stresses. A characteristic feature of shallow-angle underthrusting shown by these computations is that buried slip produces predominantly land uplift, while asthenospheric relaxation due to surface faulting results principally in surface downwarping. These distinctive patterns, also reflected in the measured deformation, are particularly useful in formulating a viable model for the entire earthquake cycle. For the model constructed in this way, coseismic faulting in the upper part of the plate transfers a load to the lower lithosphere and asthenosphere, inducing postseismic slip downdip of the seismic rupture and relaxation in the asthenosphere, these transients eventually merging into the steady buried slip and smoother asthenospheric flow that characterize the interseismic phase of the deformation cycle. Aseismic slip and asthenospheric relaxation cause the load supported by the plate-bounding fault to be gradually transferred back to the shallow locked segment of the fault, effecting the strain buildup for a subsequent earthquake, and the cycle is repeated. No explicit account of plate-driving forces is made; their net effect is presumed to be the steady buried slip that persists throughout the cycle and provides the energy that drives it. Characteristic features of the observed deformation in southwest Japan, site of the 1946 Nankaido earthquake, and in the South Kanto district, where the great 1923 earthquake occurred, are matched by this model using conventional values of lithospheric thickness (60 km) and asthenospheric viscosity (1021 P, or 1020 N s/2), although the model is not strongly tied to these exact values. Postseismic movements are adequately explained by episodic slip that occurs below the coseismic rupture, is 10–30% of the seismic slip, and acts in the same sense. Superimposed on these movements are the lesser effects of asthenospheric relaxation, which in the South Kanto district contribute significantly to the postseismic vertical level changes because post-1923 buried slip is comparatively small and involves largely strike slip movements. Interseismic subsidence in both regions is explained well by asthenospheric relaxation and less significant deformation effects due to steady aseismic slip on the lower part of the plate boundary.

Strain softening prior to two-dimensional strike slip earthquakes

Abstract: A model for two-dimensional strike slip faulting in which the fault friction is displacement softening is analyzed to estimate preearthquake crustal deformation and conditions for an earthquake instability. The friction law is initially displacement hardening but becomes softening after the peak stress is surpassed. The peak stress increases with depth to a maximum before decreasing again. The material surrounding the fault is represented by elastic plates. Several deformation histories are calculated by solving numerically the quasi-static, nonlinear problem subject to displacement boundary conditions simulating relative plate motion. When the crust is compliant or the fault is rapidly softening, an inertia-limited instability results. Prior to the instability the point of maximum fault slip rate moves upward toward the greatest peak stress position. The slip causes a rapid increase in shear strain rate at the free surface near the fault trace. Although fault slip is monotonic, the average fault stress reaches a maximum and then decreases before the instability. When instability is not possible, a similar but smoother deformation episode results. Qualitative extrapolation of the computed results suggests that crustal earthquakes may be preceded by accelerating fault slip near the focus, particularly below, and that the enhanced slip rate may cause recognizable strain and tilt anomalies at the free surface.

The Behavior of Slip During Reverse Loading of a β-Ti-Mn Alloy

Abstract: Measurements have been made of the number of slip bands and slip band level differences during forward and reverse straining, and the number of grains shoving slip, the type of slip bands, their location in the grain and their behavior during reverse loading have been noted. During reverse loading new slip appears, and new slip level differences are larger than those found in slip bands which operated during forward loading. The behavior is rationalized in terms of vacancy binding of screw dislocations. It is seen that the new slip must account for a significant amount of reverse strain.

Bending of Laminated Cantilever Beams with Interlayer Slip

Abstract: This paper deals with the load-deformation responses of laminated cantilever beams with the consideration of interlayer slip. In the analysis, a slip criterion was assumed that slip between the laminae of a beam will occur if the interlayer shear reaches a critical value. An analytical solution was obtained by extending the simple beam theory for which interlayer slip of the beam is permitted. Analysis results indicate that slip deformation not only reduces the bending stiffness of the beam, but also leads to an ultimate state in a manner similar to plastic deformation.