M. Friedman

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.

Residual elastic strain in rocks

Abstract Residual elastic strains (stresses) consist of locked-in strains , reflecting crystal distortions related to past external loads, and those that constrain them, the locking strains . The forces or stresses giving rise to locked-in and locking strains exist in rocks with no external loads across their boundaries and satisfy internal equilibrium conditions i.e., their sum is zero. The strains are stored by cementation and physical and chemical interactions between anisotropic grains while under load. The measure of residual strain provided by strain relief or X-ray methods consists of some unknown combination of locking and locked-in strains that depends on the distribution, relative magnitudes, and degrees of relaxation (strain relief method) of these components and the special bias of the measuring technique. With the X-ray technique, the bias is toward detection of strains in the most voluminous rock elements satisfying the Bragg condition for diffraction. In sandstone, therefore, the residual strains in the grains are sampled preferentially to those in the cement. The special view of residual stresses obtained from X-ray diffraction studies and supported by data from strain relief techniques has yielded significant information as follows: 1. (1) Magnitudes can be large; differential stresses between 300 and 400 bar have been measured in quartzites, sandstones, and granites. 2. (2) Residual stresses relating to Mesozoic and possibly even to Precambrian geologic events have been mapped. 3. (3) Principal axes correlate with the geometry of large-scale folds and to stresses inferred from nearby fractures and calcite twin lamellae. 4. (4) Residual stresses have been found to vary systematically along fault surfaces in such a manner as to be related to the process of sliding. Items 1–4 suggest that rocks have long-term fundamental strength; volumetric stored strain energy is commonly of the order of 10 4 erg/cm 3 . 5. (5) Stored stresses relax when grains are freed from constraints of nearest neighbors. 6. (6) They relax within 5 mm of an induced tensile fracture in sandstone probably because movements along grain boundaries occur that far from the fracture surface. 7. (7) Residual stresses influence the orientations of tensile and shear fractures induced experimentally under certain conditions of loading. 8. (8) Observed residual stresses can contribute to strength anisotropy. Items 7 and 8 are explicable from superposition of applied loads on the observed residual stresses. 9. (9) In the Barre Granite the principal axes of residual strain are subparallel to the principal directions of ultrasonic attenuation and velocity fields.

Glass-Indurated Quartz Gouge in Sliding-Friction Experiments on Sandstone

Three types of glass-indurated quartzose gouge are recognized (optically and with SEM) along the sliding surfaces of 29° to 45° precut specimens of dry Tennessee Sandstone, deformed at 0.14- to 5.0-kb confining pressure, shortening rates of 10 to 10−4/sec, 24° to 410°C, and with displacements <1.0 cm. “Welded clumps” form in tests at 24° and ≤1.0-kb confining pressure. The welded portions of each clump are composed of quartz fragments indurated by an optically isotropic matrix (index of refraction of 1.500 to 1.520) that supports brittle fracture and is probably glass. As the temperature of the experiments is increased, “fibrous patches” become widespread. These patches are vesicular and conspicuously striated, they stand out in optical relief on top of quartz grains, they contain ordered microfractures that suggest extension along the sliding direction, and their “lee” edges are marked by very fine fibers that emanate from tapered bodies rooting in the patches. At high pressures and low temperatures, “welded plates” cover much of the sliding surfaces. These are fractured and striated, but nonfibrous. The glass indicates that local silica–fusion temperatures occurred during frictional sliding. The change in the nature of the gouge is accompanied by a change in sliding mode from stick-slip (25°C) to episodic (150° to 250°C) to stable sliding (410°C), and by a progressive increase in the coefficient of sliding friction from 0.58 at 25°C, to 0.72 at 410°C.

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.

Microscopic Feather Fractures

Certain microfractures adjacent to faults in experimentally deformed cylinders of Westerly Granite form as a result of shear displacement along the primary fault, and they are oriented consistently relative to the fault surface. These fractures are described in detail because they are: (a) symptomatic of a homogeneous state of stress in the region of the fault at the time of faulting; (b) criteria to demonstrate that shear displacement has occurred along a fault; and (c) criteria to establish unequivocally the sense of shear.

Lüders' Bands in Experimentally Deformed Sandstone and Limestone

Planar deformation features inclined along planes of high shear stress and along which cataclasis is concentrated are here called “Luders9 bands.” In Coconino Sandstone (deformed dry and with pore pressure at effective confining pressures to 2.4 kb, room temperature, and at a strain rate of 10 −4 per sec) the bands begin to develop in the transitional regime and are the major deformation feature in the macroscopically ductile regime. At axial shortenings of 5 percent and more they pervade the specimen and become closer spaced and thicker with increasing strain. The bands are formed by two or more layers of moderately to highly fractured quartz grains. They are markedly different from shear fractures (or faults) of similar size that typically contain quartz gouge. The average angle between conjugate sets of bands bisected by the greatest principal compressive stress σ 1 increases with effective confining pressure from 75° to 109°. The corresponding angles between conjugate macroscopic shear fractures average 60°. The angle between Luders9 bands is essentially independent of strain at fixed effective confining pressure. In Solenhofen Limestone (deformed dry at confining pressures to 3.0 kb, 24°C, and strain rates from 10/sec to 10 −4 /sec) the Luders9 bands are developed only in the outer shell of the solid cylinders; however, in coarser grained limestones, the bands are pervasive as in the sandstone. In cylinders of Solenhofen, the bands are best developed in the transitional regime, as noted previously by Heard (1960). They do not form in the ductile regime. The average angle between conjugate sets is independent of strain and strain rate; but as for the sandstone, it increases with confining pressure from 75° to 103°, and it is at least 20 degrees larger than the corresponding angle between conjugate shear fractures which form after the Luders9 bands. Optical and SEM studies indicate that the features in both rocks are zones of intergranular and intragranular cataclasis, along which shear displacements are negligible. Because the angle between conjugate Luders9 bands is a function of the effective pressure, the bands might be used to derive depth of burial at time of deformation, provided that (1) the pore fluid pressure is assumed to be hydrostatic, and (2) the orientation of CTI, which can be the acute or obtuse bisector, is independently known. If (1) is unwarranted, then the angle between the bands could be used to infer the pore fluid pressure, provided the depth of burial is known. This approach is illustrated with reference to an occurrence of Luders9 bands in naturally deformed Entrada Sandstone, Trachyte Mesa, Utah.

Microscopic feather fractures in the faulting process

Abstract The nature and development of microscopic feather fractures (mff) are investigated in experimentally deformed intact and precut cylinders of room-dry Tennessee and Coconino Sandstone. All specimens are deformed at 25° C, and at a shortening rate of 10−4 sec−1 ; the intact ones are at confining pressures from 0.5 to 2.5 kbar; and the precut specimens at 1.0 and 1.5 kbar. Mff occur in grains adjacent to induced shear fractures or faults; they are wedge-shaped and die out within one or two grain diameters from the fault; and they make acute angles with the fault such that arrows directed into the apices of these angles on either side of the fault define its sense of shear. Occurrence of mff only after slip on precut surfaces clearly demonstrates that they form as a result of shear displacement. The average angle between the mff and fault is 10° greater than that between the load axis and the fault, and it increases with increasing confining pressure in initially intact specimens. Data suggest that the abundance of mff (mean number per grain) increases with increasing normal stress across the fault and with displacement. The wedgeshaped character of many mff and their consistent orientation at 10° to the load axis are distinguishing characteristics. Mff are shown to be parallel to the local maximum compressive stress and thus are extension microfractures. They are not to be confused with precursive micro fractures developed prior to macroscopic fracture, nor to Riedel shears developed during faulting.

Relations between Stresses Inferred from Calcite Twin Lamellae and Macrofractures, Teton Anticline, Montana

Compression axes inferred from calcite twin lamellae in eleven samples of Madison Limestone from both flanks of Teton anticline are remarkably similar. They indicate that the greatest principal stress (σ 1 ) was subparallel to the dip at one time during the folding and inclined to the bedding at other times. In three of the four samples from the plunging nose, compression axes are more diffuse than are those from the flanks. The compression axis pattern for the flank stations agrees with one of the two prominent macrofracrure patterns. The second prominent fracture assemblage indicates that at some time during the folding σ 1 was parallel to the fold axis. This orientation of the compression axis is never seen in the calcite data, even though some samples were collected immediately adjacent to macrofractures of this group. However, the fabric of a flank specimen, experimentally deformed such that the compressive load was parallel to the strike direction, clearly shows that compression axes inferred from e 1 lamellae are subparallel to the experimental σ 1 , and compression axes inferred from e 2 lamellae reflect the original natural fabric. That is, the original e 1 lamellae are demoted to e 2 lamellae by the superposed deformation. Moreover, the twin lamellae index is much higher in the experiments than in the naturally deformed rocks. Thus, in cases of superposed deformations, the calcite technique statistically maps the compression axis associated with the largest strain. Therefore, for the specimen studied, the shortening associated with σ 1 perpendicular to the fold axis probably is greater than that parallel to the fold axis.

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.