Michael R. Gross

The origin and spacing of cross joints: examples from the Monterey Formation, Santa Barbara Coastline, California

Abstract Cross joints in the Monterey Formation terminate against a series of pre-existing systematic strike-perpendicular joints. The strike-perpendicular joints act as mechanical layer boundaries during cross joint propagation, and the distance between adjacent strike-perpendicular joints represents a mechanical layer thickness. The fracture spacing index (FSI), or ratio of joint-controlled mechanical layer thickness to cross joint spacing in the Monterey Formation, is approximately 1.3. A model is proposed for cross joint propagation based on the analysis of stress reduction in the vicinity of a newly-formed joint. In this model, cross joint development follows a sequential infilling process as remote tensile stress increases with time. According to the model, the first cross joints (FSI = 0.32) propagate under a remote tensile stress of approximately -14 MPa. A second episode of cross jointing (FSI = 0.65) initiates when remote tensile stress reaches -27 MPa, and a third generation of cross joints (FSI = 1.30) develops at -57 MPa. Joints in each successive episode initiate in the midregion between existing joints where local tensile stress is highest. High remote tensile stresses may develop due to differential horizontal contraction among adjacent stratigraphic beds upon uplift and erosion.

Mechanical and fracture stratigraphy

Using examples from core studies, this article shows that separate identification of mechanical stratigraphy and fracture stratigraphy leads to a clearer understanding of fracture patterns and more accurate prediction of fracture attributes away from the wellbore. Mechanical stratigraphy subdivides stratified rock into discrete mechanical units defined by properties such as tensile strength, elastic stiffness, brittleness, and fracture mechanics properties. Fracture stratigraphy subdivides rock into fracture units according to extent, intensity, or some other observed fracture attribute. Mechanical stratigraphy is the by-product of depositional composition and structure, and chemical and mechanical changes superimposed on rock composition, texture, and interfaces after deposition. Fracture stratigraphy reflects a specific loading history and mechanical stratigraphy during failure. Because mechanical property changes reflect diagenesis and fractures evolve with loading history, mechanical stratigraphy and fracture stratigraphy need not coincide. In subsurface studies, current mechanical stratigraphy is generally measurable, but because of inherent limitations of sampling, fracture stratigraphy is commonly incompletely known. To accurately predict fractures in diagenetically and structurally complex settings, we need to use evidence of loading and mechanical property history as well as current mechanical states.

Factors controlling joint spacing in interbedded sedimentary rocks: integrating numerical models with field observations from the Monterey Formation, USA

Abstract Local tensile stress normal to a joint is reduced in the vicinity of the joint because such stresses are not transmitted across free surfaces. This stress reduction prevents the formation of new joints in the vicinity of existing joints, and thus influences joint spacing. Lateral extent of this stress reduction shadow increases with joint height, which corresponds to bed thickness for many sedimentary rocks. The linear correlation between joint spacing and bed thickness commonly observed in outcrop is a direct result of this relationship. However, other factors in addition to bed thickness influence joint spacing. We evaluate these factors through both a review of the Hobbs model for joint spacing and a 2D finite element simulation of a crack confined to a lithology-controlled mechanical unit. The stress reduction shadow increases in length with incresaing Young’s modulus of the jointing bed, though fracture stress, flaw size, flaw distribution and extensional strain all interact with bed thickness and elastic properties ultimately to control joint spacing. One explanation for the observed decrease in joint spacing with increasing Young’s modulus in outcrops of the Monterey Formation is that beds with higher Young’s moduli fail at lower magnitudes of extensional strain.

Orthogonal cross joints: do they imply a regional stress rotation?

Abstract Orthogonal cross joints extend across intervals between systematic joints in brittle sedimentary strata and abut the systematic joints at about 90° angles. These joints typically form a ‘ladder-like’ pattern if viewed on a bedding surface. A common interpretation is that orthogonal cross joints define the orientation of the regional stress field during their formation: least compressive stress perpendicular to the joints. It follows that they indicate a rotation of regional principal stresses by 90° after the formation of the systematic joints. Using a three-dimensional boundary element code (Poly3D), we considered a simple geologic case of vertical systematic fractures developing in horizontal strata under a triaxial remote load with: the maximum principal tensile stress being horizontal and perpendicular to the strike of the fractures, the intermediate principal stress being horizontal and parallel to the strike of the fractures, and the least principal tensile stress (i.e. maximum compressive stress) being vertical. The results show that the local maximum principal stress is first perpendicular, and then parallel to, the strike of the systematic fractures as the ratio of fracture spacing to height changes from greater than to less than a critical value when the horizontal remote principal stress ratio, the ratio of the intermediate remote principal stress to the maximum remote principal stress under the sign convention of positive for tensile stresses, is greater than a threshold value (∼0.2). Thus, the fracturing process changes from infilling of systematic fractures to the formation of orthogonal cross fractures. This provides an alternative mechanism for the formation of orthogonal cross joints that does not require a systematic rotation of the regional stress field by 90°. The critical spacing to height ratio for the local principal stress switch is independent of the least remote principal stress (i.e. overburden). It increases nonlinearly with increasing ratio of the horizontal remote principal stresses, and decreases nonlinearly with increasing Poissons ratio of the material.

Mechanism for joint saturation in mechanically layered rocks: an example from southern Israel

Abstract Over 700 joint spacings were measured along a 190-m scanline within a single limestone bed of the Turonian Gerofit Formation, southern Israel. By investigating joints belonging to a single systematic set confined to a bed of uniform thickness, one can factor out the major influences of bed thickness, lithology and mechanical properties on joint set development. Joint spacing distributions and fracture spacing ratios (FSR) vary dramatically along the length of the scanline, and correlate directly with throughgoing fracture zones belonging to the same tectonic stress regime. Regions cross-cut by fracture zones display narrower median joint spacings, FSR of ∼ 1.3, and unimodal joint spacing distributions. Where fracture zones are absent, joint spacings have wider medians, FSR of ∼ 0.8, and multimodal distributions. Because fracture zones most likely represent areas of high strain, and laboratory experiments demonstrate a systematic decrease in fracture spacing with increasing strain, regions of the bed cross-cut by fracture zones are likely at a more advanced stage of joint set development, and hence closer to saturation, than other regions. Joint saturation in the Gerofit Formation may be achieved by a shift in scale from single-layer to multi-layer jointing, as the development of throughgoing joints prevents the formation of additional bedding-confined joints.

Normal fault growth in layered rocks at Split Mountain, Utah: influence of mechanical stratigraphy on dip linkage, fault restriction and fault scaling

We analyze displacement profiles measured from a population of normal faults that cut across layered clastic rocks, in order to investigate the controls of mechanical layering on fault growth. Abundant fault tips and displacement minima are found at lithologic contacts, and in some cases are associated with relay structures, suggesting that lithology is responsible for controlling the location of vertical, along-dip segment linkage. Based on the locations and distributions of displacement minima and maxima within the stratigraphic section, as well as the distribution of small faults, we conclude that: (1) most faults initiate within shale beds, and (2) lithologic contacts restrict fault growth at a variety of scales. One consequence of fault restriction is the development of high displacement gradients at fault tips. Because fault tips are only temporarily pinned at bed boundaries, the degree of restriction will fluctuate as faults propagate through the section. In general, maximum displacement (Dmax) across the faults correlates with cross-sectional trace length (L). The Dmax/L ratio decreases as a function of percent shale offset by a fault, and increases as a function of near-tip displacement gradient. An empirically-derived equation relates Dmax/L to rock composition and fault tip displacement gradients, thereby providing a mechanism to predict fault dimensions in the subsurface from limited data.

Influence of mechanical stratigraphy and kinematics on fault scaling relations

In order to document effects of mechanical anisotropy, fault geometry, and structural style on displacement-length (D-L) scaling relations, we investigated fault dimensions in the lithologically heterogeneous Monterey Formation exposed along Arroyo Burro Beach, California. The faults, which range in length from several centimeters to several meters, group into two populations: small faults confined to individual mudstone beds, and larger faults that displace multiple beds and often merge into bedding plane detachments. Whereas a linear correlation exists between displacement and length for small faults, displacement across large faults is independent of length. We attribute this deviation from scale-invariance to a combination of geologic factors that influence fault growth once faults extend beyond the confines of mudstone beds. Propagation of large faults across higher moduli opal-CT porcellanite leads to a reduction in DL, as does the development of drag folds. Further scatter in DL occurs when fault tips splay as they approach detachments. Large faults eventually merge into bedding plane detachments, which originally formed due to flexural slip folding. Extremely high DL ratios are recorded for these merged faults as they accommodate block rotation within a simple shear zone. Thus, both mechanical stratigraphy and the temporal evolution of fault systems can lead to a breakdown in fault scaling relations thought to characterize isolated fault growth in a homogeneous medium.

Strain accommodated by brittle failure in adjacent units of the Monterey Formation, U.S.A.: scale effects and evidence for uniform displacement boundary conditions

Abstract Extensional strain accommodated by brittle deformation was measured in adjacent mudstone and dolostone units at Arroyo Burro beach, California. The dolostone failed in effective tension whereas the mudstone failed in shear, both in response to the same extensional tectonic event. In the mudstone unit initial bed-length and fault-displacement methods document extensional strains of 6.6% ± 0.3% and 6.0% ± 0.3%, respectively. Upon adjusting the displacement estimates according to theoretical fault displacement population analysis, the corrected strain becomes 9.7% ± 0.3% for the mudstone. Measurements of vein apertures in the dolostone document extensional strain that varies according to scale, with outcrop vein scanlines indicating a strain of 3.4% ± 0.1%, and thin-section scanlines yielding a strain of 5.8% ± 0.2. Applying theoretical fault displacement population analysis to vein apertures in dolostone shows that small veins below the detection limit of outcrop surveys contribute significantly to fracture-related strain within the dolostone. This difference in extensional strain may arise because veins measured in outcrop extend across the entire bed height and thus are controlled by the dolostone mechanical layer thickness, whereas microscopic veins measured in thin-section terminate without regard to a bounding layer. The corrected dolostone strain becomes 10.2% ± 1.0%, matching the revised strain calculated in the adjacent mudstone unit and indicating uniform displacement boundary conditions for the two markedly different lithologies. The ~10% extensional strain at Arroyo Burro indicates significant strike-parallel (NW-SE) extension accommodated by brittle failure during development of the western Transverse Ranges fold and thrust belt.

Finite-element analysis of the stress distribution around a pressurized crack in a layered elastic medium: implications for the spacing of fluid-driven joints in bedded sedimentary rock

Bedding-perpendicular joints confined to individual beds in interbedded sedimentary rocks commonly exhibit spacings which are proportional to the thickness of the jointed bed, and which vary according to lithology or structural position. The mechanical explanation for this relationship is well understood when the joints are driven by far-field crack-normal tensile stresses, but poorly understood for cracks driven by elevated fluid pressures, where the crack-driving stress is the difference between the crack-normal compression and the fluid pressure in the crack. Through a series of finite-element numerical models, we investigate how various parameters influence the driving-stress distribution around pressurized cracks in layered media, and thereby identify factors influencing the spacing of fluid-driven joints. For the situation we modeled, we observe that: (1) crack-driving stress is reduced in the vicinity of pressurized joints, and that the extent of the stress reduction depends on the contrast in elastic properties between the layers; and (2) crack-driving stress distribution depends on the ambient pore pressure during jointing. These results indicate the spacing of fluid-driven joints should depend on lithology and pore pressure.

Faulted joints: kinematics, displacement-length scaling relations and criteria for their identification

Structural geometries and kinematics based on two sets of joints, pinnate joints and fault striations, reveal that some mesoscale faults at Split Mountain, Utah, originated as joints. Unlike many other types of faults, displacements (D) across faulted joints do not scale with lengths (L) and therefore do not adhere to published fault scaling laws. Rather, fault size corresponds initially to original joint length, which in turn is controlled by bed thickness for bed-confined joints. Although faulted joints will grow in length with increasing slip, the total change in length is negligible compared to the original length, leading to an independence of D from L during early stages of joint reactivation. Therefore, attempts to predict fault length, gouge thickness, or hydrologic properties based solely upon D‐Lscaling laws could yield misleading results for faulted joints. Pinnate joints, distinguishable from wing cracks, developed within the dilational quadrants along faulted joints and help to constrain the kinematics of joint reactivation. q 2001 Elsevier Science Ltd. All rights reserved.