David A. Lockner

The role of acoustic emission in the study of rock fracture

Abstract The development of faults and shear fracture systems over a broad range of temperature and pressure and for a variety of rock types involves the growth and interaction of microcracks. Acoustic emission (AE), which is produced by rapid microcrack growth, is a ubiquitous phenomenon associated with brittle fracture and has provided a wealth of information regarding the failure process in rock. This paper reviews the successes and limitations of AE studies as applied to the fracture process in rock with emphasis on our ability to predict rock failure. Application of laboratory AE studies to larger scale problems related to the understanding of earthquake processes is also discussed. In this context, laboratory studies can be divided into the following categories. 1) Simple counting of the number of AE events prior to sample failure shows a correlation between AE rate and inelastic strain rate. Additional sorting of events by amplitude has shown that AE events obey the power law frequency-magnitude relation observed for earthquakes. These cumulative event count techniques are being used in conjunction with damage mechanics models to determine how damage accumulates during loading and to predict failure. 2) A second area of research involves the location of hypocenters of AE source events. This technique requires precise arrival time data of AE signals recorded over an array of sensors that are essentially a miniature seismic net. Analysis of the spatial and temporal variation of event hypocenters has improved our understanding of the progression of microcrack growth and clustering leading to rock failure. Recently, fracture nucleation and growth have been studied under conditions of quasi-static fault propagation by controlling stress to maintain constant AE rate. 3) A third area of study involves the analysis of full waveform data as recorded at receiver sites. One aspect of this research has been to determine fault plane solutions of AE source events from first motion data. These studies show that in addition to pure tensile and double couple events, a significant number of more complex event types occur in the period leading to fault nucleation. 4) P and S wave velocities (including spatial variations) and attenuation have been obtained by artificially generating acoustic pulses which are modified during passage through the sample.

Frictional slip of granite at hydrothermal conditions

Sliding on faults in much of the continental crust likely occurs at hydrothermal conditions, i.e., at elevated temperature and elevated pressure of aqueous pore fluids, yet there have been few relevant laboratory studies. To measure the strength, sliding behavior, and friction constitutive properties of faults at hydrothermal conditions, we slid laboratory granite faults containing a layer of granite powder (simulated gouge). Velocity stepping experiments were performed at temperatures of 23° to 600°C, pore fluid pressures PH2O of 0 (“dry”) and 100 MPa (“wet”), effective normal stress of 400 MPa, and sliding velocities V of 0.01 to 1 μm/s (0.32 to 32 m/yr). Conditions were similar to those in earlier tests on dry granite to 845°C by Lockner et al. (1986). The mechanical results define two regimes. The first regime includes dry granite up to at least 845° and wet granite below 250°C. In this regime the coefficient of friction is high (μ = 0.7 to 0.8) and depends only modestly on temperature, slip rate, and PH2O. The second regime includes wet granite above ∼350°C. In this regime friction decreases considerably with increasing temperature (temperature weakening) and with decreasing slip rate (velocity strengthening). These regimes correspond well to those identified in sliding tests on ultrafine quartz. We infer that one or more fluid-assisted deformation mechanisms are activated in the second, hydrothermal, regime and operate concurrently with cataclastic flow. Slip in the first (cool and/or dry) regime is characterized by pervasive shearing and particle size reduction. Slip in the second (hot and wet) regime is localized primarily onto narrow shear bands adjacent to the gouge-rock interfaces. Weakness of these boundary shears may result either from an abundance of phyllosilicates preferentially aligned for easy dislocation glide, or from a dependence of strength on gouge particle size. Major features of the granite data set can be fit reasonably well by a rate- and temperature-dependent, three-regime friction constitutive model (Chester, this issue). We extrapolate the experimental data and model fit in order to estimate steady state shear strength versus depth along natural, slipping faults for sliding rates as low as 31 mm/yr. We do this for two end-member cases. In the first case, pore pressure is assumed hydrostatic at all depths. Shallow crustal strength in this case is similar to that calculated in previous work from room temperature friction data, while at depths below about 9–13 km (depending on slip rate), strength becomes less sensitive to depth but sensitive to slip rate. In the second case, pore pressure is assumed to be near-lithostatic at depths below ∼5 km. Strength is low at all depths in this case (<20 MPa, in agreement with observations of “weak” faults such as the San Andreas). The predicted depth of transition from velocity weakening to velocity strengthening lies at about 13 km depth for a slip rate of 31 mm/yr, in rough agreement with the seismic-aseismic transition depth observed on mature continental faults. These results highlight the importance of fluid-assisted deformation processes active in faults at depth and the need for laboratory studies on the roles of additional factors such as fluid chemistry, large displacements, higher concentrations of phyllosilicates, and time-dependent fault healing.

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.

Fault stability inferred from granite sliding experiments at hydrothermal conditions

Seismicity on crustal faults is concentrated in the depth interval 1–3 to 12–15km. Tse and Rice (1986) suggested that the lower bound on seismicity is due to a switch with increasing temperature from velocity weakening (destabilizing) to velocity strengthening (stabilizing) friction. They inferred this transition from friction data for dry granite; however, pore fluids exist at elevated temperatures throughout the crust, and may strongly influence strength and sliding behavior. We present new data from sliding experiments on granite at elevated T (23° to 600°) plus elevated PH2O (100 MPa), Our results show velocity strengthening at room temperature, but velocity weakening from 100° to 350°C (except at 250°). From 350° to 600° there are systematic trends from velocity weakening to strong velocity strengthening, and from high to low friction; neither trend was seen in tests on dry granite. The velocity dependence data imply the potential for unstable slip in the interval 100° to 350°. Using a geotherm to map temperature to depth, this interval closely matches the observed earthquake distribution.

The effect of mineral bond strength and adsorbed water on fault gouge frictional strength

Recent studies suggest that the tendency of many fault gouge minerals to take on adsorbed or interlayer water may strongly influence their frictional strength. To test this hypothesis, triaxial sliding experiments were conducted on 1 5 different single-mineral gouges with various water-adsorbing affinities. Vacuum dried samples were sheared at 100 MPa, then saturated with water and sheared farther to compare dry and wet strengths. The coefficients of friction, µ, for the dry sheet- structure minerals (0.2-0.8), were related to mineral bond strength, and dropped 20-60% with the addition of water. For non-adsorbing minerals (µ =0.6-0.8), the strength remained unchanged after saturation. These results confirm that the ability of minerals to adsorb various amounts of water is related to their relative frictional strengths, and may explain the anomalously low strength of certain natural fault gouges.

The role of microcracking in shear-fracture propagation in granite

Microcracking related to the formation of a laboratory shear fracture in a cylinder of Westerly granite has been investigated using image-analysis computer techniques. Well away from the fracture (farfield), the deformed granite has about twice the crack density (crack length per unit area) of undeformed granite. The microcrack density increases dramatically in a process zone that surrounds the fracture tip, and the fracture tip itself has more than an order of magnitude increase in crack density over the undeformed rock. Microcrack densities are consistently higher on the dilational side of the shear than on the compressional side. Microcracks in the undeformed rock and in the far-field areas of the laboratory sample are concentrated within and along the margins of quartz crystals, but near the shear fracture they are somewhat more abundant within K-feldspar crystals. The energy release rate, gII, for mode II fracture progagation is estimated from the microcrack density data to be ≥ 1.7–8.6 kJ m−2. The microcracks that formed during the experiment are principally tensile cracks whose orientations reflect the local stress field: those formed prior to the nucleation of the fault are roughly parallel to the cylinder axis (loading direction), whereas those generated in the process zone make angles averaging 30 ° to the overall fault strike (and 20 ° to the cylinder axis). The preferred orientation and uneven distribution of microcracks in the process zone tends to pull the propagating fracture tip towards the dilational side, even though the trend is away from the overall fault strike. As a result, the propagating shear follows the microcrack trend for some distance and then changes direction in order to maintain an overall in-plane propagation path. This recurring process produces a zig-zag or sawtooth segmentation pattern similar to the sawtooth geometries of faults such as the San Andreas fault.

Quantitative measure of the variation in fault rheology due to fluid‐rock interactions

We analyze friction data from two published suites of laboratory tests on granite in order to explore and quantify the effects of temperature (T) and pore water pressure (Pp) on the sliding behavior of faults. Rate-stepping sliding tests were performed on laboratory faults in granite containing “gouge” (granite powder), both dry at 23° to 845°C [Lockner et al., 1986], and wet (Pp = 100 MPa) at 23° to 600°C [Blanpied et al., 1991, 1995]. Imposed slip velocities (V) ranged from 0.01 to 5.5 μm/s, and effective normal stresses were near 400 MPa. For dried granite at all temperatures, and wet granite below ∼300°C, the coefficient of friction (μ) shows low sensitivity to V, T, and Pp. For wet granite above ∼350°, μ drops rapidly with increasing T and shows a strong, positive rate dependence and protracted strength transients following steps in V, presumably reflecting the activity of a water-aided deformation process. By inverting strength data from velocity stepping tests we determined values for parameters in three formulations of a rate- and state-dependent constitutive law. One or two state variables were used to represent slip history effects. Each velocity step yielded an independent set of values for the nominal friction level, five constitutive parameters (transient parameters a, b1, and b2 and characteristic displacements Dc1 and Dc2), and the velocity dependence of steady state friction ∂μss/∂ ln V = a-b1−b2. Below 250°, data from dry and most wet tests are adequately modeled by using the “slip law” [Ruina, 1983] and one state variable (a = 0.003 to 0.018, b = 0.001 to +0.018, Dc ≈ 1 to 20 μm). Dried tests above 250° can also be fitted with one state variable. In contrast, wet tests above 350° require higher direct rate dependence (a = 0.03 to 0.12), plus a second state variable with large, negative amplitude (b2 = −0.03 to −0.14) and large characteristic displacement (Dc2 = 300 to >4000 μm). Thus the parameters a, b1, and b2 for wet granite show a pronounced change in their temperature dependence in the range 270° to 350°C, which may reflect a change in underlying deformation mechanism. We quantify the trends in parameter values from 25° to 600°C by piecewise linear regressions, which provide a straightforward means to incorporate the full constitutive response of granite into numerical models of fault slip. The modeling results suggest that the succeptibility for unstable (stick-slip) sliding is maximized between 90° and 360°C, in agreement with laboratory observations and consistent with the depth range of earthquakes on mature faults in the continental crust.

Low strength of deep San Andreas fault gouge from SAFOD core

The San Andreas fault accommodates 28–34 mm yr−1 of right lateral motion of the Pacific crustal plate northwestward past the North American plate. In California, the fault is composed of two distinct locked segments that have produced great earthquakes in historical times, separated by a 150-km-long creeping zone. The San Andreas Fault Observatory at Depth (SAFOD) is a scientific borehole located northwest of Parkfield, California, near the southern end of the creeping zone. Core was recovered from across the actively deforming San Andreas fault at a vertical depth of 2.7 km (ref. 1). Here we report laboratory strength measurements of these fault core materials at in situ conditions, demonstrating that at this locality and this depth the San Andreas fault is profoundly weak (coefficient of friction, 0.15) owing to the presence of the smectite clay mineral saponite, which is one of the weakest phyllosilicates known. This Mg-rich clay is the low-temperature product of metasomatic reactions between the quartzofeldspathic wall rocks and serpentinite blocks in the fault. These findings provide strong evidence that deformation of the mechanically unusual creeping portions of the San Andreas fault system is controlled by the presence of weak minerals rather than by high fluid pressure or other proposed mechanisms. The combination of these measurements of fault core strength with borehole observations yields a self-consistent picture of the stress state of the San Andreas fault at the SAFOD site, in which the fault is intrinsically weak in an otherwise strong crust.

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.

Pore fluid pressure, apparent friction, and Coulomb failure

Many recent studies of stress-triggered seismicity rely on a fault failure model with a single free parameter, the apparent coefficient of friction, presumed to be a material constant with possible values 0 ≤ μ′ ≤ 1. These studies may present a misleading view of fault strength and the role of pore fluid pressure in earthquake failure. The parameter μ′ is intended to incorporate the effects of both friction and pore pressure, but is a material constant only if changes in pore fluid pressure induced by changes in stress are proportional to the normal stress change across the potential failure plane. Although specific models of fault zones permit such a relation, neither is it known that fault zones within the Earth behave this way, nor is this behavior expected in all cases. In contrast, for an isotropic homogeneous poroelastic model the pore pressure changes are proportional to changes in mean stress, μ′ is not a material constant, and −∞ ≤ μ′ ≤ +∞. Analysis of the change in Coulomb failure stress for tectonically loaded reverse and strike-slip faults shows considerable differences between these two pore pressure models, suggesting that such models might be distinguished from one another using observations of triggered seismicity (e.g., aftershocks). We conclude that using the constant apparent friction model exclusively in studies of Coulomb failure stress is unwise and could lead to significant errors in estimated stress change and seismic hazard.