Failure Modes and Fault Morphology

The hydraulic behavior of faults and fault systems is a key consideration for a variety of subsurface activities. Faults commonly act as conduits for fluid flow and as a result the storage capacity of reservoir intervals and the sealing potential of low-permeability layers may be substantially impacted if faults are present [1-8]. Geothermal energy, groundwater management, CO₂ sequestration, subsurface hydrogen storage, and hydrocarbon production activities are often focused on formations or rock volumes where faults and fractures are present, and fault sealing versus conduit behavior is therefore a primary uncertainty with respect to subsurface fluid flow or containment potential. Of increasing importance globally is the need to implement large-scale geological storage of CO₂ [9, 10]. Safe and sustainable CO₂ sequestration relies on long-term fluid containment within subsurface reservoirs, and as such the potential for CO₂ migration and leakage along faults and fractures is often a primary risk for sequestration projects (e.g., [11-14]).

Faults and fault zones may act as seals, as conduits, or as dual conduit-seal systems [2], and networks of faults produce bulk permeability anisotropy in a rock mass [15]. Fault sealing behavior reduces bulk rock permeability and inhibits fluid flow, which may be either beneficial or detrimental. For example, fault sealing behavior may allow containment of economic oil and gas accumulations in structural traps [16], or it may lead to reservoir compartmentalization [17] which may hamper resource extraction. Fault conduit behavior increases bulk rock permeability and enhances fluid flow, resulting in both desired (e.g., development of aquifer recharge pathways; [18-21]) and undesired (e.g., fluid leakage from reservoir intervals) effects in the subsurface. Fault sealing behavior is most commonly observed in siliciclastic successions, where processes such as rock comminution, clay smear development, and juxtaposition of reservoir intervals with clay-rich sealing layers have been shown to enhance the potential for faults to act as barriers to fluid flow (e.g., [22-28]).

In carbonate successions, fault sealing behavior tends to be more difficult to predict because of the inherent heterogeneity of carbonate successions and the propensity for carbonate rocks to be chemically altered through diagenetic processes (e.g., [29]). Furthermore, brittle intervals with low matrix porosity and permeability are relatively common in carbonate successions. Faults exhibiting conduit behavior often occur in such intervals, where fault permeability may develop through dilation and self-propping behavior (e.g., [30-32]) and be enhanced by dissolution along faults and fault zones [32]. Faults with dual conduit-seal behavior have permeability properties where some zones along a fault inhibit fluid flow while others enhance bulk rock permeability [2, 4, 33, 34]. Dual conduit-seal behavior may be caused by factors such as vertical or lateral variations in fault displacement and associated changes in layer juxtapositions (e.g., [19, 35]) heterogeneity in fault zone architecture [36], variable degrees of rock comminution within a fault zone [37], and variations in cementation versus dissolution that has occurred within a fault or fault zone (e.g., [38]), among other factors.

The geometric characteristics of fault surfaces (roughness, asperities, corrugations, and variations in strike and dip) play an important role in both the fluid flow and mechanical properties of faults and fault zones. Most fault surfaces are distinctly nonplanar and as such natural fault surfaces have complex and variable geometric properties. Fault geometry typically impacts the mechanical strength of fault zones (e.g., [39]), how and where slip accumulates along faults (e.g., [40]), and the potential for reactivation of faults under changing stress and pore pressure conditions (e.g., [41]). Similarly, fault geometry can substantially impact the hydraulic properties of faults and fault zones. For example, slip on nonplanar fault surfaces can lead to self-propping and the development of dilatant patches where voids or cavities act as fluid pathways [3, 42]. Fault geometry is also important with respect to in situ stress conditions and the associated resolved stresses acting upon fault surfaces with variable orientations. In low permeability rocks, faults and fractures that are critically stressed present-day, with high slip tendency (T_s; [43]) or dilation tendency (T_d; [42]), are those most likely to act as subsurface fluid flow pathways [1, 30, 31, 44-52].

Fault geometry is primarily determined by the deformation behavior of the rock mass, which is influenced by a range of factors including rock properties, stress state, failure mode, fault segment linkage, and progressive deformation. Fault orientation variability has been shown to be influenced by variations in failure mode (i.e., tensile vs. hybrid vs. shear) on individual fault surfaces during early fault growth, with failure mode defined by rock properties (and failure envelope) and the in situ stresses at the time of fault nucleation and early growth (e.g., [45, 47, 48]). The resolution of fault mapping and associated geometries is important for determining fault slip and leakage potential (e.g., [53]). Due to the sampling limitations of subsurface datasets (i.e., limited resolution of reflection seismic data and widely spaced wellbore penetrations), however, fault geometry can only be partially constrained in the subsurface (e.g., [54, 55]). There remains a lack of quantitative studies that assess three-dimensional (3D) geometry of natural fault surfaces with respect to (i) in situ stress conditions and the associated resolved stresses acting upon fault surfaces with variable orientations, (ii) associated fault reactivation potential, and (iii) the implications for fault sealing versus conduit behavior, particularly in low-permeability rocks.

Here, we combine field measurements and observations with high-resolution photogrammetric reconstruction techniques and document that failure modes define fault geometry during the earliest stages of fault initiation and growth. Fault reconstruction via digital photogrammetry provides sufficient resolution to capture subtle changes in fault geometry and associated slip and dilation tendency, and identify complex patchworks of variable failure modes along three small-scale, carbonate-hosted normal faults at Canyon Lake Gorge, Comal County, Texas. Our results have implications for predicting fault transmissivity in the subsurface and the feedbacks between failure mode, fault geometry, and the potential for conduit versus seal behavior along faults and fault zones.

Canyon Lake Gorge, approximately 50 km northeast of San Antonio, Texas, formed due to incision and erosion by a single catastrophic flood in 2002 [56-58]. The flood exposed the main Hidden Valley fault zone and both the footwall and hanging wall of the fault in the mechanically layered Cretaceous carbonate rocks of the Glen Rose Formation. The Hidden Valley fault is a seismic-scale, ENE-WSW-striking, SSE-dipping normal fault with 55–63 m of throw and an average strike and dip of 057° and 67°, respectively [59]. Canyon Lake Gorge and the Hidden Valley fault lie within the Balcones fault system (Figure 1 [18, 59-62], which formed in the Oligocene to Miocene to accommodate regional subsidence toward the southeast associated with deposition and sedimentary loading on the Gulf of Mexico basin margin [63-69]. The Balcones fault system trends approximately NE-SW (Figure 1) and marks the transition between the tectonically stable domain of the Texas craton to the NW and the extensional domain of faulted Cretaceous to Oligocene strata that dip toward the Gulf of Mexico to the SE [69].

Here, we focus on the 3D geometries of three mesoscale faults exposed in the footwall of the Hidden Valley fault (see map and cross section insets in Figure 1(b)). Most small-scale faults exposed at Canyon Lake Gorge (including faults B and C) strike approximately parallel to the SSE-dipping Hidden Valley fault (Figure 2), with dip directions either synthetic or antithetic to the main fault [59]. Where small-scale faults are oriented obliquely to the main fault zone, this has been attributed to local stress field rotations associated with fault overlap, displacement gradients along the main Hidden Valley fault, and relay ramp formation [59, 70, 71]. Fault A in this study is oriented obliquely to the Hidden Valley fault (Figures 2 and 3) associated with a displacement gradient along the Hidden Valley fault [70]. Faults B and C strike approximately parallel to the main fault with Fault B having a synthetic dip and Fault C having an antithetic dip (Figure 2).

Field measurements of fault surface orientations (strike and dip), fault slip directions (slickenline rake on fault surfaces), and fault displacements (measured parallel to slickenlines on fault surfaces) were acquired for faults A and C. Equivalent data were previously collected from Fault B by Ferrill et al. [45] and are reproduced here. In addition to field measurements, aerial imagery of the three fault surfaces was acquired using a DJI Phantom 4 Pro unoccupied aerial vehicle (UAV). Photogrammetric reconstruction of the fault surfaces was carried out using digital imagery, with 160 images used to reconstruct Fault A, 445 images for Fault B, and 370 images for Fault C. Photogrammetric reconstructions were georeferenced with ground control points, with coordinates of control points surveyed and recorded using a real-time kinematic differential global positional system (RTKDGPS). Photogrammetric processing was carried out using Agisoft Metashape 1.7.3, following the protocols described by Cawood et al. [72].

Fault orientations and displacements measured in the field were used to calculate local stress tensors for each of the three faults using the stress inversion technique of McFarland et al. [73] in 3DStress®. Unlike most traditional stress inversion techniques that rely on fault slip direction (e.g., [74-76], this inversion approach uses only fault orientation (strike and dip) and displacement magnitude to estimate stress states, with T_s maximized on faults with the largest displacements [71]. The inversion-based stress tensors were used for subsequent analysis of T_s and T_d for each of the three analyzed faults.

Slip tendency (T_s), as defined by Morris et al. [43], is a measure of the likelihood of slip on a fault, fracture, or other geologic surface within a given stress state. Slip tendency is a function of the resolved shear stress (τ) and the resolved normal stress (σ_n) acting on a fault or fracture [43]:

The normal and shear stresses acting on a fault or fracture surface are a function of the magnitude and orientation of the principal stresses relative to the surface of interest.

Dilation tendency (T_d), as defined by Ferrill et al. [42], is the propensity for a fault, fracture, or other geologic surface to be open or dilated within a given stress state and is defined by the following equation:

where σ₁ and σ₃ are the maximum and minimum principal compressive stresses, respectively.

T_s and T_d analyses were performed in 3DStress®, using stress tensors derived for each fault (Section 4.2), field measurements of fault orientations, and photogrammetric fault surface reconstructions.

Fault A is exposed in the upper part of Canyon Lake Gorge (Figure 1(b)) on the southern edge of the Canyon Lake dam spillway and is comprised of a main fault surface and a subsidiary fault branch that is subparallel to the main fault (Figure 2(a)). Fifty-nine field measurements of fault strike, dip, displacement, and slickenline rake (where observed) were recorded from Fault A, with associated descriptions of fault morphology (e.g., observed mineralization or slickensides) recorded at each measurement position. The main fault surface has an average strike and dip of 285° and 34°, respectively (Figure 3(a)), and measured displacement of 10–15 cm for the main fault and 5 cm for the branching fault segment. For the fifty-nine measurements recorded for Fault A, associated descriptions of fault morphology record the occurrence of thirty-seven slickensided patches, fifteen euhedral calcite patches, and seven slickolite patches at measurement positions (Figure 3(a)). The term slickolite was coined by Bretz [77], who later described these features as “made by differential solution along minor fault planes in calcareous rock” [78]. Subsequent work provided further evidence that these features form by compactional shear (e.g., [79, 80]). Slickolites were documented in the Glen Rose Formation by Ferrill et al. ([15], see their Figure 7).

Fault B is exposed in the upper-middle part of Canyon Lake Gorge (Figure 1(b)) and was previously measured and described in detail by Ferrill et al. [45, 47]. The upper part of this fault surface is defined by a mosaic of slickensided and euhedral-calcite-coated patches (Figure 2(b)), with steeper patches generally associated with euhedral calcite and less steeply dipping patches associated with slickensides [81]. Thirty-six measurements of fault strike, dip, displacement (where measurable), and slickenline rake (where observed) were previously collected at the site [45, 47] and are reproduced here. Fourteen of the thirty-six fault measurements recorded at Fault B are associated with euhedral calcite patches, eighteen are associated with slickensided surfaces, and four are not associated with either euhedral calcite or slickensides (Figure 3(b)). No slickolite patches were previously reported at Fault B [45, 47]. Fault B has an average strike and dip of 059° and 46°, respectively (subparallel and synthetic to the Hidden Valley fault), and measured displacement of 3.1–6.8 cm.

Fault C is exposed in the middle part of Canyon Lake Gorge (Figure 1(b)) and is made up of three curved and linked en-echelon fault segments (Figure 2(c)). This fault surface is dominantly slickensided, though with a few patches of euhedral calcite and slickensided euhedral calcite also observed on the fault. Of the thirty measurements of fault strike, dip, and displacement at Fault B, seven are associated with euhedral calcite, five show evidence for slickensided calcite (i.e., euhedral calcite overprinted with slickensides), and eighteen are associated with slickensides only, with no calcite observed (Figure 3(c)). Slickensided patches on the fault are interpreted to represent shear failure, euhedral calcite patches are interpreted to represent dilation (with euhedral crystal growth into voids), and we interpret slickensided calcite patches as recording early dilation (and euhedral crystal growth), followed by shear displacement and slickenside development on euhedral calcite patches. Measured displacement on Fault C is 2–23 cm, with segment 1 exhibiting highest displacements (21 and 23 cm) and segment 3 exhibiting lowest displacement magnitudes (2 cm). Fault C has an average strike and dip of 236° and 45°, respectively (striking subparallel but dipping antithetic to the Hidden Valley fault), and no slickolite patches were observed at this locality.

Field measurements from the three faults assessed in this study exhibit substantial orientation variability in both dip and dip directions (Figure 3). When compared to the previously published regional stress state and associated T_s and T_d for the Hidden Valley fault and Balcones fault system (Figures 4(a) and 4(b); [25]), a substantial portion of these fault measurements are coincident with zones of low to moderate T_s. This suggests that a regional stress tensor does not adequately capture locally variable stress states responsible for the nucleation and growth of the three faults characterized here. As such, individual stress states were estimated for each of the three faults (the Fault B stress state is reproduced from Ferrill et al. [45]) using the inversion technique of McFarland et al. [73] in 3DStress®. For the stress inversion for Fault C, seven fault measurements from nearby, small-scale faults were used to improve the robustness of the inverted stress field and to provide fewer degrees of freedom for inverted principal stress orientations. These small-scale faults show similar orientations to the main Hidden Valley fault and are interpreted to be kinematically compatible, conjugate structures to Fault C. Small-scale fault orientations are provided in Figures 3 and 4. Locations of these small-scale faults with respect to Fault C are provided in online supplementary Appendix B.

Estimated principal stress orientations and relative magnitudes of the three principal stresses for each of the three faults are provided in Figure 4 and Table 1. The estimated stress orientations for Fault A markedly contrast with the regional stress state estimation of Ferrill et al. [18], which shows σ₁ as vertical, σ₂ as horizontal and trending northeast (055°), and σ₃ as horizontal and trending northwest (325°). The obliquity of Fault A with respect to the Hidden Valley fault is likely related to local stress rotations around Fault A at the time of fault nucleation and growth, consistent with their formation in a relay ramp as discussed in the analysis of the nearby system of oblique faults 100 m ESE of Fault A by Morris et al. [70].

Estimated stress orientations for Faults B and C are more consistent with the regional stress tensor of Ferrill et al. ([18], Figure 4), with σ₁ near vertical, σ₂ shallowly plunging to the northeast or southwest, and σ₃ plunging to the northwest or southeast. It should be noted that the regional stress inversion of Ferrill et al. [18] assumes a vertical σ₁ whereas our local stress inversions (Figure 4) provide solutions with subvertical σ₁ and subhorizontal σ₂ and σ_3. We interpret subvertical σ₁ and subhorizontal σ₂ and σ₃ solutions for Faults A, B, and C as being due to local rotation of sedimentary layers and early-formed, small-scale faults as slip along the main Hidden Valley fault accumulated (see Figure 1(b) for general fault zone geometry).

Field data from Fault A show that patches coated with euhedral calcite have moderate to steep dips (35-68^o) with variable (low to high) T_s and high to very high T_d. Slickensided surfaces exhibit very low to moderate dips (15-47°), high or very high T_s, and moderate to high T_d (Figures 4(c) and 4(d), Table 2). Slickolite or compactional shear fault patches on Fault A are shallowly dipping according to field measurements (8-12° dip) and exhibit moderate T_s and low to intermediate T_d. The photogrammetric reconstruction of Fault A highlights substantial small-scale variability in dip direction (Figure 5(a)) and dip magnitude (Figure 5(b)) along both the main and branching fault surfaces. The spatial distribution of observed slickensides, euhedral calcite, and slickolite surfaces on Fault A does not appear to show a systematic correspondence to dip direction (or strike) along the fault (Figure 5(a); see also field orientation data in Figure 3(a)). However, there appears to be a relationship between fault dip and the spatial distribution of observed slickensides, euhedral calcite, and slickolite surfaces (Figure 5(b)). Slickolite patches on Fault A were only observed along the shallowly dipping domain in the upper part of the fault (red squares in Figure 5(b)) which corresponds to low dip values (8-12°) recorded in field data (Figure 3; Table 2). The spatial distribution of observed euhedral calcite versus slickensided patches on Fault A shows some relation to dip magnitude on the fault, with euhedral calcite more likely to be on steeper segments and slickensides more commonly observed on moderately dipping fault patches (white and blue squares, Figure 5(b)).

Coloring the photogrammetric reconstruction of Fault A according to T_s shows that most of this fault surface has high to very high T_s for the inverted stress field (Figure 5(c)). However, portions of the fault dipping less than ~20° or more than ~55° typically exhibit moderate T_s (green patches in Figure 5(c)). In addition, moderate T_s can be observed where fault segments deviate from the dominant NNE dip direction of the fault toward NW (purple and blue patches in Figure 5(a)). In general, T_d values span a wider range than T_s data for Fault A, exhibiting low (~0.2) to very high (~0.95) T_d values (Figure 5(d)). T_d appears to be less sensitive than T_s to changes in dip direction, with dip magnitude being the dominant control on this parameter. The lowest and highest T_d values along Fault A correspond to shallowly dipping (<20°) and steeply dipping (~55°) portions of the fault, respectively (Figure 5(d)). Consistent with field data and associated T_s and T_d values for Fault A (Figures 4(c) and 4(d); Table 2), there is a general tendency for (i) observed slickolite patches coincident with shallowly dipping fault portions showing moderate T_s and low T_d, (ii) slickensided patches associated with moderate dips, high T_s, and moderate to high T_d, and (iii) euhedral calcite associated with steep dips, moderate to high T_s, and high T_d. Detailed views of the fault surface highlight these general relationships between fault morphology, dip, T_s, and T_d (Figure 5).

Field data from Fault B show that patches coated with euhedral calcite have moderate to steep dips (51-86°) with variable (low to high) T_s and high to very high T_d. Slickensided surfaces generally exhibit shallow to moderate dips (20-58°), high to very high T_s, and moderate to high T_d (Figures 4(e) and 4(f), Table 2). Detailed quantification of Fault B morphology and T_d versus T_s is provided by Ferrill et al. [45, 47] who found field evidence for both shear and hybrid failure on this fault surface. We supplement the previous work of Ferrill et al. [45, 47] here by reconstructing the 3D geometry of Fault B using UAV-based digital photogrammetry and generating a point-cloud with higher point density (0.5 cm point spacing) than was previously achieved with a terrestrial laser scanner (1 cm point spacing; [45]).

The photogrammetric reconstruction of Fault B when colored by dip direction (Figure 6(a)), dip magnitude (Figure 6(b)), T_s (Figure 6(c)), and T_d (Figure 6(d)) shows an irregular fault surface with variable orientations (Figure 6(e)) and a mosaic patchwork of variable T_s and T_d values associated with changes in dip magnitude of the fault surface. Similar to Fault A, the spatial distribution of observed slickensides and euhedral calcite on Fault B appear to shows a systematic correspondence to dip magnitude on the fault, with euhedral calcite more likely to be on steeper segments and slickensides more commonly observed on moderately or shallowly dipping fault patches (white and blue squares, Figure 6(b)). Furthermore, there is a general tendency on Fault B for (i) slickensided patches associated with low to moderate dip magnitudes, high T_s, and moderate T_d, and (ii) euhedral calcite associated with steeper dip, moderate to high T_s, and high to very T_d (Figure (6)).

Field data from Fault C show that patches coated with euhedral calcite have moderate dips (57-68°) with variable (low to high) T_s and high to very high T_d (Figures 4(g) and 4(h) and Table 2). Fault patches with slickensided calcite exhibit low to moderate dips (39-58°), moderate to high T_s, and high T_d. Slickensided surfaces exhibit moderate to steep dips (37-83°), high to very high T_s, and high T_d. The spatial distribution of field-based fault measurements associated with euhedral calcite, slickensided patches, or slickensided calcite on Fault C does not appear to be clearly related to dip direction on the photogrammetric reconstruction of the fault Figure 7(a). Patches with euhedral calcite and slickensided calcite tend to be associated with steeper dips on the photogrammetric reconstruction (Figure 7(b)); however, and both euhedral calcite and slickensided calcite are generally coincident with moderately high T_s and high or very high T_d (Figures 7(c) and 7(d)). Slickenside patches on Fault C appear to be associated with a wide range of dip magnitudes (Figure 7(b)) which is consistent with field data (Table 2). Similarly, slickensided patches are associated with a relatively wide range of T_s (moderate to very high) and T_d (moderate to high) values on the photogrammetric reconstruction (Figures 7(c) and 7(d)).

Based on the overlapping fault segments and curvature of fault-segment tips to branch lines, we interpret the now-connected Fault C formed by curved-lateral propagation and linkage of three initially isolated, overlapping faults. Dip direction values on Fault C exhibit relatively abrupt changes where the fault segments are curved (red to green zones in Figure 7(a), see annotation in Figure 7(e)) and these zones are interpreted to record the curved lateral propagation of isolated faults as they grew and eventually merged. This curved lateral fault propagation prior to fault linkage is likely to have been caused by stress rotations and perturbations at the tips of these initially isolated faults as they grew (e.g., [82-86]), eventually linking to form fault corrugations [87]. These curved fault segments form in the ideal failure orientation in the perturbed stress field at the time of their formation, but these orientations are no longer optimal after linkage occurs and the local stress conditions revert to the regional stress field [88]. Curved fault segments with strike orientations oblique to the main fault trace exhibit abrupt transitions to low and moderate T_s values (Figure 7(c)). In contrast, T_d does not appear to be strongly influenced by these abrupt changes in dip direction along the fault (Figure 7(d)).

Cross-plots of T_d versus T_s can be used to assess failure or reactivation modes within a given stress state and provide a mechanism for quantifying the potential for both dilation and slip along a fault surface [47, 48]. T_d and T_s values are a function of the orientation of a surface with respect to the principal stresses in a given stress state, and the T_d versus T_s envelope (containing all possible orientations) is defined by planes containing the three principal stresses (Figure 8). Surfaces containing σ₂ (parallel to the σ₂ azimuth but with variable dips) fall on the outer edge of the T_d versus T_s envelope, while surfaces containing σ₁ or σ₃ define the upper left and lower left inner edges of the T_d versus T_s envelope, respectively (Figure 8). Surfaces normal to the minimum principal stress exhibit maximum (1) T_d (and T_s of zero), and those normal to the maximum principal stress exhibit T_s and T_d values of zero (Figure 8).

Cross-plots of T_d versus T_s for Fault A (Figure 9(a)) show a relatively broad spectrum of T_s and T_d for field measurements, with T_s values ranging from approximately 0.2 to 0.75 and T_d values from approximately 0.2 to 1.0. Slickolite surfaces plot in the lower center portion of the graph, with low (>0.4) T_d and moderate (approximately 0.3–0.5) T_s values (Figure 9(a)). Data points associated with slickensides toward the middle upper part of the graph (T_d values of ca. 0.5–0.95) and exhibit T_s of ca. 0.45 and 0.75. Euhedral calcite data exhibit the highest T_d values (ca. 0.75–1.0) and low to moderately high T_s values (ca. 0.2–0.7). As noted above, field data for Fault A cover a broad spectrum of values within the T_d versus T_s envelope (dashed black lines in Figure 9(a)), the shape of which is defined by the inverted stress state for the fault. Euhedral calcite and slickenside data points toward the center of the envelope in Figure 9(a) reflect dip directions away from perpendicular with σ₃ (see schematic T_d vs. T_s cross-plot in Figure 8), which results in a pronounced reduction in T_s for these surfaces. This is consistent with the photogrammetric reconstruction attributes for Fault A, which show abrupt reductions in T_s where dip directions deviate from the σ₃ azimuth (Figure 5).

Field data from Fault B, in contrast, all fall approximately on the outer edge of the T_d versus T_s envelope (Figure 9(b)). This pattern shows that (i) dip magnitude varies substantially for Fault B (see Figure 9(e)), which is consistent with the photogrammetry derived dip magnitude data for this fault (Figure 6(b)), and (ii) there is very little deviation in dip direction from the σ₃ azimuth for field data (see field data positions in Figure 6(a) and σ₃ azimuth in Figure 6(e)). The T_d versus T_s plot for field data from Fault C also exhibits some spread toward the upper center of the T_d versus T_s envelope (Figure 9(c)) which, similar to Fault A, is recording deviations in dip direction away from the σ₃ azimuth. Note that data from the curved fault segments on Fault C (circled in red, Figure 9(c)) have dip directions that deviate substantially from the σ₃ azimuth, as can also be observed in the photogrammetry data (Figure 7(e)).

Plotting calculated T_d versus T_s for the photogrammetric point-clouds shows a broad spectrum of T_s and T_d for the reconstructed fault surfaces, with T_d values ranging from 0.02 to 0.99 and for Fault A (Figure 9(d)), from 0.004 to 1.0 for Fault B (Figure 9(e)), and from 0.003 to 1.0 for Fault C (Figure 9(f)). T_s values for the three faults also cover a broad spectrum, from 0.07 to 0.75 for Fault A, from 0.002 to 0.64 for Fault B, and from 0.003 to 0.64 for Fault C. There is a general trend for points with higher dip magnitudes on the three fault surfaces to exhibit higher T_d values, though this is not always the case. For example, Fault A shows a number of points with relatively high dips (light colored points in Figure 9(d)) that exhibit relatively low T_d values. The broad ranges of T_d and T_s for the reconstructed fault surfaces reflect highly variable orientations with respect to the calculated principal stresses for each fault, the relatively high numbers of data points derived from the photogrammetric reconstruction (compared to field measurements), and the variability in fault surface dip and dip direction that is not easily detected or measured using traditional field techniques.

Despite the broad spectrum of orientation variability and associated T_d and T_s values for each reconstructed fault surface (Figure 9(d) through 9(f)), distinct patterns appear for each fault when values are contoured by density in T_d versus T_s space (Figure 9(g) through 9(i)). The T_d versus T_s density plot for Fault A shows that most data fall in the zone of moderately high Td and very high Ts, with a bullseye pattern centered toward the outer edge of the T_d versus T_s envelope (Figure 9(g)). This shows that a high proportion of the points on Fault A is close to the optimal orientation for slip in the calculated stress field, though with some variability in both dip and dip direction. The T_d versus T_s point density contour plot for Fault B shows a rather different pattern, with the zone of highest point density falling along a “streak” toward the outer edge of the T_d versus T_s envelope, from moderate to high T_s values (ca. 0.5–0.7) and moderately low to moderately high T_d values (ca. 0.4–0.8) (Figure 9(h)). This pattern shows that most of the points for Fault B have dip directions approximately perpendicular to the σ₂ azimuth, but with variable dip magnitudes with respect to σ₁, from steeply dipping to very shallowly dipping (see Figure 8). The density plot for Fault C shows that most points fall along an arcuate streak toward the outer edge of the T_d versus T_s envelope, indicating that most points on Fault C are optimally oriented for slip in the calculated stress field. Although the density plot for Fault C shows some variability in dip and dip direction, the highest point densities for Fault C are tightly clustered around the zone of highest T_s.

While the overall trends described above are generally consistent for all three of the faults characterized in this study, it can be difficult to visualize how dip and dip direction relate to T_s and T_d on such complex fault surfaces. To address this directly, we generated a simplified, synthetic fault surface containing general aspects of the three faults in this study, namely (i) variations in dip magnitude, from relatively low (30°) to relatively high (80°) and (ii) dip direction (or strike) variations along the fault, from perpendicular to approximately parallel with the σ₃ azimuth (Figure 10). Where the fault is perpendicular to σ₃, those portions that dip 60° (location 1 on Figure 10(d)) have the highest T_s (i.e., ideally oriented for slip), whereas those portions with steeper (80°) or more shallow dip (30°) exhibit lower T_s values (locations 2 and 3 on Figure 10). Where the fault is curved and has a strike approaching the σ₃ azimuth (locations 4, and 6 on Figure 10), T_s shows an abrupt decrease, particularly on the lower panel dipping 60° (location 4 on Figure 10). Note that on the 30° panel of the fault model, the change in T_s is relatively minor as the fault strike changes (location 5 on Figure 10).

As observed for the three natural examples in the study, T_d on our synthetic example is strongly controlled by dip magnitude, with higher dips (location 3 on Figure 10) resulting in higher T_d values (for a normal faulting stress regime where σ₁ is vertical) (Figure 10(b)). Where the fault is curved and has a strike approaching the σ₃ azimuth, T_d also drops (locations 4 and 6 on Figure 10), but the change in T_d for this part of the fault is less pronounced than the change in T_s for the same region (Figures 10(a) and 10(b)). More shallowly dipping fault segments (location 2 on Figure 10) exhibit lower T_d values because of increased normal stresses acting upon these surfaces.

Summed T_s and T_d (Figure 10(c)) were calculated to provide a qualitative measure of the combined contribution of both T_s and T_d to fluid flow potential along a fault. While combined T_s and T_d do not provide a direct, quantitative metric of potential for fluid flow or transmissivity along a fault, both T_s and T_d have been documented as important predictors of fault and fracture permeability (e.g., [42, 51, 89]. Summed T_s and T_d may therefore be an important (albeit informal) predictor of which zones along a fault or fault zone may be more transmissive to fluids [89]. Summed T_s and T_d are highest on the modeled fault where fault segments are parallel to σ₂ and, for this example, dipping at 60° (Figure 10(c)). Both the shallowly dipping panel (location 2 on Figure 10) and the curved segments of the fault (locations 4, 5, 6 on Figure 10) exhibit low to very low combined T_s and T_d values. Finally, our synthetic fault model example provides a synoptic view of fault orientations in a given stress field and the associated effects where segments of a fault may plot within the T_d versus T_s envelope (Figure 10(d)). This example shows that surfaces containing the σ₂ azimuth fall on the outer edge of the envelope, whereas fault strikes away from the σ₂ direction yield T_d and T_s values toward the center and left of the envelope, as is shown by the natural fault examples (Figure 9).

Field data from the three normal faults examined here show a general trend for euhedral calcite patches associated with the highest dip magnitudes on each fault and that slickensided surfaces and slickolite patches are typically associated with moderate and shallow dips, respectively (Figure 11). Furthermore, we generally find that the highest T_d values are associated with euhedral calcite patches, highest T_s values with slickensided surfaces, and low to moderate T_s and T_d with slickolite patches (Figure 11). These relationships indicate a genetic link between fault morphology, fault failure mode, T_d, and T_s. Ferrill et al. [45-47] provided evidence for both shear and tensile or hybrid failure on Fault B and showed that the fault surface is made up of a mosaic patchwork of (i) euhedral calcite patches that are consistent with tensile failure on steeper fault segments (perpendicular to the minimum principal compressive stress direction) and (ii) moderately dipping fault patches that show evidence for shear failure in the form of slickensides.

Here, we supplement previous work by documenting evidence for compactional shear failure that is kinematically consistent and coeval with hybrid failure and shear failure on a single fault surface (Fault A; Figure 5). Slickolite patches are consistent with compactional shear deformation and occur along shallowly dipping (8-12° in present-day coordinates; 19-23° with respect to our estimated σ₁ orientation) segments of Fault A. These patches exhibit moderate T_s and low to moderate T_d in our estimated stress field. In the context of a normal faulting stress regime, low to moderate T_s values are due to the low shear stress and high normal stress acting to lock these areas of the fault. With their low dips, the slickolite patches are far from the ideal 60° dip (30° inclination with respect to σ₁) for shear failure surfaces where resolved shear stress is high, and T_s is maximized. As such these surfaces are severely misoriented with respect to the expected orientations of “Andersonian” normal faults [90, 91].

Low-angle normal faults (i.e., dipping <30°) are relatively common structures ([91] and references therein), and arguments for the occurrence of these structures have included (i) initial formation as steeply dipping faults and subsequent decrease in dip magnitude due to compaction (e.g., [92]), (ii) fault and block rotation of imbricate normal fault system (“domino” or “bookshelf” faulting) with increasing extension (e.g., [93]), (iii) rotation (tilting) of the maximum principal stress away from vertical, such that shear failure at 30° to the σ₁ direction produces a low angle fault (e.g., [94]), and (iv) the presence of very weak materials (e.g., phyllosilicates) along fault planes and/or fluid overpressure conditions leading to very low friction coefficients and the ability for faults to overcome high normal stresses at angles greater than 45° to σ₁ [91, 95]. Only relatively recently has the concept that the faults could nucleate as mechanically well-oriented low-angle normal faults via compactive-shear failure at a high angle to the maximum principal compressive stress been considered viable (e.g., [47, 95]).

The observations and analyses we present in this article are consistent with coeval hybrid failure, shear failure, and compactive shear failure along the same fault surface during early fault growth, with failure surfaces oriented at angles ranging from approximately 0-71° with respect to σ₁. Coeval failure along surfaces with such a wide range of angles with respect to σ₁ is consistent with fault formation via different failure modes—rather than by rotation of a high-angle normal fault—and is supported by observed mesostructures including dilation and calcite cementation, slickensides, and slickolites. We also find no evidence for the presence of phyllosilicates or clay gouge on the embryonic faults characterized in this study, and therefore, the very low friction coefficients in fault rocks documented by others (see Ferrill et al. [46] for a summary of fault friction data) are unlikely to have played a role here.

Faults close to reactivation in a given stress field have been shown to be more likely to act as hydraulic conduits in the subsurface (e.g., [1, 44, 96]). Increased T_s and T_d both equate to higher potential for hydraulic conductivity along faults and fault zones (e.g., [42, 88]), and therefore, the zones of our faults exhibiting higher T_s and T_d would likely be more transmissive under the stress conditions at the time of failure. Our simplified example shows that steeply dipping surfaces striking parallel to σ₂ would likely have the highest combined T_s and T_d values, whereas shallowly dipping surfaces with the same strike would have substantially lower combined T_s and T_d values for a given normal faulting stress state. As such, more steeply dipping normal fault segments (striking parallel to σ₂ and for a vertical σ₁) would likely be more transmissive to fluids. If, however, stress conditions changed (e.g., from a normal faulting to a thrust faulting stress regime), faults or segments of faults with higher T_s and T_d values at the time of failure may experience reductions in these values, and conversely, zones with low T_s and T_d at the time of failure may become more transmissive to fluid flow.

Faults with higher T_s and T_d values at the time of failure are likely to experience volume neutral (shear) or volume gain (positive dilation) behavior, whereas segments with low T_s and T_d are more likely to have experienced volume loss (negative dilation) through compaction (Figure 11; cf. [47]). Dilatant fault segments may only have been partially cemented, leading to “self-propping” behavior and retention of fault permeability. In contrast, slickolite (compactive shear) segments will likely have experienced compaction, mineral dissolution, local reprecipitation (occluding porosity), and concentration of insoluble material—all of which would likely cause the fault to behave as a barrier to fluid flow [97, 98]. It should be noted that variations in dip magnitude along a fault surface may lead to a kinematic and geometric interdependence between faults segments (Figure 11, block diagrams). Where shear failure is favored on an optimally oriented surface (Figure 11, label 1) continued displacement along that segment of the fault leads to continued compactional shear on less steeply dipping surfaces (Figure 11, label 2) and dilation on more steeply dipping surfaces (Figure 11, label 3). Because of this geometric interdependence between fault segments with varying dips, it may be expected that dilation on steeper fault segments and compactional shear on more shallowly dipping segments may be a long-lived process that continues as fault displacement accumulates. Furthermore, failure-mode-determined fault geometry would likely persist long after any potential changes in stress conditions acting on a fault or fault system, and therefore, even if stress conditions changed and T_s and T_d were modified, the hydraulic properties of a fault zone, as determined by early failure mode and subsequent fault growth, could be retained despite any later changes in stress conditions.

The faults studied here have highly irregular surfaces. Our data show that the complex geometries on these small-scale faults (cm-scale displacements) are primarily defined by failure modes during fault initiation and early growth. As documented by Ferrill et al. [32], fault zone geometries are defined by failure modes at fault initiation and during the earliest stages of fault growth, and these fault zone characteristics (e.g., refracted fault profiles) may persist for many incremental slip events as small-scale faults grow and accumulate displacement. Eventually, with continued displacement and repeated slip events, many of the asperities observed on the small-scale faults in this study would likely be smoothed and straightened by shortcut faults with continued growth of the fault zone [88, 99]. In detail, therefore, the complex morphologies documented on the three faults in this study would likely become smoothed with continued growth and displacement accumulation. Nevertheless, strike and dip changes along faults at the seismic scale are commonly observed (e.g., [100, 101]) and by implication T_s and T_d will likely be highly variable along faults, regardless of fault size and displacement magnitude.

As shown by Michie et al. [101], more detailed fault interpretations generally lead to greater complexity of interpreted fault surfaces, and as a result, greater variability in T_s and T_d. Given the resolution of seismic data, the detail and complexity shown in the examples here will not be imaged in the subsurface. It is reasonable, however, to expect that the complexity in fault surface geometry shown here will be present at some scale along faults in the subsurface, regardless of fault size. The feedbacks between fault geometry, failure mode, and the potential for conduit versus seal behavior along faults and fault zones documented in this study are therefore likely applicable to faults at all scales and in a multitude of geologic settings.

1. We combine field data and close-range digital photogrammetry to characterize the surface morphology of three normal faults with cm-scale displacements in mechanically layered carbonates of the Cretaceous Glen Rose Formation at Canyon Lake Gorge, Comal County, Texas. Analyses provide evidence for complex fault surface geometries, a broad spectrum and complex spatial distributions of slip tendency and dilation tendency along faults, and variable failure behavior.

2. We find that (i) steeper fault segments are typically associated with euhedral calcite and exhibit moderate to high slip tendency and high to very high dilation tendency; (ii) moderate to steep dips are typically associated with slickensides and these fault segments exhibit high slip tendency and moderate to high dilation tendency; and (iii) shallowly dipping surfaces are associated with slickolite patches and exhibit moderate slip tendency and low dilation tendency. Fault surfaces oblique to the dominant slip direction (i.e., along curved fault segments) tend to be dominated by slickensides (with little evidence for slickolites or euhedral calcite) and these fault segments tend to exhibit lower slip and dilation tendency values than segments dipping parallel to the dominant slip direction.

3. Our results are consistent with hybrid failure on steeper fault segments, shear failure on moderately dipping segments, and compactive shear failure on shallowly dipping segments. One of the studied faults (Fault A) shows evidence for three failure modes (hybrid, shear, and compactive shear) along the same fault surface, and the other two faults (B and C) show evidence of both hybrid and shear failure. Field observations and kinematic (displacement) compatibility indicate that these distinct failure modes were coevally active on fault surfaces during fault slip.

4. The failure modes documented here are consistent with volume gain along the fault where hybrid failure occurred, volume loss for compactive shear fault segments, and volume neutral effects (i.e., no gain or loss) where shear failure occurred. Geometric compatibility considerations suggest that with continued displacement along optimally oriented fault segments, compactional shear will persist on less steeply dipping surfaces, as will dilation on more steeply dipping surfaces. Complex fault morphology, variable slip tendency and dilation tendency, patchworks of distinct failure modes along faults, and associated effects on volume gain versus loss will likely result in dual conduit-seal behavior.

Field data are provided in Appendices A and B, and the photogrammetric reconstructions of the three faults analyzed in this study can be downloaded from sketchfab.com (URLs for each photogrammetric model can be found in the captions for Figures 5-7). Restrictions apply to the availability of other data, which were generated with funding from a proprietary Southwest Research Institute project (#15-R6107). Additional data are available from the corresponding author upon request.

The authors declare that there is no conflict of interest regarding the publication of this article.

This work was supported by SwRI Internal Research and Development project #15-R6107.

The authors thank Jaynellen Kerr, Lisa Walzem, the Gorge Preservation Society, and the Guadalupe Blanco River Authority for research access to Canyon Lake Gorge. We thank Harry Bellow for assistance in the field and with data processing. We are grateful to two anonymous reviewers for their constructive feedback and to James Evans and Elizabeth Petrie for editorial handling.

Fault orientation, displacement, and morphology data are provided in Appendices A and B.