Study Area

The studied river is in the Paraná Volcanic Province (South America), which is one of the largest igneous provinces of continental basalts on Earth (^{Frank et al., 2009}). This volcanism was dated between 137 and 127 Ma (^{Turner et al., 1994}) and about 90% of the rocks are basalts and andesites (^{Piccirillo et al., 1988}; ^{Lopes, 2008}).

The area is a bedrock reach of the Bananas River, which is a tributary of the Jordão River (Figure 1), which in turn is a tributary of the right branch of the Iguaçu River in southern Brazil. This bedrock reach is a knickzone, that is, a reach with a higher slope situated between reaches with lower relative slopes comprising a sequence of small knickpoints and rapids (Figure 2). The bedrock reach has a variable width of 45 to 90 m and a length of 400 m. This area was selected because of the excellent exposure of bedrock, especially during the winter low flows.

Figure 1 (a) Location of the study area in the regional context and (b) in relation to the main drainage and main structural lineaments, according to the Serviço Geológico do Paraná (2013). (c) Shaded relief map with some lineaments (red lines) and the study area (yellow box). 

Figure 2 Longitudinal profile of the studied reach and selected field views. Jointing pattern are not to scale. Note that the positions of the sample areas are approximate because the profile was outlined more to the right side of the channel while the sample areas were located near the left side. 

The studied reach is approximately 80 m upstream from an intersection with a structural lineament (N45E), which is approximately 18 km long (Figure 1c). Another lineament (N70E) is situated about 500 m downstream of the study area. Considering that these lineaments may represent fault lines, fracturing of the Bananas River bedrock may have been affected by the stress associated with these faults or other regional structures (Figure 1b). One possible effect of this stress is an increase in the fracture density of the basalts near these lineaments.

The basaltic flows in the region surrounding the study area are of the simple type (^{Walker, 1971}), and are characterized by large lateral extensions and large thicknesses (30 m on average; ^{Nardy, 1995}). The flows have thick massive basalt cores with relatively thin zones at the top (0.3-3.0 m) consisted of amygdaloidal basalt filled with quartz, chalcedony, and zeolites (^{Arioli et al., 2008}; ^{Serviço Geológico do Paraná, 2013}). Locally, in the Bananas reach, the outcrops share these regional morphological characteristics. The upper part is a vesicular-amygdaloidal zone with approximately 3 m thick. The lower part consists of massive basalt with an outcrop thickness of approximately 6 m (Figure 2). The flow structure is similar to that described by ^{Thordarson & Self (1998)} for what they called proximal sections in the Roza Member of the Columbia River Basalt Group. Unlike the pattern widely described in the literature, in which hexagonal columns are well developed, the basalts in this area are not columnar with well-defined geometry. In the core of the lava flow, the main joints have well-developed curvilinear faces that produce columns of variable horizontal dimensions, with maximum value less than 1 m. The curved joints tend to be tapered at the base. The main joints intersect with other joints, many of which are short, while others are longer and straighter.

According to ^{Piccirillo et al. (1988)}, the central region of the Paraná Volcanic Province (and study area) occupies a transitional zone between southern (basalts TiO₂ < 0.2%) and northern regions (basalts TiO₂ > 0.2%) based on geochemical and petrographical criteria. The rocks exposed in the riverbed and surrounding area are dark gray with mesoscopic fine-grained phaneritic to aphanitic texture. The low density of vesicles viewed in the exposed riverbed (Figure 2) is related to the base of that basaltic flow zone.

Fracture Directions

The main fracture directions differed among sample area (Figure 4) and a more detailed analysis revealed some peculiarities. First, the lineament directions (N45E and N70E) did not correspond to the main direction offractures in any of the sample areas, except in area 0435 where the direction N50-60E is remarkable. Another peculiarity involved fractures with main directions close to North (~20°), which appeared in four areas. Directions close to East-West occurred in three of the seven areas. In addition to the presence of preferential maxima in most areas the fractures exhibit a broad range of directions, except for the upstream area (2784), in which the number of fractures was smaller and concentrated in two distinct directions.

Figure 4 Fracture directions in the sample areas of the studied reach. The four-digit numbers identify the sample areas (see Figure 3); letters L, M and U indicate the Lower, Middle and Upper segments of the reach, respectively, according the river flow direction (see Figure 6); and (n) is the number of fractures. The diagrams are arranged sequentially from downstream to upstream. 

Unlike field sampling, the high-resolution RPA images allowed us to observe the major fractures (i.e., the longest ones) in the bed (Figure 5). The directions of these major fractures have four maxima, one oriented NW (5070) and three oriented NE (10-20, 50-70, and 80-90). If only the main and secondary maxima of the circular samples (Figure 3) are observed, there is some level of correspondence with the RPA survey. All circular sample areas had some maxima that corresponded to the RPA survey. Areas 2758 and 2764 presented the highest correspondences with three maxima each one.

Erosion Axes versus Fracture Direction

The main erosion axes of the studied reach have two well-marked maxima at N00-10E and N80-90E (Figure 6). The N80-90E direction coincides with the major maximum of the bed fracture directions (Figure 5). By contrast, the directional axes at N00-10E are close to another directional maximum of fractures oriented N10-20E. The number of erosion axes with a NW direction is lower than the number with NE directions; however, there is a small concentration around the N50-70W direction, which coincides with one of the main fracture directions (Figure 5).

Figure 5 Fractures in the bedrock reach, according to the RPA image survey and the respective rose diagram. 

In the studied reach, the river channel develops a wide curve, changing the flow direction, which in turn can influence which fracture directions facilitate erosion. To verify this hypothesis, the direction of the erosion axes was evaluated separately in three channel segments (Figure 6). In fact, each segment has a different direction distribution. In the upper segment, erosion axes with a direction of N60-70E are predominant. In the middle segment, the main direction is N80-90E, whereas in the lower segment, the main direction is N10-20E. The lower segment is distinguished from the others by the almost absolute predominance of a single erosion axis direction. Each of these major directions of the erosion axes coincides with the major directions of bed fracture (Figure 5). In the upper segment, even the minor directions of the erosion axes correspond to major fracture directions.

Figure 6 (a) Main erosion axes in the studied river reach, (b) general distribution of directions, and (c) distribution by channel segments (L: Lower, M: Middle, U: Upper) according to the change in flow direction, indicated by an arrow in a dashed-line. 

The overall channel flow direction changes in each segment of the reach. It ranges from 50 NW in the upper segment to 40 NW in the middle segment and finally 30 NW in the lower segment. The smallest angle between the general direction of flow in the channel and the main direction of the erosion axes in each segment is 40-60°. In the upper segment, where three erosion axes dominate, the angle with respect to the main direction is 60°, that with respect to the secondary direction is 40°, and that with respect to the third direction is 50°. Although there are differences in the angular relationship between erosion axes and channel flow direction, there is a consistency in the values around 50°.

As noted earlier, some fracture directions surveyed in the circular areas match the maxima obtained from the RPA (Figures 4 and 5), while others do not. Unmatched directions are related to minor and multidirectional fractures, which may be tectonic or cooling joints. These fractures are not related to the directions of erosion axes but contribute to overall erosion by plucking. An example of these distinct roles is evidenced in sample area 3684 (Figure 7). In this area, a conjugate system of tectonic fractures is well-defined. The N85W main fracture act as a control on the erosion direction. The river flow direction at this site is approximately N40W, which result in an angle of 45° to the main fracture. Minor and long joints are crossed by the main fracture, producing small blocks ready for plucking. In fact, erosion by plucking produced a small step in the bed. Here and in other places in the study area the main fracture is opening and facilitates hydraulic wedging (^{Hancock et al., 1998}), which occur as clasts are trapped in fractures, forcing displacement of blocks.

Figure 7 Example of differential role of fractures in erosion of riverbed in the study area. (a) Vertical view of sample area 3684. Heavy lines highlight the conjugate system of tectonic fractures, and the arrow indicate river flow direction. (b) Upstream oblique view of the area. 

Fracture Density

Table 1 presents the fracture density calculated from measurements made in the seven sample areas. The areas appear in the order of their location along the analyzed reach, that is, from downstream to upstream (Figure 3). Data analysis reveals that fracture density tends to decrease in the upstream direction. The more upstream area (2784) is on the amygdaloidal basalt. At the other end of the analyzed transect, by contrast, the fracture density of area 0435 is three times higher than area 2784. Sample area 0435 is situated on a massive basalt and is closest (~80 m) to the lineament N45E which river crosses.

Table 1 Fracture density in Bananas River sampling areas. 

n: number of fractures that intersect the circumference of the sample area; R: sample area radius (meters); D: fracture density according ^{Mauldon et al. (2001)}, D = n/4R.

Tectonic Fractures and Cooling Joints

Basaltic rocks have many joints owing to the cooling process of lava. These joints assume various directions depending on their location in the lava flow body or even in a limited area. As shown in Figures 3 and 4, there is a wide distribution of fracture directions in the study area. However, tectonic fracturing is possibly indicated by the presence of some main directions, that agree with some authors (e.g., ^{Rogers et al., 1996}).

The presence of tectonic fractures in the study area is directly confirmed by some field observations (Figures 3 and 7); however, considering that the joint directions are distributed among several classes, fractures of tectonic origin may overprint other types of fractures because pre-existing joints may accommodate subsequent tectonic stress (^{Patrick Muffler et al., 1994}; ^{Grant & Kattenhorn, 2004}; ^{Moir et al., 2010}).

Main Fractures and Erosion

The importance of main fractures to erosion in the studied river reach is highlighted by the strong relationship between the erosion axis directions and the main fracture directions (Figures 5 and 6). The tectonic nature of some fractures with greater pervasiveness and directional continuity makes them preferable for erosion. This also may be true for some long (3-4 m) cooling joints. The more abundant and multidirectional small joints act to control the plucking process because they limit the polyhedral blocks, but not to determine the main erosion direction (Figure 7).

Most of the main erosion axes, as defined in this study, are related to step-pool morphology zones. The erosive evolution of these zones from long fractures can be understood primarily in terms of the higher density of fractures along one direction. Over a long fracture, the number of intersections with other natural basalt joints becomes larger. In addition, tectonic fractures will often have subsidiary (pinned) joints, which increase the density of rock discontinuities along the main direction (^{Peacock, 2001}). As a result, the blocks available for simple plucking and breakage by impacts from sediments in transit (macroabrasion, ^{Whipple et al., 2000a}) are potentially smaller than those in other bed areas and erosion is concentrated along this line (Figure 7).

These preferential linear erosion zones may eventually be interrupted owing to local variations in the channel flow direction and/or the presence of basalt joints. Especially at the intermediate levels of the thick basaltic flows of the Paraná Basin Province (^{Serviço Geológico do Paraná, 2013}) and of the studied area, columns with metric dimensions (height and width) delimited by joints with curvilinear planes are common. The river flow can create alternative paths along these joints.

Flow and Erosion Direction

As noted earlier (Results section), the overall flow direction makes an angle of 40-60° with respect to the main direction of the erosion axes in each segment into which the reach has been divided. Furthermore, these axes directions correspond to major fracture directions. The slope of the channel has no discernible effect on this angular relationship. In the lower segment, which has a higher slope, the angle is 40°. In the middle segment, which has a smaller slope, the angle is 50°. The slope of the upper segment is between those of the other two segments; however, the main angular relationship is 60°, although the 40° and 50° relationships also occur in secondary directions. The angular relationship between the flow and fracture directions (erosion axes) within the observed range apparently depends on the variability of the channel flow hydrodynamics, the variability of the interaction between tectonic fractures and cooling joints, and the lithological characteristics.

Considering the large number of variables involved, the only possible conclusion is that the average relationship between the channel flow direction and erosion axis direction is on the order of 50°. Satellite observations of other parts of the Bananas River and other rivers in the region, which run over basalts, confirm the average angular relationship of 50° between the direction of flow and the erosion axes, especially the knickpoint face directions. ^{Miller (1991)}, who studied rivers in siliciclastic and carbonate rocks, also frequently observed oblique arrangements of knickpoints generated by fractures. Fracturing is much more complex in basalts of the study area than in that sedimentary rocks. The presence of more pervasive and continuous tectonic fractures seems to be essential for establishing the angular relationship with the flow direction, similar to the case in simpler fracture systems.

Why the river flow tends to have this specific angular relationship with the major fractures remains an open question. Although a definitive answer requires further investigation, it is possible to deduce that angles much smaller than 40° between the flow direction and the direction of these pervasive fractures favor the adjustment of the channel along the structures. As several surveys have shown, rivers tend to exploit directions represented by vertical fractures (e.g., ^{Eyles et al., 1997}; ^{Pelletier et al., 2009}). Flume experiments (^{Dubinski & Wohl, 2013}; ^{Wilkinson et al., 2018}) with regular fracturing suggest that an orthogonal arrangement of fractures with respect to the flow direction favors the removal of bed blocks. Although the experimental results presented by ^{George et al. (2015)} for blocks with complex geometries indicate that the erodibility is greater when the angle with the flow is 75°, it is worth noting that this is the angle with respect to the central axis and not that with respect to the face of the block, owing to its tetragonal geometry. Correcting the angle to that with respect to the face of the block gives an approximate value of 55°, which is consistent with the average angle obtained for the Bananas River.

Fracture Density Variation

^{Lima & Binda (2013)} found that the average fracture density in the basalts of the Das Pedras River, close to the Bananas River (Figure 1), in the reaches associated with structural lineaments, is 6.05 m/m². The average obtained for the Bananas River study (6.7 m/m²) is similar (Table 1). Overlap between tectonic fractures and basalt joints occurs effectively, as confirmed by the presence of preferential directions (Figure 5) and field observations (Figure 7). This implies that the fracture density is increased by tectonic effects. As previously described, two major lineaments are close enough to the area to eventually contribute to the generation of fractures. However, the upstream decrease in fracture density (Table 1) is depending on the distance from the structural lineament (N45E) that the channel crosses? The maximum fracture density (9.2) appears in the zone closest to that lineament (Table 1). Sample area 2784 is farthest from the lineament and has the lowest fracture density (3.73). Contrary to what was expected if the study area is associated with a damage zone, there is no maximum direction parallel to the lineament (N45E), although it is possible for joints to form at high angles to the strike of a fault (^{Kattenhorn et al., 2000}).

Fracture density in basalts varies depending on the internal lava flow structure. In fact, area 2784 is on an amygdaloidal zone, whereas the others are on massive basalt. For amygdaloidal zones, fracture densities equal to or greater than those of massive zones have been reported (^{Faust, 1977}; ^{Thordarson & Self, 1998}), although lower densities are also possible (^{Lima & Binda, 2013}).

One aspect that favors the damage zone hypothesis is the gradual decrease in fracture densities upstream. Transitions in the pattern of fractures between internal zones of the lava flows are usually abrupt. Moreover, the absence of fractures parallel to the lineament could be masked by the cooling joints which served to accommodate subsequent tectonic stress, as described in the first section of this discussion. Further and detailed analysis will be necessary to describe the nature of the lineament and to define if there is a real relationship with the pattern of fracture density detected in the study area.

Fracture Density and Erosion

Regardless of the causative factor, could the variation in the fracture density affect the erosion processes? Theoretically, variation in fracture density can affect the type of erosion processes that occur and their intensity. Low fracture density, as found upstream in the study area, favors abrasion (^{Whipple et al., 2000b}). The formation of potholes indicates abrasive processes. However, in the studied reach, these abrasive features appear in both upper and lower segments, regardless of the different fracture densities (9.6 and 3.7, respectively). Despite these signs of abrasion, plucking and macroabrasion are the main processes acting along the entire reach.

The increase in fracture density (Table 1), which coincides with massive basalt zone, favors plucking because it decreases the size of the rock blocks. By contrast, the decrease in fractures densities culminates in an amygdaloidal basalt zone (sample area 2784) that is less resistant and more susceptible to weathering (^{Lima & Binda, 2013}). Low fracture density limits the plucking of blocks because they are larger. However, the high susceptibility to weathering and low rock resistance favor macroabrasion (^{Small et al., 2015}). This is observed in the increase of the chipping features of the bed surface (sample areas 3674 and 2784, Figure 3) and in the smoothing of the reach morphology (Figure 2). While erodibility may be the same throughout the reach, bed morphology and slopes may differ.