John Handin

Experimental studies relating to microfracture in sandstone

Abstract A fundamental understanding of the relation between stress concentrations at grain contacts and microfractures in granular aggregates is obtained through two-dimensional photomechanical model studies and is tested through observational studies of experimentally deformed sandstone discs, glass beads, and quartz sand. In uncemented aggregates, the state of stress in each grain is controlled by the manner in which the applied load is transmitted across grain contacts. The angles between lines connecting pairs of contacts and the axis of the principal load acting at the boundaries of the aggregate determine which of all contacts will be most highly stressed or “critical”. Microfractures follow that maximum principal stress trajectory which connects critical contacts, and they propagate through those points where the magnitude of the local maximum stress difference is the greatest. Microfractures, therefore, are extension fractures. It then follows that both the locations and orientations of fractures can be predicted if the state of stress in the grains is known. Positioning of critical contacts depends primarily on sorting, packing, grain shapes, and the boundary load conditions applied to the aggregate. Some critical contacts and, therefore, microfractures tend to join together in a series or “chain”. Orientations of chains are most strongly influenced by the direction of the maximum compressive load at the boundary of the aggregate. A hydrostatic load applied on the boundaries of an aggregate can cause microfracturing within grains. Orientations for microfractures and contact lines are random in poorly sorted aggregates, but they are influenced by packing in well sorted aggregates. Grains of cemented aggregates are more highly stressed at their centers than at contacts. By analogy, microfracture orientations depend strongly on the position of the greatest load axis and only slightly on the low-magnitude stress concentrations at contacts. These microfractures parallel the greatest principal stress trajectory in regions where the magnitude of the maximum stress difference is greatest. These observations lead to the conclusion that fractures in grains of cemented aggregates are also extension fractures and should exhibit a higher degree of preferred orientation than in uncemented counterparts. These conclusions hold when cementing materials have about the same elastic moduli as the grains. Cements may be so weak that the aggregate behaves as if it were uncemented in terms of microfracture fabric, or so stiff that the major part of the load is transmitted by the cement, and the composite is no longer an aggregate in the mechanical sense.

Rheology of rocksalt

We review progress in experimental determinations of transient and steady-state flow properties and processes of natural rocksalt aggregates, focusing primarily on results from Avery Island, Louisiana, domal salt. The steady-state flow field-established from constant stress and constant strain-rate tests at temperatures from 50 to 200°C, strain rates from 10−5 to 10−9 s−1 and differential stresses, σ, from 20.7 to 2.5 MPa-has been separated into two flow regimes, each fit by a power-law relation. At the higher stresses and strain rates this relation is e=1.6 ×10−4exp(−68.1RT.10−3)σ5.3 for which the pre-exponential constant is expressed in MPa−5.3 s−1 and the apparent activation energy is in J mol−1. Creep rates predicted by equation (A) do not differ appreciably from those predicted previously. The relatively low stress, low strain-rate data are very well fit by e=8.1 ×10−5exp(−51.6RT.10−3 σ2.4 which is comparable conditions, predicts creep rates higher and equivalent viscosities lower than does equation (A) by two orders of magnitude. The change in behavior from (A) to (B) is ascribed to a change in rate-limiting mechanism from cross-slip of screw dislocations to the climb of edge dislocations in this dry material. Subgrain formation dominates microstructural development during steady-state flow of salt and, from determinations of average subgrain diameters in crystals from 20 different rocksalt bodies, flow stress levels between 0.6 and 1.4 MPa have been estimated. These values do not bear directly on arguments concerning the nature of forces initiating salt pillow growth because, apparently, evidence relating to the early deformational history has been overprinted. At that stage, fluid-assisted grain boundary diffusional processes might dominate dislocation creep, leading to a linear stress-strain rate mechanical response. Considering buoyancy forces alone, behavior described by equation (B) rather than (A) reduces the relief necessary to initiate pillow growth but a 1000-fold amplification is required to produce stress differences near 1 MPa. That forces other than buoyancy are important is indicated by the occurrence of these same paleostress levels in bedded salts and in shallow offshore concordant intrusions. Differential loading generally provides the most plausible initial driving force for the growth of diapiric salt structures.

The Sliding Characteristics of Sandstone on Quartz Fault-Gouge

SummaryThree types of triaxial compression experiments are used to characterize the frictional processes during sliding on quartz gouge. They are: 1) pre-cut Tennessee Sandstone sliding on an artificial layer of quartz gouge; 2) fractured Coconino Sandstone sliding along experimentally produced shear fractures; and 3) a fine-grained quartz aggregate deformed in compression. The specimens were deformed to 2.0 kb confining pressure at room temperature and displacement rates from 10−2 to 10−5 cm/sec dry and with water. There is a transition in sliding mode from stick-slip at confining pressures<0.7 kb to stable sliding at>0.7 kb. This transition is accompanied by a change from sliding at the sandstone-gouge contact (stick-slip) to riding on a layer of cataclastically flowing gouge (stable sliding). Quartz gouge between the pre-cut surfaces of Tennessee Sandstone lowers both the kinetic coefficient of friction and the magnitude of the stick-slip stress drops compared to those for a pre-cut surface alone. Stick-slip stress drops are preceded by stable sliding at displacements of 10−5 cm/sec. For a decrease in displacement rate between 10−3 and 10−5 cm/sec, stress-drops magnitudes increase from 25 to 50 bars. Tests on saturated quartz gouge show sufficient permeability to permit fluidpressure equilibrium within compacted gouge in 10 to 30 seconds; thus the principle of effective stress should hold for the fault zone with quartz gouge. Our results suggest that at effective confining pressures of less than 2.0 kb, if a fault zone contains quartz gouge, laboratory-type stick-slip can be an earthquake-source mechanism only if a planar sliding-surface develops, and then only when the effective confining pressure is less than 0.7 kb.

Mechanical behaviour of rock salt: phenomenology and micromechanisms

Abstract The mechanical behaviour of rock salt is very complex over the ranges of stress and temperature usually encountered in geoengineering. During the past decade substantial progress has been made in measuring and understanding this behaviour, primarily because of the studies that support proposed disposal of nuclear wastes in salt formations. Safe nuclear waste disposal in salt requires a fundamental understanding of its mechanical behaviour to predict performance of nuclear waste repositories for times much longer than those usually encountered in conventional geoengineering practice. This understanding of the mechanical behaviour relies on accurate measurements of the macroscopic phenomenology and interpretation of the role of micromechanisms in producing the observed phenomena.

Experimental folding of rocks under confining pressure: Part III. Faulted drape folds in multilithologic layered specimens

Drape folds and reverse faults are produced experimentally at confining pressures to 2.0 kb and shortening rates of 10 −3 to 10 −6 sec −1 by displacing a block of brittle sandstone (2 by 3 by 12.6 cm) along a lubricated saw cut into one to five initially intact layers (0.2 to 1.0 cm thick and as much as 12.6 cm long) of limestone, sandstone, and rock salt. The saw cut is inclined at from 30° to 90° to the layer boundary. The deformation is characterized from studies of fault geometry, displacements and sequence, bedding-plane slip, layer-thickness changes, and the development of fault gouge, fold hinges, microfractures, calcite twin lamellae, and dimensional orientations of grains (in the rock salt). Stress trajectories are inferred from faults, microfractures, and calcite twin lamellae, and strains are calculated from layer-thickness changes and from calcite twin lamellae. Reverse faults curving concave downward propagate upward from the saw cut in the forcing block. With increasing displacement along the precut faults, the faults and associated gouge zones in the layer steepen and become progressively younger toward the upthrown block as displacement increases. The faults are preceded by swarms of extension microfractures that form throughout the deformation and that are the best clues to the stress trajectories. The downthrown layers are thickened by uniform flow and by repetition caused by the faulting. They are displaced away from the faults by bedding-plane slip. Trajectories of the greatest principal compressive stress (σ 1 ) are inclined at low angles to the layer boundaries near the faults and become perpendicular to these boundaries away from the fault. The maximum deformation of the downthrown block occurs when the saw cut is inclined at about 65° to the layering. The upthrown layers are all extended parallel to the layering and perpendicular to the fold axes, as indicated by extension fractures, thinned layers, and calcite twin lamellae and the development of graben zones and low-angle normal faults that are conjugate to the reverse faults. The layers are translated by bedding-plane slip away from the fault zone. Trajectories of σ 1 are inclined from 45° to 90° to the layering. The fabric data are internally consistent, and inferred stresses are in good agreement with those calculated from an elastic solution of the experimental boundary conditions. Principal strains calculated from calcite twin lamellae are within an average of 0.01 of those calculated from layer-thickness changes and permit clear resolution of individual events in domains of superposed deformations.

Specimen-apparatus interaction during stick-slip in a tri axial compression machine: A decoupled two-degree-of-freedom model

Abstract The stick-slip of frictional sliding depends not only on material properties but also on the elastic and inertial properties of the loading system. To compare data from different testing machines or to apply them to the problem of natural seismogenic faulting, one must account for the differences in stiffness and mass. We develop a simple mechanical model to describe the stick-slip oscillation during frictional sliding in a triaxial-compression machine. The experimental system, the loading frame and rock specimen with precut sliding surface, is divided into two subsystems across this surface. The model is based upon two key assumptions: the kinetic friction is constant regardless of the relative motion of the subsystems, and the elastic restoring force is uniform throughout each subsystem. The first assumption leads to the decoupling of the subsystems, and the behavior of each becomes mathematically analogous to that of a simple spring/mass/slider-block model, owing to the second assumption. The theory agrees well with the experimental data from the dynamic measurements of stick-slip. The displacement-time function is of cosine form, the rise time of stick-slip is constant, and the relation between force drop and average displacement rate is linear. From this model we argue that the differences in the frictional behavior of experimental fault-gouges may indeed be ascribed to differences in the material properties of their specimens because the elastic and inertial properties of a particular testing machine are little influenced by the specimen itself, so long as all specimens are of about the same size. However, interlaboratory correlations may well be invalid unless machine effects are properly accounted for.

Thermal expansion and cracking of three confined water-saturated igneous rocks to 800°C

SummarySolutions of engineering problems of very deep drilling, geothermal energy production, and high-level nuclear-waste isolation require adequate understanding of the mechanical and transport properties of rocks at relatively low pressures but high temperatures. Accordingly, the thermal expansions of water-saturated Charcoal Granite, Mt. Hood Andesite, and Cuerbio Basalt have been measured at effective confining pressures (Pe) of 5, 50, and 100 MPa to 800° C. The mean coefficient of linear thermal expansion (α) is a function of lithology,Pe, temperature (T) and initial porosity (ϕ). For example, for the Charcoal Granite, α increases withT at all pressures. The signature of the alpha-beta transition of quartz is more pronounced at the lower pressures; at 100 MPa α nearly mimics that of a crack-free rock forT<300° C.α for the andesite atPe=5 MPa ranges from 10 to 15×10−6/°C from 200° to 400° C then decreases gradually to 10.1×10−6/°C at 800° C. At 50 MPa α ranges from 11.7×10−6/°C at 100° C to 8.6×10−6 at 200°C, then increases at a much lower rate to 11×10−6 at 600° C. The basalt, however, has an essentially constant α (11×10−6/°C) forT>150°C at the lower pressure and shows but a small increase in α from 6 to 9×10−6 from 100° to 800° C at 50 MPa.The difference between measured values of thermal expansion and those calculated from simple mixture-theory relates to new crack porosity generated as a result of differential thermal expansion at the anisotropic grain scale. For the granite, a two to three order of magnitude increase in permeability (k) is predicted from the relation,k∝φ3.

Experimental folding of rocks under confining pressure, Part VIII—Forced folding of unconsolidated sand and of lubricated layers of limestone and sandstone

Field and laboratory data suggest that variations in structural style are associated with differences in lithologic composition, stratigraphic sequence, and the mechanical behavior of the layers that are drape (forced) folded by differential vertical movements of underlying essentially rigid blocks. This hypothesis is tested by study of experimental, faulted, drape folds in veneers of loose, dry, unconsolidated sand and in multilithologic layered sequences with lubricated interfaces produced under confining pressures to 200 MPa (2 kb) at 25 °C. Deformation of the sand veneer provides a classic example of cataclastic flow. Forced folds develop as a result of microfracturing, rigid-body rotation of grains and fragments, and faulting and gouge development. The sand veneer is thinned drastically in the zone of faulting. The multilithologic, layered veneers with lubricated interfaces exhibit the same magnitudes of “bedding-plane” slip and somewhat more variability in the senses of slip than do specimens not lubricated. With lubrication, however, there is less deformation of the leading edge of the forcing block, less extensile faulting in the upthrown block, and more folding without faulting in the veneer.

Experimental folding of rocks under confining pressure: Part II. Buckling of multilayered rock beams

Specimens composed of as many as five layers of various combinations of dry Coconino Sandstone (brittle) and Indiana Limestone (ductile) are folded at 1-kb confining pressure. Stress-shortening curves for specimens with aspect ratios ≥20 are nearly linear up to a maximum stress (critical buckling stress) and then show pronounced postbuckling work-softening. For specimens of equal total thickness, the average maximum stress decreases with an increase in the number (and thickness) of limestone relative to sandstone layers. A single beam of limestone or sandstone has larger maximum stress than does the corresponding three-layer specimen of equal thickness. Curves for limestone specimens composed of from one to five layers and with aspect ratios ≤3 are monotonic and show poorly defined yield regions and pronounced work-hardening. Both thick-beam (aspect ratios of 7 to 13) and thin-beam (aspects ratios of 20 or more) folds tentatively are regarded as buckles because instabilities probably are involved in the folding. Fold (anticlinal) shape depends on the mechanical behavior of the bottom layer. When the ductile limestone is lowest, the fold shape is nearly sinusoidal; when the brittle sandstone is lowest, the anticline has a chevron shape. “Bedding-plane” slip is a maximum in the inflection region on the flanks, and the sense of slip is the reverse of that in classical flexural-slip folding. Dynamic petrofabric interpretations of small thrust and normal faults, macrofractures and microfractures, compression and extension axes derived from calcite twin lamellae, and the twin-lamellae spacing index indicate that although bedding-plane slip occurs, the entire layered specimen acts as a single mechanical beam throughout most of the folding. In thin, multilithologic folds, the apparent neutral surface is displaced from the center toward the compressed side. In thick, multilayered limestone specimens, large axial shortening prior to bending displaces the neutral surface toward the region of extension, so that even the uppermost layer in the anticlinal hinge can be in the zone of layer-parallel compression.

Kinematics of experimental forced folds and their relevance to cross-section balancing

Abstract We report the results of a series of laboratory experiments in which packages of layers (consisting of rock and lead) are deformed under 50 MPa confining pressure into forced folds by the uplift and rotation of pre-machined steel forcing blocks. The models are not fully scaled, but the geometries resulting form the deformation are remarkably similar to many natural forced folds observed in the U.S. Rocky Mountains foreland. During the folding, detachment and quantifiable layer-parallel translation occur between the layered sequence and the forcing assembly, confirming limited observations from earlier model studies. Away from the fold, there is a pattern of movement in which the layered sequence first moves away from the uplift, but, with greater structural relief, those motions reverse their sense to become layer-parallel translations towards the uplift. The very ductile lead unit at the base of the layered sequence flows laterally, especially across the crest of the uplift to the downthrown block, in response to pressure gradients which are inherent to asymmetric uplifts. The flow of this ductile unit causes layer-parallel translation of the rock layers, thereby transporting material into the fold. If the models were to be treated as proposed cross sections, and if they were subjected to the usual techniques of cross-section balancing, incorrect interpretations would result; this is because there are no suitable sites for either pin lines or no-flow boundaries.