1. Introduction
Fault and fracture networks are very common in the upper brittle crust. Fractures occur in a wide range of geodynamic settings (e.g. Hancock & Engelder, Reference Hancock and Engelder1989), including extensional systems (e.g. Angelier & Colletta, Reference Angelier and Colletta1983; Ramsay & Huber, Reference Ramsay and Huber1983), thrust and fold belts (e.g. Hancock, Reference Hancock1985; Tavani et al. Reference Tavani, Storti, Lacombe, Corradetti, Muñoz and Mazzoli2015), diapiric structures (e.g. Rowan et al. Reference Rowan, Muñoz, Giles, Roca, Hearon, Fiduk, Ferrer and Fischer2020), post-orogenic collapse and stabilization of cratons (Mondal & Mamtani, Reference Mondal and Mamtani2016; Mondal et al. Reference Mondal, Bhowmick, Das and Patsa2020). Fracture formation often involves reactivation of the pre-existing host rock fabric under a compatible stress field (Donath, Reference Donath1961; Hoek, Reference Hoek1964; Attewell & Sandford, Reference Attewell and Sandford1974; Ikari et al. Reference Ikari, Neimeijer and Marone2015; Mazzarini et al. Reference Mazzarini, Musumeci, Viola, Garofalo and Mattila2019; Bhowmick & Mondal, Reference Bhowmick and Mondal2020). Upper crustal fluids are mostly channelized through these fracture systems under variable fluid pressure conditions generating a widespread network of veins (Sibson, Reference Sibson1992, Reference Sibson1996, Reference Sibson2000; Jolly & Sanderson, Reference Jolly and Sanderson1997; Mondal & Mamtani, Reference Mondal and Mamtani2013; Mazzarini et al. Reference Mazzarini, Musumeci, Viola, Garofalo and Mattila2019; Bhowmick & Mondal, Reference Bhowmick and Mondal2020). Faults and fractures are most likely to accommodate repeated slip episodes over a period of time, especially if reactivated by fluids (Curzi et al. Reference Curzi, Aldega, Bernasconi, Berra, Billi, Boschi, Franchini, Van der Lelij, Viola and Carminati2020). However, whether a fracture will behave as a conduit or a barrier depends on its mode of reactivation (Ferrill et al. Reference Ferrill, Evans, McGinnis, Morris, Smart, Wigginton, Gulliver, Lehrmann, de Zoeten and Sickmann2017a, Reference Ferrill, Morris and McGinnis2019b, Reference Ferrill, Smart and Morris2020). The external stress field plays a key role in fracture formation/propagation. But within the same stress field the favourably oriented fractures are reactivated multiple times while the misoriented ones remain inactive/closed. The probability of reactivation depends on the orientation of the fracture surface with respect to principal stress direction along with the frictional characteristics of the host rock. Slip is possible when the maximum resolved shear stress overcomes/equals the coefficient of friction (Morris et al. Reference Morris, Ferrill and Henderson1996). The vein emplacement mechanism within pre-existing fractures depends on the availability of fluids and P f magnitudes high enough to generate slip/dilation. Thus, finding out the eminence of slip over dilation or vice versa can be effective for understanding the deformation behaviour in fractures (Ferrill et al. Reference Ferrill, Smart and Morris2020). Quantifying the failure mode in fractures that have been reactivated also helps to estimate the volumetric changes associated with vein emplacements. Slip versus dilation patterns can be functional for inferring the failure mode in fractures within a stress field, at the time of deformation (Ferrill et al. Reference Ferrill, Evans, McGinnis, Morris, Smart, Wigginton, Gulliver, Lehrmann, de Zoeten and Sickmann2017a, Reference Ferrill, Morris and McGinnis2019b, Reference Ferrill, Smart and Morris2020). Tensional failure and shear failure can be easily identified and thus segregated from field observations. However, hybrid failures are comparatively difficult to understand, especially if the failure mode changes along the fracture strike/dip orientation.
The present study involves the analysis of veins with multiple orientations in the metavolcanics of the Chitradurga greenstone belt (CGB) of western Dharwar craton. The fractures and faults of the study area are a product of the tectonic stress field associated with the late-stage deformation in Dharwar craton (Sarma et al. Reference Sarma, Fletcher, Rasmussen, McNaughton, Mohan and Groves2011; Mondal & Mamtani, Reference Mondal and Mamtani2016; Mondal & Acharyya, Reference Mondal and Acharyya2018). The pre-existing foliation fabric (∼NW–SE; ∼337/69° NE) in the metabasalts has been exploited by propagating late fractures and faults (Mondal & Mamtani, Reference Mondal and Mamtani2013; Bhowmick & Mondal, Reference Bhowmick and Mondal2020). The states of stress and P f conditions that led to the reactivation of these fractures and faults have been evaluated in the previous study (Bhowmick & Mondal, Reference Bhowmick and Mondal2020). However, the reactivation potential of these fractures based on their orientation needs to be inferred. This gives a clear idea of the role played by fracture orientations in channelizing fluids and primarily establishes it as the most important criterion for fracture reactivation within an external stress field. Vein thickness and abundance are found to be maximum, parallel to the pre-existing foliation (∼NW–SE) of the metabasalts. However, some fractures remained closed even under high P f conditions. Slip versus dilation tendency patterns help to quantify the failure modes and volumetric changes along all of these fractures.
2. Background of the study
Dharwar craton, an integral part of the Indian subcontinent, is known to preserve the age-old Archaean continental crust >3.0 Ga (Jayananda et al. Reference Jayananda, Chardon, Peucat and Capdevila2006). The eastern and western blocks of the Dharwar craton (EDC and WDC) amalgamated between 2.75 and 2.51 Ga, with their accretion along the Chitradurga shear zone (CSZ; see Fig. 1; e.g. Naqvi & Rogers, Reference Naqvi and Rogers1987; Chadwick et al. Reference Chadwick, Vasudev and Hedge2003; Jayananda et al. Reference Jayananda, Chardon, Peucat and Capdevila2006). The metasedimentary sequences of the Chitradurga schist belt (CSB; lying on the eastern part of WDC) record three phases of deformation, D1, D2, D3 (Chadwick et al. Reference Chadwick, Ramakrishnan, Vasudev and Viswanatha1989; Jayananda et al. Reference Jayananda, Chardon, Peucat and Capdevila2006; Mondal & Mamtani, Reference Mondal and Mamtani2014; Mondal, Reference Mondal2018). The D1/D2 coaxial deformation with NE–SW-directed compression generated tight to isoclinal asymmetric folds with NW–SE-striking axial plane (Chakrabarti et al. Reference Chakrabarti, Mallick, Pyne and Guha2006; Mondal & Mamtani, Reference Mondal and Mamtani2014). This regional deformation also generated a ∼NW–SE-oriented magnetic fabric in the metabasalts apparently devoid of mesoscopic foliation (as evident from anisotropy in magnetic susceptibility (AMS) analysis; Bhowmick & Mondal, Reference Bhowmick and Mondal2020). Early D3 deformation (NW–SE-directed compression) superposed the D1/D2 structures, resulting in a dome-basin geometry in the metasedimentary sequences (Chakrabarti et al. Reference Chakrabarti, Mallick, Pyne and Guha2006; Mondal & Mamtani, Reference Mondal and Mamtani2014). The late D3, WNW–ESE to E–W compression (see Fig. 1) led to the formation of brittle structures in the metabasalts. D3 deformation, coeval with the sinistral movement along CSZ, led to the reactivation of the pre-existing fabric (∼NW–SE) in metabasalts. The D3 compression also aided in generating fracture and fault planes with specific orientations (R, Y, P, R′, X, T) and movement sense resembling a Riedel shear system (Hancock, Reference Hancock1985), with CSZ as the primary shear boundary. R and P are the low-angle synthetic fractures to the shear boundary; Y is parallel to the shear boundary. R′ and X are the high-angle antithetic shear fractures, whereas T forms the tensile fractures parallel to the compression direction. It is also envisaged that shear partitioning along such primary shear components generated multiple orientations of faults and fractures hosting quartz veins of variable thickness (see supplementary sheet-1 in Bhowmick & Mondal, Reference Bhowmick and Mondal2020; Mondal et al. Reference Mondal, Bhowmick, Das and Patsa2020).
Fig. 1. (a) Regional map of WDC and EDC, South Indian Shield (after Chadwick et al. Reference Chadwick, Vasudev and Hedge2003), within the Indian subcontinent (inset). EDC = eastern Dharwar craton; WDC = western Dharwar craton; TTG = tonalite–trondhjemite–granodiorite; Supracrustals = volcano-sedimentary assemblages. (b) Digital elevation model of the Chitradurga Schist Belt (modified after Jayananda et al. Reference Jayananda, Peucat, Chardon, Krishna Rao, Fanning and Corfu2013). Eastern boundary of the Chitradurga Schist Belt, representing the Chitradurga Shear Zone (CSZ), marked with dotted black line (in (b)). Yellow box near Chitradurga demarcates the study area. Stress tensor obtained from palaeostress analysis (right dihedron method) using oblique slip normal fault and strike-slip fault data recorded from the metabasalts of the study area. Red arrow marks the extension direction (σ 3), and brown arrow marks the principal compression direction. The histogram shows the minimum values for counting deviation. n and nt are the number of data accepted out of the total number of data used for obtaining the best-fit stress tensor respectively. R (stress ratio) = (σ 2 − σ 3)/(σ 1 − σ 3). Maximum extension is NNE–SSW directed (from Bhowmick & Mondal, Reference Bhowmick and Mondal2020).
The quartz veins show criss-cross patterns and are often displaced by each other, so the sense of movement along the fractures containing them is evident (Fig. 2a, b). Some of these veins have crystals growing perpendicular to the vein wall as an evidence of dilational opening of the fractures (Fig. 2c). Most of the quartz veins are NNW–SSE-striking (Fig. 2d), with multiple median lines indicating a crack-seal mechanism suggesting recurrent cracking events due to cyclic fluid ingression (see fig. 3g in Bhowmick & Mondal, Reference Bhowmick and Mondal2020). The NW–SE-trending (∼337/69° NE) pre-existing fabric provided an easy pathway for fluid flow and vein emplacement considering vein abundance parallel to this orientation. The maximum width and length of the quartz veins are found to be ∼0.3 m (thickness) and ∼130 m respectively. Some of the thick quartz veins accommodate series of moderately to steeply dipping oblique-slip normal faults with slickenside lineations (Fig. 2e). Fault-slip data (mostly oblique-slip normal faults and a few strike-slip faults) used for palaeostress analysis reveal an overall NNE–SSW-directed extension on account of WNW–ESE compression related to the late D3 deformation (Fig. 1; Bhowmick & Mondal, Reference Bhowmick and Mondal2020). In some instances, angular host metabasalt enclaves (clasts) are enclosed within the thick quartz veins, insinuating the effects of fault-valve action in the region or the occurrence of hydrofractures (Fig. 2f). Vein thicknesses along fractures oriented parallel to the magnetic fabric are found to be maximum (maximum recorded thickness ∼0.3 m; see supplementary sheet-1 in the Supplementary Material available online at https://doi.org/10.1017/S0016756821000881); most of these veins are extensional shear veins (vein type). The process of fracture formation, reactivation and faulting is related to the late D3 deformation with intermittent cycles of fluid pressure build-up leading to fluid-induced faulting, rupturing and vein emplacement in the region (Bhowmick & Mondal, Reference Bhowmick and Mondal2020).
Fig. 2. Field photographs from the study area. (a) Quartz veins in metabasalts having a criss-cross orientation. (b) Cross-cutting nature in quartz veins showing dextral displacement (marked by yellow half-arrows). (c) Close-up view of a quartz vein in metabasalt showing crystal growth direction (orange arrow) perpendicular to the vein wall. (d) Rose diagram showing strike orientation of quartz veins. (e) NE-dipping quartz vein showing slickenside lineations (maximum width recorded = ∼0.3 m), inset showing close-up of the fault plane found in (e). Marker pen placed along the orientation of the slickenside lineations. (f) Angular chunks of metabasalt (enclaves) enclosed within faulted quartz vein, denoting fault-valve action. Dotted red line demarcates the enclave boundaries. Black arrow marks the slickenside lineations on the fault plane. Blue arrow in the photographs marks the north direction.
Fig. 3. States of stress and fluid pressure (P f) conditions using vein orientation data from the study area (from Bhowmick & Mondal, Reference Bhowmick and Mondal2020). (a–d) Lower-hemisphere equal-area projection of pole to veins. (a) Vein pole data showing girdle distribution, implying P f > σ 2. (b) Vein pole data forming WSW cluster, P f < σ 2. (c) Vein pole data forming NE cluster, P f < σ 2. (d) Vein pole data forming SE cluster, P f < σ 2 (following Jolly & Sanderson, Reference Jolly and Sanderson1997). The empty space devoid of vein pole data helps to determine the position of σ 1 (in (a), using Bingham statistics of the Stereonet 9 software); cluster maxima define σ 3 (from (b–d)). Angles θ 1, θ 2 and θ 3 are measured, and used to determine the stress ratios (Φ) and driving pressure ratios (R′) respectively. Colour scheme of the legends indicates variation in the contour density. Pink circle (σ 1), pink triangle (σ 2), pink square (σ 3). (e–h) 3D Mohr circle diagrams: (e) for high P f condition; (f) for WSW cluster; (g) for NE cluster; (h) for SE cluster. Red dots represent pole-to-vein data; red line represents the reactivation envelope for cohesionless fractures. Vein pole data lying within the blue zone, i.e. to the left of the P f (black) line, represent fractures susceptible to reactivation (Fractend code available via GitHub (Healy, Reference Healy2017)). Only a limited range of fractures are susceptible to reactivatation (in (f–h)).
3. Methodology
3.a. States of stress and fluid pressure condition
The fluid pressure conditions and the states of stress under which the veins formed in the region have already been documented in Bhowmick & Mondal (Reference Bhowmick and Mondal2020). We have considered the P f conditions obtained from the methods proposed by Jolly & Sanderson (Reference Jolly and Sanderson1997), using vein orientation data (Bhowmick & Mondal, Reference Bhowmick and Mondal2020). From the studies of Jolly & Sanderson (Reference Jolly and Sanderson1997) it is evident that girdle distribution of vein pole data indicates P f > σ 2; this suggests a large number of fracture orientations are susceptible to reactivation. However, clustered distribution of vein pole data indicate P f < σ 2, which suggests a limited range of fracture orientations can be reactivated. Further, parameters like stress ratio (Φ), driving pressure ratio (R′) and P f magnitudes can be calculated depending upon the type of distribution (girdle/cluster), using the following equations as proposed by Jolly & Sanderson (Reference Jolly and Sanderson1997) and Baer et al. (Reference Baer, Beyth and Reches1994).
$$R' = {{{P_{\rm{f}}} - {\sigma _3}} \over {{\sigma _1} - {\sigma _3}}} = {{1 + \cos 2{\theta _2}} \over 2}.$$
For P f > σ 2,
$$\Phi = {{{\sigma _{\rm{2}}} - {\sigma _3}} \over {{\sigma _1} - {\sigma _3}}} = 1 - {{1 - \cos 2{\theta _2}} \over {1 - \cos 2{\theta _3}}}.$$
For P f <σ 2,
$$\Phi = {{{\sigma _{\rm{2}}} - {\sigma _3}} \over {{\sigma _1} - {\sigma _3}}} = {{1 + \cos 2{\theta _2}} \over {1 + \cos 2{\theta _1}}}.$$
The lower-hemisphere equal-area projection of pole to vein data (378 quartz veins; see supplementary sheet-2 in the Supplementary Material available online at https://doi.org/10.1017/S0016756821000881) in Figure 3a shows a girdle distribution suggesting P f > σ 2, a high fluid pressure condition. The orientations of the principal stress axes (σ 1, σ 2 and σ 3) are determined from this distribution using Bingham statistics of the Stereonet 9 software. σ 1 (sub-vertical) lies within the empty space devoid of vein pole data. σ 1 σ 2, σ 2 σ 3 and σ 1 σ 3 planes are constructed, and the ranges of fracture orientations measured with angles θ 2 and θ 3 along the σ 1 σ 3 and σ 1 σ 2 planes are determined (θ 2 = 27°, θ 3 = 59°; see Fig. 3a), following Jolly & Sanderson (Reference Jolly and Sanderson1997). Within the girdle distribution of vein pole data, three distinct clusters have been identified based on the relative density maxima of the pole to the vein distribution data. The number of clusters obtained has been assessed through mixed Bingham analysis using K vs BIC (i.e. the number of Bingham components of a mixed Bingham distribution vs Bayesian information criterion; Yamaji & Sato, Reference Yamaji and Sato2011). It has been found that the lowest BIC values are obtained for K = 3 (number of feasible clusters for the given dataset). This justifies the selection of the three data clusters for the analysis. The contour interval and significance level for each of the clusters are selected in order to accommodate the maximum number of data points for obtaining statistically viable data clusters. The WSW cluster (33 vein data, Fig. 3b) is the highest-density cluster around the σ 3 axis and has been plotted independently. This indicates abundance of NNW–SSE to NW–SE-trending veins with maximum thickness (supplementary sheet-1 in the Supplementary Material available online at https://doi.org/10.1017/S0016756821000881) oriented parallel to the magnetic fabric of the metabasalt host rocks. A favourably oriented anisotropy lowers the shear strength of the host rock, generating slip at a minimum compressive stress. Moreover, Vishnu et al. (Reference Vishnu, Lahiri and Mamtani2018) have established a relationship between the magnetic anisotropy and rock strength anisotropy in the metabasalts of CSB. Thus, the pre-existing anisotropy of the metabasalts played a significant role in fracture propagation and vein emplacement (Bhowmick & Mondal, Reference Bhowmick and Mondal2020). The contour interval of the clusters has been extended beyond the data points to incorporate the maximum range of fracture orientations (θ) lying parallel/sub-parallel to the magnetic anisotropy of the host rock. Along with the WSW cluster (highest-density cluster), the SE cluster (110 vein data) and the NE cluster (with highest data spreading, 76 vein data) are evaluated separately (see supplementary sheet-2 in the Supplementary Material available online at https://doi.org/10.1017/S0016756821000881). For each of the clusters, the principal stress axes orientations (σ 1, σ 2 and σ 3) are determined and the σ 1 σ 2, σ 2 σ 3 and σ 1 σ 3 planes are constructed. Ranges of fracture orientations θ 1 and θ 2 are obtained along the σ 2 σ 3 and σ 1 σ 3 planes respectively, where θ 1 = 38°, θ 2 = 43.2° (WSW cluster, Fig. 3b); θ 1 = 32°, θ 2 = 35° (NE cluster, Fig. 3c); θ 1 = 30°, θ 2 = 44° (SE cluster, Fig. 3d). The derived parameters Φ, R′ and P f magnitudes for each of the clusters and the girdle distribution of vein pole data are given in Section 4.a.
3.b. Dilation tendency, slip tendency and fracture susceptibility analysis
Dilation tendency stands for the propensity of a fracture surface to reactivate through dilation under a prevailing stress field. It signifies plane normal opening of a fracture surface, expressed as
$${T_d} = \left( {{\sigma _1}-{\sigma _n}} \right)/{\sigma _D}$$
where (σ D = σ 1 – σ 3); σ D is differential stress, σ n is normal stress (Ferrill et al. Reference Ferrill, Winterle, Wittmeyer, Sims, Colton, Armstrong and Morris1999; Stephens et al. Reference Stephens, Walker, Healy, Bubeck, England and McCaffrey2017).
Slip tendency is denoted by the ratio of shear stress (σ s) to normal stress (σ n), expressed as
$${T_{\rm s}} = {\sigma _s}/{\sigma _n}$$
It depends on the state of stress, orientation of a fracture surface within a three-dimensional stress field and the frictional characteristics of the host rock (Morris et al. Reference Morris, Ferrill and Henderson1996). Fracture susceptibility (S f), is the variation of fluid pressure (ΔP f) within a fracture surface indicating fluid-induced shear reactivation, expressed as
$${S_{\rm{f}}} = {\sigma _{{n}}}-\left( {{\sigma _{{s}}}/{\mu _{{s}}}} \right)$$
Fracture reactivation depends on the shear and normal stresses acting on the fracture plane, along with the cohesion (= 0 in this case) and the static coefficient of friction, µ s (Mildren et al. Reference Mildren, Hillis and Kaldi2002; Stephens et al. Reference Stephens, Walker, Healy, Bubeck, England and McCaffrey2017).
We have calculated the angle θ between fracture plane normal and the maximum compressive stress, σ 1, using the Stereonet 9 software and numerically quantified the normal and shear stress magnitudes for each fracture plane. Both normal and shear stress magnitudes are dependent on the maximum and minimum principal stresses (σ 1, σ 3) quantified later (see Section 4.a). Fractend code (Healy, Reference Healy2017) has been used to obtain the lower-hemisphere equal-area projections of vein pole data accentuating slip tendency, dilation tendency and fracture susceptibility variations for all the respective clusters (low P f conditions) and high P f conditions (Bhowmick & Mondal, Reference Bhowmick and Mondal2020). Slip and dilation tendency values are numerically determined for each of the fracture orientations. The generated data (see supplementary sheet-2 in the Supplementary Material available online at https://doi.org/10.1017/S0016756821000881) are used in the later sections to understand the dependence of these parameters on the fracture orientations, states of stress and P f conditions.
3.c. Determining the opening angle of fractures
Opening angle (µ) is calculated by deviation of the dilation vector from the plane normal to the fracture surface. Previously, field-based measurements of intrusion attitude and the opening angle were used to constrain tectonic stress axes (Stephens et al. Reference Stephens, Walker, Healy, Bubeck and England2018). Normally, for extensional fractures (Mode-I opening) the dilation vector is parallel to the plane-normal/σ 3 axis. For extensional shear fractures, opening angle is measured in between the plane normal and the offset of the marker beds (giving the dilation vector) along the margin of veins/intrusions. Thus, it can help to distinguish between extensional and extensional-shear fractures directly from field evidence. However, if such offset markers are absent along the intrusion margin it becomes difficult to directly trace the plane-oblique dilation vector. In such cases, the opening angle of fractures can be quantified using the shear stress (τ), normal stress (σ n) and P f acting on the fracture plane at the time of vein emplacement (Delaney et al. Reference Delaney, Pollard, Zioney and McKee1986; Jolly & Sanderson, Reference Jolly and Sanderson1997). It is expressed as the ratio between the shear stress and the fluid overpressure/dilation (Delaney et al. Reference Delaney, Pollard, Zioney and McKee1986).
$$\mu = {\tan ^{ - 1}}\left({\tau \over {P_{\rm{f}} - \sigma_{\rm{n}}}}\right)$$
When shear to dilation ratio is unity, the opening angle is 45°, a feasible condition for extensional shear reactivation. Once the fluid overpressure exceeds shear stress, the opening angle reduces, ensuring dilational opening of the fractures. However, in the reverse situation, i.e. shear exceeding dilation, fractures tend to slip (shear reactivation). We have numerically quantified the opening angles for all the veins. Ranges of opening angles for the most prominent fracture orientations that were reactivated under the variable fluid pressure conditions help to determine the predominance of slip versus dilation on fracture reactivation.
4. Results
4.a. Fluid pressure determination
The girdle and cluster distribution of vein pole data from 378 quartz veins (see supplementary sheet-2 in the Supplementary Material available online at https://doi.org/10.1017/S0016756821000881) have been used to obtain the high and respective low P f conditions assisting vein emplacement in the metabasalts (Fig. 3, modified from Bhowmick & Mondal, Reference Bhowmick and Mondal2020). The P f magnitudes used in this study are instances of high and low P f conditions indicating cyclic variation of P f in response to the tectonic stress field and availability of fluid for vein emplacement. The approximated P f values are close enough and befitting for a shallow crustal vein emplacement (∼2.4 km) process within the prevailing stress field (Bhowmick & Mondal, Reference Bhowmick and Mondal2020). Further, these values help to document the reactivation potential of the pre-existing fractures that mediated fluid flow in the region.
The principal stress magnitudes are evaluated considering the depth of fracturing and faulting to be 2.4 km according to Bhowmick & Mondal (Reference Bhowmick and Mondal2020). In a normal faulting regime, σ v = σ 1, using σ 1 = hρg, where h = depth of fracturing in metabasalts (∼2.4 km), ρ = approximate bulk density of crust (2700 kg/m3), g = 9.8 m/s2, σ 1 = 63.5 MPa. Similarly, using the empirical approach by McGarr (Reference McGarr1980) and Mazzarini et al. (Reference Mazzarini, Musumeci, Viola, Garofalo and Mattila2019), at a crustal depth <7 km, the differential stress (Δσ) = 2τ m, where τ m is the maximum shear stress at depth z (in km): τ m = 5.0 + 6.6z. Therefore, at ∼2.4 km, σ 3 = 21.82 MPa (Bhowmick & Mondal, Reference Bhowmick and Mondal2020).
For girdle distribution of vein pole data (Fig. 3a), implying high P f condition (P f > σ 2), Φ = 0.72, R′ = 0.8, P f = 55.164 MPa (Fig. 3a, e). For the respective clusters, implying low P f conditions (P f<σ 2), Φ = 0.85, R′ = 0.53, P f = 43.91 MPa (WSW cluster, Fig. 3b, f); Φ = 0.93, R′ = 0.67, P f = 49.74 MPa (NE cluster, Fig. 3c, g); Φ = 0.69, R′ = 0.52, P f = 43.49 MPa (SE cluster, Fig. 3d, h). We have further used these values to analyse the influence of these parameters on the reactivation potential of the veins.
4.b. Dilation tendency, slip tendency and fracture susceptibility
We have obtained graphs determining dilation tendency, slip tendency and fracture susceptibility variation for vein orientations at different stress ratios (Φ). Figure 4 shows the range of fracture orientations for the clusters and vein girdle with variation in slip tendency values at different stress ratios (Φ). Similarly, Figure 5 shows the range of fracture orientations for all clusters and the vein girdle with variation in dilation tendency values at different stress ratios (Φ). Figure 6 shows the range of fracture orientations for the vein clusters and girdle with variation in fracture susceptibility values at different stress ratios (Φ). Figure 7 represents the range of vein orientations for the vein clusters and girdle, consistent with the changes in driving pressure ratio (R′). In order to visualize the role of P f in slip tendency variation for the respective strike orientation of veins under both high and low P f conditions, strike orientation is plotted against R′ (see supplementary sheet-3 in the Supplementary Material available online at https://doi.org/10.1017/S0016756821000881).
Fig. 4. Slip tendency variation with the states of stress for the respective strike orientation of veins under both high and low P f conditions. The coloured rectangles represent the ranges of strike orientation and the stress ratio values for each stress state. Lower–hemisphere equal-area projection of vein pole data (red dots) showing slip tendency variation with stress ratio (Fractend code available via GitHub (Healy, Reference Healy2017)). The warm colour zones represent vein orientations with high slip tendency values (high shear to normal stress). ‘Thermal’ colour scheme from Thyng et al. (Reference Thyng, Greene, Hetland, Zimmerle and DiMarco2016). White square (σ 1), white diamond (σ 2), white triangle (σ 3).
Fig. 5. Dilation tendency variation with the states of stress for the respective strike orientation of veins under both high and low P f conditions. The coloured rectangles represent the ranges of strike orientation and the stress ratio values for each stress state. Lower-hemisphere equal-area projection of vein pole data (red dots) showing dilation tendency variation with stress ratio (Fractend code available via GitHub (Healy, Reference Healy2017)). The warm colour zones represent vein orientations with high dilation tendency values (indicating fracture perpendicular opening). ‘Thermal’ colour scheme from Thyng et al. (2016). White square (σ 1), white diamond (σ 2), white triangle (σ 3).
Fig. 6. Fracture susceptibility variation with the states of stress for the respective strike orientation of veins under both high and low P f conditions. The coloured rectangles represent the ranges of strike orientation and the stress ratio values for each stress state. Lower-hemisphere equal-area projection of vein pole data (red dots) showing variation in fracture susceptibility with stress ratio (Fractend code available via GitHub (Healy, Reference Healy2017)). The warm colour zones represent vein orientations with low P f variation, i.e. high reactivation potential / high fluid influx. ‘Thermal’ colour scheme from Thyng et al. (2016). White square (σ 1), white diamond (σ 2), white triangle (σ 3).
Fig. 7. Variation in driving pressure ratio with strike orientation of veins for both high and low P f conditions. The coloured rectangles represent the ranges of strike orientation and the driving pressure ratio values for each stress state. Lower-hemisphere equal-area projection of vein pole data (white and grey dots) for each stress state (Stereonet 9 software). Pink circle (σ 1), pink triangle (σ 2), pink square (σ 3).
5. Discussion
5.a. Dependence of slip tendency, dilation tendency and fracture susceptibility on the states of stress and fracture orientation
Field studies show multiple median lines within a single quartz vein as evidence of a crack-seal mechanism, indicating cyclic fluid ingression and fault-valve action in the region. The vein emplacement mechanism within pre-existing discontinuities depends on the regional stress field (far-field), stress ratio and fluid pressure condition; such that the fluid pressure build-up exceeds the stresses acting on the discontinuity wall enabling dilation/slip along the discontinuity planes, a mechanism known as fault-valve action. Subsequently, fluid flows into the discontinuities, a phenomenon analogous to burping, triggering a drop in the fluid pressure leading to the formation of veins. Thus, repeated cycles of elevated and depleted fluid pressure generate cross-cutting veins (Sibson, Reference Sibson1992, Reference Sibson1996; Miller et al., Reference Miller, Goldfarb, Gehrels and Snee1994; Mondal & Mamtani, Reference Mondal and Mamtani2013). Therefore, veins with multiple orientations, forming criss-cross patterns (mesh-like structure) in the field have been attributed to such P f variations. Usually, a high P f influx is followed by multiple low P f cycles that can reactivate a small range of fractures, before the P f is again sufficiently high to reactivate a wider range of fractures. Therefore, it is envisaged that such cyclic variation in P f continues until the entire fluid source is exhausted. However, it is very difficult to quantify the exact number of such high and low P f cycles and the precise P f magnitude for each cycle from such a vast event. We could only provide a few instances of this P f variation from our field observations and data distribution pattern. After a high P f cycle, the pressure suddenly drops and minerals are precipitated, sealing the fractures until the next phase of P f rise. Therefore, two consecutive high P f cycles cannot take place simultaneously. However, it is more likely that multiple low P f cycles can follow a high P f cycle and in that case the girdle and clusters might overlap. Therefore, the respective clusters and the girdle distribution of vein pole data each represent a P f condition under which a fracture may reactivate. Figure 4 shows the range of fracture orientations for the respective stress ratios along with the lower-hemisphere stereoplots showing slip tendency variation for each stress state. The role of P f in slip tendency analysis shows that under both high and low P f conditions the fractures oriented parallel/sub-parallel to the magnetic fabric have high slip tendency (supplementary sheet-3 in the Supplementary Material available online at https://doi.org/10.1017/S0016756821000881). For the WSW and NE clusters (considering the maximum cluster density), the orientations showing maximum slip tendency values are mostly consistent with the pre-existing magnetic fabric of the metabasalts, that were reactivated multiple times under both high and low P f conditions. However, for the SE cluster (with highest data spreading) the orientations are comparable to the R′, X and T range of fractures representing the Riedel shear components.
Similarly, Figure 5 gives the range of fracture orientations for the respective stress ratios, along with the lower-hemisphere stereoplots showing dilation tendency variation for each stress state. The warm zones consistent for high dilation tendency values partly overlap the warm zones for high slip tendency values. The fracture orientations lying within this overlapping zone might have suffered high dilation ≥0.8 with moderately high slip tendency ≥0.6.
Figure 6 gives the range of fracture orientations for the respective stress ratios with the lower-hemisphere stereoplots showing fracture susceptibility variation for each stress state. The warm zones indicate less variation in fluid pressure (ΔP f), implying high fluid influx and high chances of fluid-induced fracture reactivation. Thus, vein pole data lying within the warm zone consistent with high dilation and moderately high slip tendency will certainly encounter high fracture susceptibility.
5.b. Fracture orientation vis-à-vis driving pressure ratio
The wide range of fracture orientations in the metabasalts were selectively reactivated under variable P f conditions. Driven by the tectonic stresses, the process of fracture formation/propagation continued with intermittent cycles of fluid pressure build-up, leading to fluid-induced faulting and reactivation of the pre-existing fractures (Bhowmick & Mondal, Reference Bhowmick and Mondal2020). Chances of hydrofracturing are prominent even without a lithostatic and supra-lithostatic fluid pressure, when P f exceeds the normal stress (σ n) and the tensile strength of the rock. For some fracture orientations, the P f value was not high enough to overcome the σ n and tensile strength of the host. However, the instances of P f conditions inferred can be further used to enunciate the range of fracture orientations that were favourably oriented for reactivation under a particular P f magnitude. In Figure 7, the range of fracture orientations consistent with the derived driving pressure ratios (R′) and P f magnitudes are given along with the stereoplots for all the clusters (low P f) and girdle distribution (high P f) of vein pole data. It is to be noted that at the highest driving pressure ratio (R′ = 0.8)/highest P f magnitude (P f ∼ 55.164 MPa), graphically all possible orientations are susceptible to reactivation. However, from field observations we have found fractures devoid of vein infillings. Even under high P f conditions and irrespective of fluid availability such misoriented fractures could not be reactivated under the prevailing stress field. However, lack of connectivity to a fluid source could also be the possible reason for the absence of veins in these fractures.
5.c. Opening angle versus fracture orientation
The opening angles for fractures vary, depending on the mode of reactivation. For dilational fractures (plane normal opening) the range is narrow, whereas for shear fractures (dilation vector inclined to the plane normal) the range broadens. Figure 8 gives the opening angle range for each of the clusters along with their lower-hemisphere equal-area stereoplots. The 3D Mohr circles also provide the respective fluid pressure lines, beyond which fractures cannot reactivate. The warm colour zones with lower range of opening angles represent dilational opening, while with increasing shear-to-dilation ratio the colour gradually attains a darker shade. The white zone in the stereoplots stands for the closed fractures misoriented for reactivation within the prevailing stress field. However, with increasing P f, gradually the white area reduces to an elliptical space (Fig. 8h).
Fig. 8. Opening angle variation in veins for the respective states of stress and increasing P f. (a–d) 3D Mohr circle diagrams denoting the changes in opening angle with increasing P f. (e–h) Lower-hemisphere equal-area projection of vein pole data denoting the corresponding clusters and the high P f girdle (Fractend code available via GitHub (Healy, Reference Healy2017)): (e) SE cluster; (f) WSW cluster; (g) NE cluster; (h) high P f girdle. (a–c) Even in low P f conditions, the favourably oriented fractures have a lower range of opening angles, indicating fracture perpendicular opening. (d) In high P f conditions, all possible vein orientations are reactivated with a broader range of opening angles. (e–h) With increasing P f, the white space for closed/misoriented fractures reduces (unsuitable for reactivation). ‘Thermal’ colour scheme from Thyng et al. (2016).
The numerically derived slip and dilation tendency values along with the opening angles for the vein orientations have been used to obtain the graphs in Figures 9 and 10. The detailed interpretation of these graphs and their implications in this study have been elaborated in this section. Fracture orientations of the study area are a product of the tectonic stress field related to the late D3 deformation, forming a Riedel shear system with CSZ as the shear boundary (Bhowmick & Mondal, Reference Bhowmick and Mondal2020). Some of the prominent fractures (R, Y and P) propagated parallel to the pre-existing fabric (∼NW–SE; 337/69° NE) of the metabasalts (WSW and NE clusters). Out of these, the steeply dipping ones are dilational with dilation tendency ≥0.8 and opening angles ranging between 0° and 20° (see Fig. 9). However, the moderately dipping fractures with high dilation tendency ≥0.8 and moderately high slip tendency ≥0.6, are consistent with opening angles ranging between 20° and 70° (Fig. 9). Other fractures resembling the R′, X and T shear components (SE cluster) have opening angles ranging between 0° and 50°, indicating moderate slip tendency with high dilation tendency (Fig. 9). The fracture orientations with negative opening angles lying within the white elliptical space of the stereoplot (see Fig. 9) are closed fractures; those could have reactivated only under fluid overpressure (P f > σ n). These orientations could be related to compactive shear fractures, but such field evidence was not perceived.
Fig. 9. Opening angle as a function of fracture orientation. Major fracture/fault orientations (given in rose diagram) and their respective range of opening angles (graphically represented). Lower-hemisphere equal-area projection showing the range of opening angles for the veins and closed fractures respectively (Fractend code available via GitHub (Healy, Reference Healy2017)). ‘Thermal’ colour scheme from Thyng et al. (2016). Misoriented fractures (closed fractures) are observed even at the highest determined P f.
Fig. 10. General graphical relation between slip tendency and dilation tendency (after Ferrill et al. Reference Ferrill, Smart and Morris2019a) defining the mode of failure in the fractures and faults of the study area. Range of opening angles specified for each mode of failure indicating an overall volumetric gain due to vein emplacement.
5.d. Mode of failure: slip tendency versus dilation tendency
The numerically obtained slip versus dilation tendency data plotted in Figure 10 match the expected trend as discussed in Ferrill et al. (Reference Ferrill, Smart and Morris2019a). The pattern shows the reactivation modes and volumetric changes along the prominent fracture orientations. We have found that most of the steeply dipping fractures (Fig. 11) underwent tensional failure (Fig. 10) with opening angles ranging between 0° and 20° (also see Fig. 9), while the moderately dipping ones (Fig. 11) suffered shear failure (Fig. 10), with opening angles ranging between 20° and 80° (also Fig. 9). In between both, there is a transitional range of hybrid fractures (Fig. 10) consistent with both moderately high slip and dilation tendency, with opening angles ranging between 30° and 50°. Considering the number of data lying within the zone of tensional and hybrid fractures, it is evident that there has been an overall volumetric gain in the metabasalts, with the steady influx of fluid triggering the process of vein emplacement. This is also in accordance with the transtensional to pure strike-slip stress regime for which R′ = 2 – R, where R′ and R are the stress regime index and stress ratio respectively. For transtensional to pure strike-slip stress regime, R′ value ranges between 1 and 1.5 (Delvaux & Sperner, Reference Delvaux and Sperner2003). In this study, R′ = 1.25 suggests a transtensional to pure strike-slip stress regime under which the fractures and faults were reactivated, as evident from the palaeostress analysis (see section 4.5 in Bhowmick & Mondal, Reference Bhowmick and Mondal2020)).
Fig. 11. Slip versus dilation tendency pattern showing dependence of these parameters on the dip of the fracture plane. The coloured symbols represent the dip (°) ranges of the fractures. Dips of <30° and 30–45° (fracture plane dip) are consistent with compactive failure and compactive shear failure with negative opening angles (very low dilation tendency). Dip of 45–60° stands for shear failure (high slip tendency). Dip of 60–75° stands for hybrid failure (moderate slip and dilation tendency); medium to high opening angles. Dip of 75–90° consistent with tensional fractures (high dilation tendency), low opening angles.
The faults and fractures of the metabasalts of Chitradurga region are investigated to analyse their reactivation potential and failure modes. The brittle structures being related to the regional D3 deformation (late phase) suffered fluid-induced reactivation under multiple P f cycles in the presence of the tectonic stress field (WNW–ESE-directed compression related to late D3 deformation). The variation of parameters like slip tendency, dilation tendency and fracture susceptibility with fracture orientation and stress ratios have been graphically examined. Fracture orientations parallel to the pre-existing metabasalt fabric (WSW and NE clusters) hosting quartz veins of maximum thickness give higher values for both slip/dilation tendencies. Among these, the steeply dipping fractures (∼75–90°) underwent tensional failure (high dilation tendency; Fig. 11), while shear failure is evident in the moderately dipping ones (∼45–60°; high slip tendency). T fractures are dominantly tensile from field evidences. The rest of the fractures resembling X and R′ components (SE cluster) along with some of the R, Y, P fractures range between tensile and shear modes, with hybrid mode forming a transition between both.
6. Conclusions
Reactivation potential of fractures can be successfully evaluated from parameters like slip tendency, dilation tendency, fracture susceptibility and opening angle, where field data are inadequate to determine the failure modes in fractures. Variation in failure mode along fracture surfaces is controlled by the dip of the fracture plane in spite of having similar orientations with respect to the far-field compression (tectonic stress). Obtaining slip versus dilation tendency and opening angle versus fracture orientation patterns are extremely useful for understanding the reactivation potential, deformation behaviour and failure modes in fracture networks that otherwise lack direct field evidence, especially if such reactivations are fluid-induced and multiple fluid pressure changes make it difficult to segregate the individual cycles.
Acknowledgements
This study is an extended part of SB’s doctoral research, being funded by DST Inspire (IF170912). The study is mostly funded by the Indian Statistical Institute research grant, and partly funded by DST-SERB (file no. ECR/2015/000079) and RUSA 2.0 to TKM. The Geological Survey of India (Bangalore) is acknowledged for helping with logistic support and discussions during fieldwork. We personally thank Dr Thirukumaran Venugopal. Discussions with Dr Kevin J Smart were immensely useful. Detailed reviews by Prof. Francesco Mazzarini and an anonymous reviewer helped to improve the paper considerably. Editorial handling by Prof. Stefano Tavani and Prof. Olivier Lacombe is greatly appreciated. Assistance provided by Ayan Patsa, Subha Saha and Swarnasree Mondal is acknowledged. SB also acknowledges the wholehearted support and blessings of Sunil Kumar Bhowmick, Gouri Bhowmick, Ranendranath Chakraborty and Chanchal Pandey.
Conflicts of interest
None.
Supplementary material
To view supplementary material for this article, please visit https://doi.org/10.1017/S0016756821000881
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