Direct Measurement of Contact Area And Seismic Stress Along a Sliding Interface

Seismic stress drop is an important metric for understanding the kinematics of injection-induced frictional sliding. Seismic stress drop is commonly estimated from Brune’s corner frequency model and the assumption of a double couple source rather than from direct knowledge of the size of the slipping junction, which is impractical to impossible in the field but can be achieved in the laboratory. A direct shear experiment comprised of PMMA sliding blocks were used as an analog of weak, compliant rock interfaces that might exhibit contact melting. A pressure-sensitive film was employed to localize and size, and measure normal stress upon contact junction. The film allowed measurement of contact asperities with spatial resolution of 5 μm x 5 μm, and contact stresses to within ± 1.5 Pa. Final estimation of junction area were made optically using digital image processing techniques. Initially the surface is repeatedly loaded, at 3.5 MPa for 60 s loading cycles, where real contact area increased ~14 to 48% in low and high normally stressed regions, respectively, in three subsequent tests. These changes were mainly attributed to the healing of the interface; a process commonly observed in rock at scale. Subsequently, the slider was subjected to an impulse shear load, which resulted in full rupture of the interface. Spatial measurements of preand post-slip contact area show a ~ 233.6 % increase in low stress contacts (12-17 MPa) and ~ 99.8 % decrease in high stress contacts (37.5-50 MPa). Visualization of the interface, preand post-slip, shows evidence of micromechanical processes and elastic-plastic interactions at the junction level. to estimate the force-time functions for asperity rupture. McLaskey and Glaser [6, 7] used nano-seismology to model source characteristics with respect to asperity rupture on a PMMA-PMMA interface at the nano-scale. McLaskey and Glaser [7] observed that the seismograms recorded for fault nucleation along a PMMA-PMMA interface are similar to those of rock at the km-scale. For this reason, further investigations are being pursued using PMMA as the fault medium. These methods also provided important mechanical insight (i.e, the absolute amplitude and directional component of the force released during singular asperity rupture at the mmscale) and will be applied in future works. 1.1. Contact Mechanics Static stress drop is a common source parameter used in the interpretation of earthquakes. This static stress drop is, quantitatively, a stress decrease along the fault after an earthquake, averaged over a given rupture surface area [8, 9]. Whether estimates of stress drop are independent or dependant of the scalar seismic moment (Mo) remains a controversial topic in the seismic community. Many studies generalize static stress drop as independent of source dimension and seismic moment drop [10-13]. These findings, which assume that earthquake source properties are scale invariant, report a wide range of stress-drop values, but they lie within commonly accepted amplitudes. These models are therefore scale invariant and provide the means to relate earthquakes observed in the laboratory to those observed in situ. As a squeezing force, , is applied to two bodies, see Figure 1, these forces are transmitted through a group of contacts comprising a relatively small area. The stresses incurred at these contact junctions, may result in localized yielding. The topography of the interfaces will tend to deform plastically, or fracture, until the small population of contact area is sufficient to carry the squeezing force, , without further yielding. This area of contact is known as the area of real contact, , and differs quite dramatically from the nominal (or apparent) area of contact, . Dieterich and Kilgore [14, 15] confirmed, using optical experiments, that populations of ‘island-like’ contact regions, known as asperities, were transmitting the stresses between two PMMA bodies, subjected to a nominal squeezing pressure of 2.5 MPa, through 0.5-0.35 % real contact area. In later studies, Persson et al. [16; 17] suggested that since surface roughness is length-scale dependant, these asperities must be composed of smaller asperities, until a limiting factor such as an atomic length of lattice constant, which is depicted in the magnified images of Figure 1. Figure 1. Simple schematic depicting the contact between two solids with nominally flat surfaces that remain rough when examined a various length-scales. The ratio of real to apparent contact, , is linearly related to the normal and shear force applied in the far-field, and , respectively. In micromechanics [18], single asperity to asperity contact is formulated for randomly rough surfaces [19]. Greenwood and Williamson [20] were the first to derive a mathematical treatise for these realistic surfaces. Their model assumed that the interacting surfaces where composed of spherical bumps of varying heights. These random heights where defined mathematical as a Probability Density Function (PDF) of interchangeable distributions. If we examine two spherical elastic bodies squeezed into contact and subjected to shear (e.g. [21]), with shear stiffness given by Mindlin and Deresiewicz [22], the region of contact remains circular. As the shear force (FS) increases, partial slip begins at the outer edge of the asperity until the entire surface is fully sliding. The force required to induce full slip is FS = μFN, where μ is the asperity scale coefficient of friction. When an asperity slips, or breaks off during sliding, elastic stress waves propagates throughout the body, perturbing the shear stress over the remaining contacts. If the perturbation in shear stress and applied far-field shear stress at a particular asperity is less than μFN , the asperity will remain in contact, but with decreased contact area that depends nonlinearly on the shear stress perturbation. If the perturbation is equal to μFN, this neighboring asperity will also enter full sliding and stress waves will be subsequently emitted from these events. Kemeny and Hagaman [23], among others [24, 25], have examined the dislocation mechanics of circular asperities on a heterogeneous fault. Studies on fault roughness [26-30] suggest there may be a critical topological parameter that easily scales from N F