Granite rock towers shaped by mesh‐like joint sets, which formed in the shallower portion of a granite body during cooling at depth

Granite is fractured according to the stress state during the cooling stage, providing predispositions for later topographic evolution. This study clarified that triangular mesh‐like joints can be made during granite cooling and that they can become the structural causes for the formation of rock towers and corestones on the ground. Tengu rock, which consists of rock towers and granite corestones in Hiroshima, was investigated using an unmanned air vehicle. The rock towers were shaped by high‐angle mesh‐like joints, which were likely made during the cooling of the granite and are dominated by three joint sets. All the joint sets have sharp planar surfaces, which suggests that they are brittle fractures. One joint set is cut by the other two joint sets, frequently accompanies aplite and quartz veins and is developed in the whole exposed granite; this set likely formed first during cooling and then was penetrated by aplite from depth. The other two joint sets are high‐angle conjugate joint sets, are limited to the shallower portion of the granite pluton and do not extend deeper, which strongly suggests that they formed in a rapidly cooled shallower portion of the pluton, probably near its roof. These three joint sets form rock columns with parallelogram cross‐sections, in which incipient corestones were made. Subsurface weathering along the joints and subsequent exhumation of the weathering products formed the present rock towers and corestones only in the shallower portion of the granite.


| INTRODUCTION
Granite is distributed worldwide and underlies 13% of Japan.Granite forms characteristic topography, such as tors, rock towers, and boulder fields (Migo n, 2006;Twidale, 1982;Twidale & Vidal Romani, 2005), which are attributed to weathering along primary joints and subsequent exhumation of the weathering products (Linton, 1955), while it is sometimes considered a periglacial product (Palmer & Neilson, 1962).
Granitoids are fractured during their cooling stage, and researchers have long believed that the primary joints are orthogonal since the pioneering work by Cloos (1921) and Cloos (1922) (Bahat et al., 2005), but recent 3D observations have clarified new views of joints in granite.
Joints in granite used to be observed from limited angles, either from the ground surface or from the air.Instead, the recently developed unmanned air vehicle (UAV) and image processing software structure from motion (SfM) have been successfully used in geomorphological and geological studies (Bemis et al., 2014;James & Robson, 2012;Kasprzak et al., 2018).Using these techniques, some granitoid rock towers have been demonstrated to be shaped by columnar joints (Chigira, 2021;Chigira, 2022) with irregularly shaped polygonal cross-sections; these columnar joints separate rock bodies between parallel joints, which formed during an early stage of cooling according to the tectonic stress and thermal stress.Such a sequence, however, should be dependent on the stress history and cooling history of a granitoid pluton, and other cases should exist.Chigira and Hirata (2021) studied the Kui boulder field and found that the boulder field consists of corestones and rock prisms, which were inherited from rock columns shaped by columnar joints (Chigira & Hirata, 2021).
The purpose of this study is to characterize the Tengu rock, which consists of rock towers and corestones surrounded by systematic mesh-like high-angle joints in Hiroshima, using UAV and SfM (Figure 1).Such a combination is different from the columnar joints of granitoids with irregularly shaped polygonal cross-sections reported by Chigira (2021Chigira ( , 2022)), and this combination should have a special history, which is discussed in this paper.

| GEOLOGICAL SETTING
The study site is on Nomi Island of Etajima city to the south of Hiroshima city, where Cretaceous Kure Granite, a type of Hiroshima Granite, is distributed (Higashimoto et al., 1984;Matsuura, 1996) (Figure 1a,b).The Kure Granite at the study site is a medium-to coarse-grained biotite granite, and to its west is fine-grained biotite granite (Matsuura, 1996).The boundary between these granites is high in angle near the study site, but 15 km west of the study site, the fine-grained granite overlies the coarse-grained granite, with a horizontal boundary whose structure is similar to that in Hiroshima, suggesting that the fine-grained granite is slightly below the roof of a batholith (Takahashi, 1993).The coarse-grained granite is K-Ar dated to 81.6 ± 4.1 Ma and 89.0 ± 4.5 Ma, and the finegrained granite is dated to 79.7 ± 4.8 Ma and 85.7 ± 4.3 Ma at Kure (Figure 1b; Higashimoto et al., 1984).These two granites are intruded by NNE-SSW-trending dikes of microdiorite and granite porphyry (Figure 1b); the former is less than 1 m thick and sometimes displaced without a brittle fault in the juxtaposing granite, suggesting that its intrusion occurred when the granite was still ductile (Matsuura, 1996).The granodiorite dikes are up to 200 m thick (Matsuura, 1996).
Tengu rock is on a ridge that is 200 m in elevation and located east of Nomi Island (Figures 1c and 2a).The term Tengu rock has been used comprehensively because there is more than one rock tower in the area, and Tengu rock is not specific.Tengu is a folktale figure with a long nose, and the name has been given to a rock tower at the study site.The granite around Tengu rock has a rather smooth surface at lower elevations and shows tower-like shapes on ridge tops at higher elevations (Figure 2a,b).

| METHODS
A field survey was conducted using UAVs and geological mapping, particularly of joints.The UAV that was used was a DJI Mavic 2 pro, which has an L1D-20c camera with a focal length of 10.26 mm and a 1-inch sensor, and the resulting images have a pixel size of 23.41 by 23.41 μm.Ground control points were not used, and onboard GPS was used instead.This method was not an obstacle for this study because a 2-m long scale set horizontally on an outcrop was measured to be 2.0 m long in the 3D model, as described later.The average flight height of the UAV was 53 m.
Fifty images with overlapping areas were taken and used for the following analysis.UAV images were processed using structure from motion (SfM) software, Metashape version 1.6.3from Agisoft to perform 3D analysis.Orthophotos and digital elevation models (DEMs) were made by SfM software and analyzed in the geographic information system of QGIS 3.14 (http://qgis.osgeo.org), which is an open-source platform.Contour maps were made, and joints were analyzed on this platform.Polygon areas, perimeters, and joint directions were measured using the field calculator provided on the platform.
Field mapping was performed for joints, with a special focus on their distribution, attitudes, and relative relationships.

| General morphology
Three-dimensional observations in this study clarified the topographic features of the Tengu rock area, of which rock towers reach nearly 7 m high (Figure 3).These rock towers are on a ridge top, where joints shape the rock towers (Figures 4,5,and 6).The edges of the rock towers are not sharp but rather rounded, and internal chamfering cracks or rindlets are sometimes present (Figure 6f).With the rock   6c), which suggests that the corestones were made after the formation of these two joint sets (J2 and J3, which are described later).On the surfaces of the corestones, there might have been grus, which is now eroded but is still in the forest along the northwestern side of the area shown in Figure 6a (i in Figure 4).The corestones, therefore, were likely made by subsurface spheroidal weathering of the rock columns.
The horizontal cross-sections of the rock towers and corestones vary from trigonal to hexagonal, with rounded irregular shapes F I G U R E 4 Distribution of joints and massive areas.(a) Orthophoto of the study area.i and ii show the areas of Figures 6a and 10a, respectively.(b) Joint distribution.Note that the east-west-and NNE-SSW-trending joints do not continue to lower elevations, where massive granite is exposed.XX 0 and YY 0 are profile lines shown in Figure 5.
(Figure 7).The cross-sections of the corestones and rock towers can be observed and measured on the orthophotograph because the joints that shape the rock towers are nearly vertical, as is stated later.The areas of the cross-sections vary from 0.1 to 14.1 m 2 , with an average of 1.4 m 2 , and the perimeters vary from 1.2 to 14.3 m, with an average of 3.8 m.These sizes are dependent on the intervals of the joints.

| Joints and massive portion of granite
Joints are developed on top of the ridge in the study area (Figures 4   and 6a,b) and show a mesh-like pattern, with three distinctly identifiable dominant directions (Figures 4, 6a,b, and 8): they are all highangle and strike northwest-southeast (Joint set 1, J1), NNE-SSW (Joint set 2, J2) and east-west (Joint set 3, J3) (Figure 8).These joints generally have no visible displacements but rarely have several cmscale displacements along them (Figure 9a).J1 joints frequently accompany aplite veins up to 10 cm thick (Figure 9d) and quartz veins up to a few cm thick (Figure 9a,c,d).Its intervals vary from a few 10 cm to 4 m.J1 joints are cut by J2 and J3 joints (Figure 9a,c; Table 1).J2 joints lack filling materials and cut J1 joints, sometimes with a few cm of right-lateral offset (Figure 9a).J2 joints cut J3 joints or are cut by J3 joints.J3 joints also lack filling materials.Riedel shears (Logan et al., 1979) were found along J3 joints (Figure 9b), which suggests that the joints had left-lateral displacement.Slickenlines, however, could not be observed on the Riedel shears and the joints because those surfaces were not easily cut out from the outcrop.
J1 joints are distributed in the lower and higher areas in the study area, but J2 and J3 are distributed only in the higher elevations (Figures 4 and 5).They do not appear in the lower elevations on their geometrical extensions (Figure 4a).On the other hand, the whole study site is underlain by massive granite with J1 joints at lower elevations (Figure 4).
The transition from jointed granite to underlying massive granite is well observed in the middle of the study area (ii in Figure 4a), of which a close-up view is shown in Figure 10.In the northern part of Figure 10a, there is a rock column (Figure 10b), of which the base is underlain by massive granite.The joints that shape the column disappear downward in the massive portion.The granite of the column is weakly weathered medium-grained porphyritic biotite granite with rounded quartz grains (Figure 10c) that gradually transitions to the massive portion, which consists of medium-grained equigranular biotite granite (Figure 10d).The massive portion of granite is moderately weathered; it disintegrates when hit with a hammer.This massive portion may correspond to the decomposed granite of Durgin (1977).The granite of rock towers is not always porphyritic granite but is frequently the same as the massive, equigranular biotite granite.

| DISCUSSION
The jointing of a cooling granite pluton may reflect the tectonic stress state, as well as the cooling history.The joints in the granite studied in this paper consist of three high-angle joint sets at high elevations, which form rock columns with rhombus cross-sections, but consist of only one set at lower elevations.Outcrop distributions and relative relationships of joint systems in the study area reveal a characteristic jointing history, as shown in Figure 11.J1 joints that frequently accompany aplite and quartz veins are distributed at lower elevations as well as higher elevations, while J2 and J3 joints are limited at higher elevations.Bergbauer and Martel (1999) and Martel and Bergbauer (1997) examined the stress states of a granite pluton during cooling and concluded that parallel cooling joints are made by the combination of tectonic and thermal stresses.The J1 joints could be explained as such joints made during the cooling of the granite pluton with the maximum compressional stress axis trending northwest-southeast.The granite pluton is inferred to have continued to cool particularly faster near the roof (Figure 11b).The J2 and J3 joints were made exclusively in its upper portion, which might have been cooled faster than the lower, inner portion of granite (Figure 11c).This faster cooling may be supported by the fact that some of the rock columns surrounded by joints J2 and J3 consist of porphyritic granite with F I G U R E 5 Topographic profiles along the profiles shown in Figure 4.Note that rock columns are at higher elevations, while massive rock is at lower elevations.rounded quartz grains.The J2 and J3 joints were observed to cut each other as previously described, which suggests that they were made contemporarily.In addition, east-west-trending J3 joints NNE-SSW-trending J2 and J3 joints is approximately 65 .These facts suggest that J2 and J3 could be conjugate joint sets (Davis et al., 2012) with a maximum compressional axis in the northeastsouthwest direction (Figure 11c).If so, the stress states must have changed since the intrusion of the granite pluton when the J1 joints were made.Regardless, the reason why the shallower portion of the granite pluton (the higher elevation portion) was fractured and the deeper portion was not could be attributed to the temperatures and stress levels of the pluton; the deeper granite might have been still ductile, while the shallower portion behaved in a brittle manner, although numerical data have not been obtained.The thickness of this brittle zone cannot be estimated because the materials immediately above the exposure at Tengu rock have been removed.Fabbri et al. (2004)  separated by columnar joints, which form rock columns with irregularly shaped cross-sections.They inferred that the parallel joints were made during the cooling of the granite under the combination of regional and thermal stresses and that subsequent cooling induced volume contraction to form columnar joints.They described columnar joints that developed on ridges, but on the other hand, the lower portions of the gullies on Mt.Mizugaki and Mt.Jizogadake exhibit microsheeting without columnar jointing, which may suggest that the lower inner portion of the granite bodies slowly cooled down and became massive, which would have been microsheeted by unloading (Chigira, 2001).In the study area in this paper, the granite was first separated by parallel joints accompanying aplite and quartz veins and then cut by probable conjugate joints in its upper portion rather than irregularly shaped columnar joints.Whether such conjugate joints or columnar joints are made is likely dependent on the ambient stress field; columnar joints might be made under isostatic stress, and conjugate joints could be made under deviatoric stresses.The granite in Mt.Mizugaki is a medium-grained granite and is characterized by rounded quartz grains, similar to those at this study site, which indicates that the granitic melt ascended rapidly after crystallization started (Cobbing, 2000).The granite in the study site was cut by mesh-like joints and not by columnar joints, but it presumably was followed by volume contraction, which contributed to the formation of incipient corestones.
The boundary between the granite at the study site and finegrained granite to the west is at a high angle near the study site (Matsuura, 1996), but 15 km west of the study site, the fine-grained granite overlies the coarse-grained granite with a horizontal boundary whose structure is similar to that in Hiroshima and suggests that the fine-grained granite is immediately below the roof of a batholith (Takahashi, 1993).This may indicate that the study site is close to the roof of the granite pluton and that mesh-like joints may be made immediately below the roof (Figure 11c).
After the settlement of the granite at a depth at which Cretaceous strata are present, the study site was upheaved and eroded to expose the current outcrops (Figure 11d).The topographic history Note: "Number" is a working sample name.Within the same row, the numbers show the order of joint formation.For example, in sample #1, the J2 joint cuts the J1 joint, suggesting that the J1 joint formed, followed by the J2 joint.Note that J2 joints cut J3 joints in #2 and #3 but are reversed in #10 and #101.
around the study site is not well known, but the rock towers and incipient must have been made by subsurface weathering in the ground and the following removal of weathering products.
Currently, the massive granite is slightly weathered, resulting in a rough surface that can be scraped with a hammer, while the granite separated by the J2 and J3 joint sets is hard.Chigira and Hirata (2021) Photographs of Tengu rock and the surrounding area.(a) Tengu rock consists of more than one rock tower.(b) Outcrops around Tengu rock.The arrow shows the camera angle of the image in (a).

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I G U R E 3 Oblique view of Tengu rock made from the 3D model.i and ii show the areas of Figures 6a and 10a, respectively.The heights of the rock towers were measured on the 3D model.towers, there are incipient corestones, which are not detached from the outcrops but protrude from the surrounding rock surfaces (Figure 6c-e).Some incipient corestones are in a parallelogram made by two sets of joints (Figure may have left-lateral displacements, as suggested by the Riedel shears.The NNE-SSW-trending J2 joint may have rightlateral displacement, and the intersection angle between the F I G U R E 6 Outcrops in the study area.(a) Orthophoto.A two-meter-long scale set horizontally on the outcrop was measured as 2.0 m on the 3D model.(b) Orthophoto delineating joints, corestones, and rock columns.(c) Incipient corestones embedded in the rock mass.(d) Corestones and small rock towers.(e) Corestone and rock towers.(f) Rounded top of a rock tower with rindlets.Each red and white portion in the scale bar is 20 cm long.The locations of e and f are shown in Figure 7 as i and ii, respectively.
discussed the fault activity and stress regime in the Chugoku area, including Hiroshima, and concluded that northeast first-order faults developed in this area and that their sense was left-lateral during the Late Cretaceous-Paleocene (70-60 Ma) and changed to right-lateral during the Plio-Quaternary.The maximum compressive stress axis for the northeast-southwest-trending left-lateral fault is in the north-south direction, deviating from the northeast-southwest inferred from the J1 and J2 joints.Chigira (2021) and Chigira (2022) investigated rock towers of Miocene granite on Mt.Mizugaki and Mt.Jizogadake, central Japan, and found that granite rock slabs between parallel joints were F I G U R E 7 Distribution of corestones and rock columns and their size distributions.(a) Distributions plotted on an orthophoto.i and ii show the locations of Figure 6e,f, respectively.(b) Histogram of the areas of horizontal cross-sections of corestones and rock columns.(c) Histogram of the perimeters of horizontal cross-sections of corestones and rock columns.F I G U R E 8 Joint directions in the study area.(a) Rose diagram.(b) Equal-area stereographic projections on the lower hemisphere.The contouring is one percentage area.For J1, J2, and J3, see the text.The data number is 19.

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I G U R E 9 Joint photographs.(a) NNE-trending joint (J2) and northwesttrending joint with a quartz vein (J1).J1 is cut by J2 with several cm of right-lateral offset.(b) J2 and E-trending joint (J3).J3 consists of Riedel shears, which suggest left-lateral displacement.(c) J1 and J3.J3 cuts J1 but without offset.(d) northwesttrending aplite and quartz vein.T A B L E 1 Order of joint formation.
investigated the Kui boulder field at elevations from 400 to 600 m located 65 km northeast of the study site and clarified that it was made from the subsurface weathering of granodiorite rock columns and groundwater erosion.The granite at this study site had incipient shapes of corestones in rock blocks surrounded by mesh-like joints, which suggests that rock volume contraction could have continued after the formation of meshlike joints.

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I G U R E 1 0 Outcrop of the transitional area from jointed granite to massive granite.(a) Orthophoto made from the 3D model.The location is shown as ii in Figure 4. (b) Rock column standing on massive granite.(c) Porphyritic granite with rounded quartz grains, which forms the rock column.The diameter of the coin hole is 5 mm.(d) Equigranular granite, which forms the massive granite.