Z. Reches

Nucleation and growth of faults in brittle rocks

We present a model for the nucleation and growth of faults in intact brittle rocks. The model is based on recent experiments that utilize acoustic emission events to monitor faulting processes in Westerly granite. In these experiments a fault initiated at one site without significant preceding damage. The fault propagated in its own plane with a leading zone of intense microcracking. We propose here that faults in granites nucleate and propagate by the interaction of tensile microcracks in the following style. During early loading, tensile microcracking occurs randomly, with no significant crack interaction and with no relation to the location or inclination of the future fault. As the load reaches the ultimate strength, nucleation initiates when a few tensile microcracks interact and enhance the dilation of one another. They create a process zone that is a region with closely spaced microcracks. In highly loaded rock, the stress field associated with microcrack dilation forces crack interaction to spread in an unstable manner and recursive geometry. Thus the process zone propagates unstably into the intact rock. As the process zone lengthens, its central part yields by shear and a fault nucleus forms. The fault nucleus grows in the wake of the propagating process zone. The stress fields associated with shear along the fault further enhance the microcrack dilation in the process zone. The analysis shows that faults should propagate in their own plane, making an angle of 20°–30° with the maximum compression axis. This model provides a physical basis for “internal friction,” the empirical parameter of the Coulomb criterion.

Evaluation of mechanical rock properties using a Schmidt Hammer

The Schmidt Hammer was developed in 1948 for non-destructive testing of concrete hardness [1], and was later used to estimate rock strength [2,3]. It consists of a spring-loaded mass that is released against a plunger when the hammer is pressed onto a hard surface. The plunger impacts the surface and the mass recoils; the rebound value of the mass is measured either by a sliding pointer or electronically. Hammer rebound readings are considered consistent and reproducible [4‐6]. Such fast, non-destructive and in situ evaluations of rock mechanical parameters reduce the expenses for sample collection and laboratory testing. Consequently, the mechanical parameters can be determined in dense arrays of field measurements that reflect the real inherent inhomogeneity of rock masses [7]. Schmidt Hammers were used to estimate the strength of concrete and rocks [2,8‐11] via empirical correlations between rebound readings and compressive strength determined from standard tests [2,8,11]. This Technical Note extends these correlations, and we present new correlations between rebound readings of seven rock types and their measured laboratory values of Young’s modulus, uniaxial compressive strength and density. The studied rocks include soft chalk, limestones, sandstone and stiA igneous rocks, covering a wide range of rock elasticity. These new correlations have already been used for a detailed field study of rock damage [7].

Particle size and energetics of gouge from earthquake rupture zones

Grain size reduction and gouge formation are found to be ubiquitous in brittle faults at all scales, and most slip along mature faults is observed to have been localized within gouge zones. This fine-grain gouge is thought to control earthquake instability, and thus understanding its properties is central to an understanding of the earthquake process. Here we show that gouge from the San Andreas fault, California, with ∼160 km slip, and the rupture zone of a recent earthquake in a South African mine with only ∼0.4 m slip, display similar characteristics, in that ultrafine grains approach the nanometre scale, gouge surface areas approach 80 m2 g-1, and grain size distribution is non-fractal. These observations challenge the common perception that gouge texture is fractal and that gouge surface energy is a negligible contributor to the earthquake energy budget. We propose that the observed fine-grain gouge is not related to quasi-static cumulative slip, but is instead formed by dynamic rock pulverization during the propagation of a single earthquake.

Fault weakening and earthquake instability by powder lubrication

Earthquake instability has long been attributed to fault weakening during accelerated slip, and a central question of earthquake physics is identifying the mechanisms that control this weakening. Even with much experimental effort, the weakening mechanisms have remained enigmatic. Here we present evidence for dynamic weakening of experimental faults that are sheared at velocities approaching earthquake slip rates. The experimental faults, which were made of room-dry, solid granite blocks, quickly wore to form a fine-grain rock powder known as gouge. At modest slip velocities of 10–60 mm s−1, this newly formed gouge organized itself into a thin deforming layer that reduced the fault’s strength by a factor of 2–3. After slip, the gouge rapidly ‘aged’ and the fault regained its strength in a matter of hours to days. Therefore, only newly formed gouge can weaken the experimental faults. Dynamic gouge formation is expected to be a common and effective mechanism of earthquake instability in the brittle crust as (1) gouge always forms during fault slip; (2) fault-gouge behaves similarly to industrial powder lubricants; (3) dynamic gouge formation explains various significant earthquake properties; and (4) gouge lubricant can form for a wide range of fault configurations, compositions and temperatures.

Dikes emplaced into fractured basement, Timna Igneous Complex, Israel

Dikes are usually envisioned as arrays of parallel segments dilated perpendicular to the direction of the least compressive stress. We describe here four dikes of highly irregular shape intruded in the fractured basement in the Timna Igneous Complex, southern Israel. The dikes include a doleritic dike, 2.3 km long and 1.6 m to 32 m thick, and three andesitic dikes, up to 1.5 km long and 8 m thick. The dikes each display significant variations of dip (up to 60°), strike (up to 160°) and thickness. The thickness variations correlate better with the segment attitude than with the position along the dikes. We show that the irregular shapes of the Timna dikes are the result of emplacement into fractured host rock under different paleostress states and driving pressures. Three dilation styles that differ by the geometry of the initial cracks are analyzed: an array of randomly oriented cracks (style A), a single linear crack (style B), and an array of interconnected, nonparallel cracks (style C). The analysis of style A provides the stress state during dike emplacement, including the orientations of the three principal stresses (σ1 ≥ σ2 ≥ σ3), the stress ratio ϕ = (σ2 - σ3)/(σ1 - σ3), and the normalized driving pressure R = (Pm - σ3)/(σ1 - σ3). The stress ratio ϕ indicates the shape of the stress ellipsoid and it ranges from ϕ = 0 for σ2 = σ3 (prolate ellipsoid) to ϕ = 1 for σ1 = σ2 (oblate ellipsoid). The normalized driving pressure R indicates the relative magnitude of the internal magma pressure Pm with respect to the tectonic stresses, and it ranges from R = 0 for Pm = σ3 to R = 1 for Pm = σ1. We found that for three dikes in Timna, ϕ ∼ 0.25, indicating small differences between the two horizontal principal stresses, and for one dike ∼ 0.9, indicating a large difference between the two horizontal principal stresses. The normalized driving pressure R is about 0.08 in two horizontally propagating dikes and about 0.25 in two vertically propagating dikes. Style B predicts an elliptical thickness profile along the dike due to dilation of a linear crack; this prediction agrees with the profile of one of the dikes. The predicted thicknesses due to dilation of the interconnected array of cracks (style C) are in good agreement with the thickness variations of the doleritic dike, and in fair agreement with two of the andesitic dikes. Deviations from the ideal geometry suggest separate stages of propagation and dilation in some of the dike segments.

Constraints on the strength of the upper crust from stress inversion of fault slip data

The coefficient of friction of small faults in the field are estimated here by stress inversion of fault slip data. The small faults that were measured in Israel and the Grand Canyon, Arizona, are considered as representing natural friction experiments. The stresses associated with the faulting are determined by a stress inversion method which incorporates the Coulomb failure criterion [Reches, 1987]. The coefficients of friction determined for 27 fault clusters in limestone, sandstone, and basalt range from 0.0 to 1.3 with mean value of 0.58 ± 0.37. These values are in general agreement with the friction of 0.6–0.85 determined from laboratory experiments. The magnitudes of the calculated principal stresses are compared with in situ stress measurements in similar tectonic environments.

Holocene tectonic deformation along the western margins of the Dead Sea

Abstract To assess the young tectonic activity along the western margins of the Dead Sea and north of the lake, faults were studied within sediments which are up to 60,000 years old. The western margins of the Dead Sea are dominated by normal, step faults which are exposed up to 2 km east of the morphological escarpment of the basin. The rate of subsidence accommodated by these normal faults is estimated to be about 0.85 mm/y. The distribution of the faults suggests that Holocene fault activity was most intense in the northwestern corner of the Dead Sea. North of the lake, left-lateral slip along the Jordan fault produced both local compression and extension. Small reverse faults and folds exposed along this fault indicate a minimum left-lateral slip rate of 0.7 mm/y.

Dynamic fracture by large extraterrestrial impacts as the origin of shatter cones.

A large impact by a comet or meteorite releases an enormous amount of energy, which evaporates, melts and fractures the surrounding rocks. Distinctive features of such impacts are ‘shatter cones’, deformed rocks characterized by hierarchical striated features. Although such features have been used for decades as unequivocal fingerprints of large-body impacts, the process by which shatter cones form has remained enigmatic. Here we show that the distinctive shatter-cone striations naturally result from nonlinear waves (front waves) that propagate along a fracture front. This explains the observed systematic increase of striation angles with the distance from the impact. Shatter-cone networks, typically spanning many scales, can be understood as hierarchical bifurcations of the fracture front, which is generated by the immense energy flux carried by the initial, impact-generated, shock waves. Our quantitative predictions based on this theory are supported by field measurements at the Kentland and Vredefort impact sites. These measurements indicate that shatter cones near to the impact site were formed by fractures propagating at nearly the Rayleigh wave speed of the host rocks, whereas the furthest shatter cones observed (about 40 km from the impact site) were formed by fronts moving more slowly. These results provide insight into impact dynamics as well as dissipative mechanisms in solids subjected to sudden, extremely intense fluxes of energy.

Dynamic fracturing: field and experimental observations

Abstract We analyzed a system of complex joints in thick dolomite layers that are exposed within the western margins of the Dead Sea basin. These joints display two dominant features: ‘tree-like’ branching and a gradual increase of density that leads to local fragmentation. The development of this joint system is investigated in laboratory experiments with samples of brittle/ductile layered composites. The samples were subjected to layer-parallel extension and displayed three styles of fracturing: planar fractures, known from previous tests; branching fractures and clustering fractures, observed here for the first time in layered composites. Based on fracture morphology, we deduced that the branching and clustering fractures in the experiments, and the tree-like, closely spaced joints in the field, propagated at dynamic, high-velocity growth rates. It is proposed that the morphological features described here could be used as field criteria to recognize dynamic rates of rock fracturing.

Mechanical aspects of pull-apart basins and push-up swells with applications to the Dead Sea transform

Abstract Pull-apart basins and push-up swells are common features at steps along strike-slip faults. The structure of these features is examined here for two types of rheology: perfect brittle and perfect ductile. The stress fields derived for the step area predict that fault patterns, mode of deformation and vertical displacement are different for the two rheologies. These predictions are illustrated for basins and swells developed in laboratory experiments with modelling materials. The structure of basins and swells along the Dead Sea transform is discussed here. The pull-apart basins display an intensively faulted southern end and a gently dipping flexure at the northern end. A consistent dissimilarity appears between the structures of the eastern and western boundary faults of the basins. According to the present interpretation, these dissimilarities reflect a relatively ductile crust in Arabia and a relatively brittle crust in Sinai-Israel.