Introduction

Nowadays, the UAV technology is accessible and reliable giving new opportunities in different applications (Shakhatreh et al. 2019). In particular, the use of UAV has revolutionized the way of data acquisition in topographic surveys and mapping due to their ability to visualize and represent millimetric scale features by processing a group of high-resolution aerial photographs (Vollgger and Cruden 2016). As has been underlined in different manuscripts (Inama et al. 2020) the use of UAV in any geological survey permits a better inspection of large and non-accessible areas; minimizes time of data collection, and exposure of the technical manpower to hazardous conditions (Bamford et al. 2020). As Tiruneh et al. (2013) describe areas such as active mines and bench slopes can pose rock fall hazard to the personnel collecting the data. On the other hand, mapping of the orientation of discontinuities, is essential for different geological studies, including geotechnical analyses and hazard assessment (Tannant 2015; Menegoni et al. 2019 and 2021). For example, on a rock slope, this property largely controls the optimal angle of stability, while in tunnel design, it helps to analyze the failure mode of rock blocks: geometrical arrangement of the discontinuities together with the orientation of the tunnel axis produce complex deformation patterns. However, there are in literature different studies that map and characterized discontinuities by using photogrammetric-derived data of rock surfaces (Sturzenegger et al. 2011; Tiruneh et al. 2013; Chesley et al. 2017), some of them demonstrate that this technique permits a fast extraction of accurate structural measurements as spatial variations in fold geometries and orientations (Vollgger and Cruden 2016; Menegoni et al. 2018; Panara et al. 2022), or determination of block size and shape distribution along a rock mass (Buyer et al. 2020; Jaboyedoff et al. 2020; Menegoni 2020). On the other hand, a complete rock mass characterization also includes the knowledge of the properties of the rock matrix: the study of the stress – strain behavior, fracture process, as well as elastic moduli in a specimen under axial compression, could help in a better understanding of rock mass strength.

This investigation was mainly focused on mapping discontinuities and characterizing rock masses using UAV photogrammetry, laboratory analyses and the application of a code written in python language that includes the use of k-Means and RANSAC algorithms. The proposed machine learning approach/algorithm was validated or placed into a global context by using well-known and well-characterized cases (Lato et al. 2013; Wu et al. 2020). On the contrary, the final products including 3D models need to be verified, scaled and calibrated based on detailed data collected in the field using traditional surveys, as a description of regional and local structural-geology, as well as detailed characterization of intact rock and discontinuities, in turn vital in terms of the attribution of real parameters and future construction of different conceptual models, including ground water flow or any geological phenomena (Piras et al. 2017).

Geological settings of the studied area

The study zone is in the Sierra Madre Oriental into the border of the eastern part of the Trans-Mexican Volcanic Belt, particularly among Chignahuapan, Zacatlán and Tetela de Ocampo villages (Fig. 1a and b), into those described as part of the Basement of the Acoculco Caldera Complex. In general terms, is composed by the Oaxaquia block, considered as a crustal fragment (Ortega-Gutierrez et al. 1995) and described as a sedimentary range resulting from the accretion of the southern part of the North American craton. The basal part of the Oaxaquia block is composed of Precambrian crystalline gneisses and anorthosites (Keppie et al. 2003). This basal part is overlain by Paleozoic sedimentary rocks in turn covered by Permian volcanic and volcaniclastic rocks and early Mesozoic turbidites thick succession, deformed in the early Jurassic. This succession is unconformably overlain by overlapping assemblage made up of Jurassic-Cretaceous redbeds or marine volcanic / sedimentary rocks interbedded with felsic volcanic rocks (Centeno-García 2017). All this rock sequence in the Acoculco region has been associated to the Sierra Madre Oriental, is intruded by different granitic bodies (Sosa-Ceballos et al. 2018; Avellán et al. 2018), and on the top of this sequence there are different hydrothermally altered basaltic-andesite lava flows (Fig. 2) García-Palomo et al. (2002).

Fig. 1
figure 1

(a) Illustrative map of the central part of México, including the trace of the TMVB, the most representative cities, as well as the studied zone. Image was constructed by GeoMapApp, a free application of earth science exploration and visualization (http://www.geomapapp.org). (b) Localization map of Acoculco Caldera Complex, including villages of the region, most representative structural alignments, as well as rose diagrams. Image was obtained by the fusion of two SPOT images (multispectral and panchromatic with 10 and 2.5 m of resolution, respectively). Abbreviations are: G = Guadalajara, Gu = Guanajuato, Mo = Morelia, Me = México City, Pu = Puebla, Pa = Pachuca, SMOC = Sierra Madre Occidental, SMO = Sierra Madre Oriental, SMS = Sierra Madre del Sur, Ch = Chignahuapan, Pa = El Paredón village, AZ = Agua Zarca village, Ac = Acoculco village, Tl = Tlapizahua village, Tu = Tulancingo, Hu = Huauchinango, Ze = Zempoala

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Fig. 2
figure 2

Geological map over a shaded relief model (obtained by the fusion of two SPOT images [multispectral and panchromatic with 10 and 2.5 m of resolution, respectively]). Red circles indicate the location of each described section. Geological information was assigned according to the geological fieldwork and bibliography (Sosa-Ceballos et al. 2018; Avellán et al. 2018)

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The entire region is tectonically affected by different systems, in fact it is located at the intersection of two regional fault systems that have been conditioned an orthogonal arrangement creating graben and horsts (Lermo et al. 2009; García-Palomo et al. 2002, 2018; Avellán et al. 2018, 2020) (Fig. 3): (1) The NE-SW trend system considered as the most important fault system in the region, consisting of normal faults with a left lateral component, regionally related to the Tlaxco-Chignahuapan graben and Rosario-Acoculco horst where Acoculco Caldera Complex is located; (2) the oldest NW-SE trend system, which is following the trend of fold axes and horse faults of the Sierra Madre Oriental and is regionally related to Tulancingo Tlaxco fault system. Locally, a W-E trend set is recognizable and is more related to the local structures of the inner caldera (Fig. 1b). The northwestern part of the region is composed by Apan Tezontepec Volcanic Field (e.g. Miocene, rocks, Pliocene rocks, Quaternary monogenetic volcanoes, García-Palomo et al. 2018), while the southern part of the region is composed by the Peñuela Volcanic Complex composed by different riolitic, dacitic - riodacitic, and andesitic volcanic structures K-Ar dated at 12.7 ± 0.6 Ma (García-Palomo et al. 2002). The central part of the region is composed of the Acoculco Caldera Complex, including syn-caldera, early post-caldera, and late post-caldera sequences (Fig. 2).

Fig. 3
figure 3

(a) Sequence of 1,375 overlapping aerial photographs (images for the detailed survey of the rock mass are included) acquired by a UAV over an area of 0.226 km2. (b) panoramic view of the study area reconstructed by the digital elevation model. All stations in the horizontal plane and control points in the slope plane were used to calibrate the models. (c) panoramic view of the basal part of the study rock mass (some marks of the basic topographic survey, where anchor bolts were installed are also visible)

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Methods

The workflow of this research is as follows: (1) collection of geological - structural information of the region, (2) field work including collection of rock samples, structural data, stratigraphic surveys, and fracture mapping based on UAV flights, (3) intact rock characterization by laboratory tests and analysis of rock mass discontinuities from different scales, including outcrop scale, (4) rock mass discontinuities recognition based on UAV photogrammetry, and (5) rock mass classification based on the joint analysis of all results.

In this sense, the Fig. 1, localization map of the area, was constructed by editing figures extracted from GeoMapApp data exploration and visualization tool (http://www.geomapapp.org), while Fig. 2, the geological map of the study area, was constructed using the previous geological data of Sosa-Ceballos et al. (2018) and Avellán et al. (2018) and the information acquired during the geological fieldwork, including the description of the stratigraphic succession of the rock units. Geological information was projected on thematic maps (e.g. shaded relief models) constructed by processing digital topography (DEM data with 15 m of resolution), scale 1:50,000 of the Instituto Nacional de Estadística, Geografía e Informática (INEGI), and a fusion of two SPOT images (multispectral and panchromatic with 6 and 1.5 m of resolution, respectively). Samples to describe units and to implement future laboratory tests were selected according to the distribution of the outcrops, in this work localized between Chignaupan and Zacatlán cities, into the rock units related to the basement of the Acoculco Caldera Complex (Fig. 2).

Intact rock characterization

This section integrates a brief description of the implemented methodology, some basic concepts are included to improve or reinforce our final conclusions and technical considerations. All cylindrical specimens and laboratory tests were prepared and performed, respectively following the standards (e.g. ASTM D4543, 2019) to compare or place our results in a global context. All collected samples were generally described according to those properties observed in hand-collected specimens and in thin sections by means of optical microscopy. Physical properties such as grain density (ρ), effective porosity (ηe) was measured to evaluate the mechanical behavior and the strength of the specimens. In turn, mechanical values of the specimens together with detailed characterization of discontinuities in mass scale, including orientation and condition were necessary to attribute properties of the rock masses.

Physical properties

Particle density or real density (ρ) of each sample was determined with the Quantachrome 1200e pycnometer, designed to measure the true volume of solid materials by employing the Archimedes principle of fluid displacement and gas expansion (Boyle’s Law). The helium gas (99.999% ultra-high purity) was used as the displacing fluid since it penetrates the finest pores assuring maximum accuracy (ASTM D5550, 2014). Bulk density (γ) was determined by basic methods (e.g. vacuum water saturation) (ASTM D7263-21, 2021). It should be considered that basic different methods for calculating the γ of a material could differ based on how void space in the samples are handled (see ASTM D7263-21, 2021 for a good review). In turn, Effective porosity (ηe) was initially obtained following the procedure recommended by ISRM (2007) by means of vacuum water saturation test. Procedure includes: the oven drying of samples at a temperature of 70 ºC for 48 h and three 5-hour cycles of the samples placed in a vacuum at 20 ± 7-mbar pressure. The pore size distribution and effective porosity (ηe) were quantified using a Quantachrome, PoreMaster® 33, mercury porosimeter. This method provides a wide range of information like the pore size distribution (0.0064 μm – 1 mm), the total pore volume or porosity, the skeletal and apparent density, and the specific surface area of a sample (see Giesche 2006; for a general overview).

Uniaxial compressive strength and elastic moduli

In general terms the mechanical behavior of rock is defined by the relationship of the stress and strain parameters. As largely highlighted in literature (e.g. Baud et al. 2014) these parameters are very useful in rock engineering, including rock mass classification. Uniaxial compressive test was performed following standard procedures (ASTM D7012-10, 2010) on a 250 kN GDS VIS servo-controlled hydraulic testing frame at a constant displacement rate of 4 mm/h. Stress and strains were recorded continuously during each test by two load cells (internal [inside the load cell] and external [integrated in the compression ring]). The elastic constant (elastic modulus [E]) was calculated as the average slope of the elastic section of each stress-strain curve.

Rock mass discontinuities characterization from outcrop scale

All rock masses present different sets of discontinuities (e.g. beddings, other surfaces of weakness) corresponding to the evolution of the regional stress field (complex deformation history), their detailed characterization is critical or extremely important to any geological work, including the assignation of properties of rock units for the construction of any geological conceptual model. In this way, a detailed characterization of all identified set of discontinuities have been performed according to basic and widely used methodology discussed in recent bibliography (e.g. Palmström 2005), which consists in measure different characteristics including: (1) characteristics that establish the block size and shape, including the number of the discontinuity sets, their spatial distribution and orientation, their spacing, and their persistence; (2) characteristics that establish or contribute to the mechanical behavior of the mass, including joint strength, aperture, roughness (e.g. smoothness of joint surface), general characteristics of the condition of the wall discontinuity and filling materials. In addition, a detailed characterization of the discontinuities in the field also includes a brief evaluation of the presence of geological elements as folds and faults, their length, number, and the angle formed with each set of discontinuities (Peacock and Sanderson 2018). However, the number of discontinuity sets were firstly identified based on detailed observation and basic geometric analysis involves the description and measurement of the orientation of planes directly on the outcrop. According to the terms exposed previously orientation of planes were measure in dip direction / dip format with a 0–360◦ azimuth graduation compass-clinometer. Spacing of two successive discontinuities of the same set, orientated clearly parallel to each other, as well as the aperture (the distance perpendicular to both sides of discontinuity walls), were measured using a metric and millimetric tape, respectively. In turn, surface roughness was evaluated according to the joint roughness coefficient (JRC) using a profilometer (Barton comb). Waviness of joint plane was evaluated in a 10 m scale (Barton and Choubey, 1977; Jiang et al. 2006; Özvan et al. 2014). The Joint wall strength (JCS) was measured by use of the large, applied Schmidt Rebound Hammer, according to the Standard (Aydin 2008). The Rock Quality Designation index (RQD) was calculated from the spacing of discontinuity sets using the volumetric joint count index (Jv) (Palmström 1974) and the RQD-Jv correlation formula of Palmström 1974. Finally, general characteristics of the condition of wall discontinuities were described according to their physical characteristics, while the filling materials were defined according to a rough identification of size of particles (e.g. silty, sandy).

Rock mass discontinuities recognition based on UAV photogrammetry

This section was focused on mapping discontinuities using UAV photogrammetry. Particularly, discontinuity sets affecting the rock masses were recognized using a 3D point cloud and a pyhton algorithm for the semi-automatic extraction of the discontinuity planes (available at PolaRepository). Similarly to the DSE algorithm of Riquelme et al. (2014), the python algorithm presented in this work analyzes the point clouds and extracts the orientation of the exposed discontinuity surfaces classifying them in discontinuity plane. Both the algorithm and the point cloud datatset, used in this work, Tetela outcrop, are retrievable from a repository, at PolaRepository.

UAV survey, data acquisition and processing

Part of the field work includes a basic topographic survey conducted by a Topcom OS series total station to calibrate the UAV high resolution aerial photograph. The topographic survey consisted principally of the establishment of stations and control points: the stations were strategically distributed all along the outcrop in the horizontal plane, while the control points according to the total slope area and UAV survey plan (e.g. number and overlapping of images). All stations in horizontal plane and control points in slope plane were positioned by installing a series of millimetric marked anchor bolts, glugged by vinylester chemical mortar resin. Finally, each station and control point were coded and referenced (Fig. 3).

The UAV photogrammetric regional and detailed or local surveys were performed according to those described in bibliography (Vollgger and Cruden 2016; Piras et al. 2017; Panara et al. 2022) using a Phantom 4 PRO/PRO+ equipped by a downward-facing RGB camera, FC6310 model with next characteristics: resolution 5472 × 3078; focal length, 8.8 mm; pixel size 2.53 × 2.53 μm. The basic steps of both UAV photogrammetric surveys include a plan of aerial capture data, their datasets are reported in Fig. 3 and included as follow: (1) The UAV photogrammetric regional survey covers an area of 0.226 km2, consists of 1,375 images acquired at a maintained altitude of 82 m, while (2) the UAV photogrammetric detailed survey, Tetela outcrop covers an area of 813 m2, consists of 639 images acquired at an altitude of 61 m and as the regional survey, both surveys ensuring at least the 90% of overlap and sidelap (Fig. 3). Image processing including integration of spatial data, image alignment, point cloud generation, 3D model construction, and model georeferencing were performed using one of the most commercial solutions for 3D reconstruction using digital images (Agisoft Photoscan photogrammetry software, http://www.agisoft.com) following the steps summarized in Menegoni et al. (2019 and 2021). The quality settings were selected according to the number and size of photos, and according to the point cloud density of each project. For the specific case of Tetela outcrop to get a model with acceptable resolution we select medium quality. However, the main advantage of using this software respect to other post-processing software as Cloud Compare is that the information of the normal vector of each point is also automatically extracted considering the camera position. In fact, through the programming process, using our proposed code written in python language (available at PolaRepository), both the information of the coordinates x, y, z, and of the normal vectors are used to map the plane of discontinuities.

Recognition of discontinuity sets

As a preprocessing step to ensure the effective use of the proposed code, the 3D point cloud was treatment by removing all points that belong to vegetation, including bushes using CloudCompare free software (https://www.cloudcompare.org/main.html). The 3D point cloud was treatment through (1) basic operations as manual selection and segmentation of points or areas of points, and (2) use of Canupo plugin that permits an automatic point cloud classification. After these processes, the 3D point cloud was exported as .txt file including the RGB colour value and X, Y, Z coordinates and the normal vectors coordinates values for each point. According to the workflow included in Fig. 4, the method of recognition of sets of discontinuities consists of the next basic steps: (1) apply the K-means algorithm to group the points from a 3D point cloud, based on the angle of the corresponding normal vectors, (2) determine the optimal number of clusters or groups of points by applying the Elbow Method (Kaufman and Rousseeuw 1990). The result is a first proposal of groups of points that are associated to the sets of discontinuity planes in the 3D space defined by the point cloud. (3) In the next step, the proposal group is refined using the k-Nearest Neighbors algorithm, to, through a neighborhood of 9 already pre-classified neighboring points and the Euclidean distance as a distance metric, reinforce membership (or not) of each point to its corresponding group. (4) separation of groups of points associated with planes that, as they belong to the same set, have the same angle of its normal vector, but whose spatial separation is significant, for which it is necessary to differentiate them from each other. Point groups (planes) in this situation will be seen as two or more dense regions, separated by a considerable distance. The plane separation process is carried out with the DBSCAN algorithm (Density-Based Spatial Clustering of Applications with Noise) (Ester et al. 1996), taking advantage of its skills to determine dense regions of points, with a distance threshold ε = 0.02 and 1,000 for the point classification decision as core points. In this stage, a verification threshold is added to discard groups whose cardinality is equal to or less than 300 (this value depends on the resolution/spacing of the 3D point cloud), under the assumption that these points were generated by noise, that is, irregularities or too small fractures in the rock masses.

Fig. 4
figure 4

Workflow of the proposed methodology of the recognition of discontinuity sets

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Plane equations and dip direction/dip features

The point groups determined up to this point are associated with specific planes in 3D space so, from here on, they will be referred to as “planes”. Therefore, these planes are analyzed once again, set by set, starting (in each set) with the plane whose point group has the highest cardinality; plane that is called “the best consensus plane” in the set. The objective is to determine the equation Ax + By + Cz + D = 0 of this best consensus plane in space using the RANSAC algorithm (with a distance threshold of 0.5 and 10,000 iterations). Thus, the algorithm obtains the best fit with respect to all points that make up the group, that is, the smallest sum of the perpendicular Euclidean distances from each point to the plane (Derpanis 2010). Subsequently, and under the assumption that the rest of the planes in the same set are parallel to the plane of the best consensus, the equation of each of these other planes is determined from the equation already given, modified only in the parameter D, whose value depends on the Euclidean (perpendicular) distance between the plane of the best consensus and each of these other planes. The parameter Di for each of these other planes i is determined as the average of the perpendicular distance of each of the points of the group associated with plane i with respect to the best consensus plane. Finally, the dip direction and dip features of each plane are calculated from the parameters A, B and C of their respective parametric equations. Figure 4 presents a schematic of the adjustment process of fracture planes to the 3D point cloud.

Validation method

Validation of the methodology was done following the procedures included in Riquelme et al. (2014) and Wu et al. (2020). The intention to use previously verified models is to prove, valid or set our procedures in a global context. Validation consists in applying our proposed methodology into three different cases, including our study case: Case 1, Validation Model-Ouray, includes a road cut slope localized in Ouray, Colorado, USA, proposed as a standard or as a test database by Lato et al. (2013) and used as benchmark by Riquelme et al. (2014), Kong et al., (2020), and Wu et al. (2020) and, therefore, it can be used to highlight the improvements of our methods; Case 2, Tetela study, refers to our study case of the Acoculco region, particularly The Tetela outcrop; and Case 3, Validation Model-Ciclovia, refers to a road slope studied case proposed as a standard of verification of internal works. This case was proposed because is well characterized (has been used as teaching material) and because it is very close to our workplace. It is localized into the Atécuaro Ignimbritic sequence, characterized by different grades of welding and composed by different elements as lithics and pumice fragments. This last case was used to perform a second clustering process by using K-means algorithm to identify individual planes and to improve the computational sensitivity and calculation of planes geometry. Information of the 3D point clouds of all cases, as well as the proposed code written in python lenguage are placed in: PolaRepository.

Rock mass classification

Rock Mass Rating (RMR) scheme was used to perform a basic assessment of the composition and properties of rock masses of the Acoculco region including an estimation of the strength. To determine such fundamental parameters, geomechanical data was collected into a survey sheet, as described in Sect. 3.2. Our fundamental purpose of using RMR classification scheme together with detailed laboratory characterization of each involved rock unit is to construct, in the future, a series of conceptual models of the area which, in turn, could be of considerable use in the first step of modelling different natural processes as fluid flow, strength and deformation. As can be reviewed from bibliography, there are many rock mass classification systems developed for general purposes but also for specific applications (e.g. Bertuzzi et al. 2016; Morelli 2017). As described and large reviewed in bibliography (e.g. Khatik and Nandi 2018) the RMR scheme uses a well-established scale composed by five different parameters including (1) strength of the intact rock material; (2) Rock Quality Designation RQD; (3) spacing of discontinuities; (4) condition of discontinuities; and (5) groundwater conditions. In general terms, the way in which these parameters are incorporated into the classification is by assigning a rating value.

Obtained results

Rock samples were collected from those described as part of the basement of the Acoculco Caldera (Fig. 2), as previously described composed by a series of folded upper Jurassic to upper Cretaceous limestones belong to the Sierra Madre Oriental and well exposed all along the eastern part of the Caldera Complex, between Chignahuapan and Zacatlán cities (Fig. 2). The sequence in this area is composed by parallel stratified micritic limestones with nodules of black flint, affected by fractures (some of them perpendicular to the stratification) (Fig. 5a and b) filled with secondary minerals (e.g. calcite), also millimetric minerals of pyrite are recognizable in hand specimen. All sequences are completely folded, in fact several types of folds resulting from the combination of several kinematical mechanisms as chevron folds are recognizable all along the region (Fig. 5c). In accordance with field observations and data collection, in general all the described outcrops in the region are affected by seven different set of discontinuities.

Fig. 5
figure 5

(a) Panoramic view of outcrop Acb-4, composed by folded limestones sequence. The 3D dash yellow line indicates the trace and the way the folds cut or intrude the scarp. (b) local view of outcrop Acb-1, view of the stratified micritic limestones with nodules of black flint, affected by discontinuities (perpendicular to the stratification). Stereographic representation of the discontinuities identified in this outcrop is also included. (c) typical type of folds resulting from the combination of several kinematical mechanisms. Orientation values of limbs as well as chevron fold in dip direction / dip format are also integrated

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The general characteristics of the rock unit according to hand specimen, thin section description and characterization of properties could be summarized as follow: the matrix is micritic mud-supported with ellipsoidal allochems with different sizes (< 1 mm) (carbonate grains, 15%) and oriented parallel to the lamination and bioclasts in minor proportion (gastropods, < 2%) (Fig. 6a). Discontinuities filled with carbonate are also observable, some of them perpendicular to the lamination or at least with a high angle (some of them cross to each other and in some cases are cutting grains [Fig. 6c]). Microstylolites in the same direction of lamination cutting the fracture systems are recognizable (Fig. 6c-e). Moreover, some opaque minerals with hexagonal and cubic shapes are found (Fig. 6b). Even if some micropores are identified (Fig. 6f), the associated porosity is of secondary origin associated with discontinuities and stylolites. Summary of properties with its corresponding standard deviation is included in Table 1. The values are analyzed and discussed in the next section by plotting and comparing them against each other.

Fig. 6
figure 6

(a) microscopic view of gastropod. (b) microscopic view of an oxide. (c) microscopic view detailed of stylolites displacing refilled discontinuities. ellipsoidal allochems are also observed (d) SEM view of stylolites. (e) SEM view of discontinuities and their forks. (f) SEM view of a micropore

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Table 1 Summary of physical properties determined for the limestone. All values are given as an average with its corresponding standard deviation
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As could be observed from Table 1 the rock properties measured on different samples (same lithology) of the region are in a narrow range (e.g. grain density ranges from 2.54 to 2.69 g / cm3). The range of the values classify the whole rock as very dense, with a very low percentage of pores (ηT < 5.53%), some of them (ηeHg range from 0.18 to 0.44%) classified as micro-pores (1000 –0.0070 μm). According to ηeHg, particularly to the cumulative mercury intrusion (cm3/g) versus pore diameter (µm), the diameter of pores (ø) of samples are distributed into different groups ranging from 0.08 to 0.3 (0.1 dominant ø), from 3 to 10 μm (5 dominant ø), and from 10 to 200 μm (90 dominant ø) for sample Acb7; and from 0.008 to 0.5 (0.4 dominant ø), from 4 to 20 (5 dominant ø), and from 30 to 150 μm (100 dominant ø) for sample Acb3. In addition, basic characterization, as microscopic analyses suggest that the variation between the values of the properties is close related to the characteristics of each specimen (see values of AcTcOc unit). Particularly, specimens containing stylolites and/or refilled discontinuities (Fig. 6) present the high values of ηeHg, ηe and ηT. Additional studies (e.g. ηe, permeability [K]) on fractured specimens (not included in this work) suggest that the ηe could be incremented by 50%. As could be observed from Table 1 values of ηe are very low (ηe < 0.67%) and seem to increase in specimens with some anisotropies.

Strength of the intact rock and relationship between physical properties

As could be observed from Table 1; Fig. 7a-d all samples show high values of strength, ranging from 49.44 ± 8.01 to 99.91 ± 8.30 MPa for sample AcTcOc to sample Acb7, respectively (it should be note that samples AcP2 and AcPc were not led to failure due to the characteristics of the load frame used for tests). High values of strength (> 160 MPa) of the same units have been reported in other studies (Weydt et al. 2020). In general, samples containing a certain degree of anisotropy show low strength (sample AcTcOc, Fig. 7c). As graphically described in Fig. 7a-c, almost all specimens contain microcracks (e.g. stylolite, refilled discontinuities), some of them subparallel oriented with respect to the maximum stress direction reducing considerably the strength. Particularly, AcTcOc sample shows the lowest strength due to the large content of anisotropy as lent of flint and stylolites. On the contrary, the low percentage of pores and their sizes seems to have no high influence on the strength. In fact, it is well known that the value of the uniaxial compressive strength decreases with increasing porosity values (e.g. Bubeck et al. 2017) and that the strength and the mode of fracture could be controlled by the content of pores, its size and distribution (Baud et al. 2014).

Fig. 7
figure 7

Stress – strain curve for each cylindrical specimen of 53 mm of diameter. Values of uniaxial compressive strength is also included in Table 1. (a) curves for Acb3 specimens. It contains a refill discontinuity subparallel oriented to the maximum stress. (b) curves for Acb-7 specimens. (c) curves for AcPc specimens. (d) curves for AcTcOc specimens. It contains lents of flint. Note: some specimens from the Acb7 unit were not led to failure due to the characteristics of the load frame used for testing. Some samples from Acb7 were loaded to a maximum stress of around 203.96 MPa (Weydt et al. 2020)

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Characteristics of rock mass discontinuities from outcrop scale

According to the detailed collected data in all the outcrops (Fig. 2), including the orientation and quality condition of discontinuities, the rock unit is composed of seven different sets of discontinuities, including the bedding plane (orientation depends on the geometry of the folds). As shown in Figs. 5 and 8; Table 2, the K1 and K2 are related to the bedding sequence (K1 limb 1, K2 limb 2); K3, K4, K5, and K6 sets oriented almost perpendicular to the stratification of the sequence are related to shear and tensile discontinuities due to folding (e.g. diagonal, transverse, longitudinal); particularly K7 with almost same direction to K2 are not well recognized in all of the outcrops (Fig. 8b). Moreover, there is another set associated with folds, local faults, and chevron folds (352º/30º) (Fig. 5c), well exposed in outcrops localized near Zacatlán city, including Acb14 (Fig. 2). Their individual characteristics are as follow:

Fig. 8
figure 8

(a) Panoramic view of outcrop Acb-14. Different sets of discontinuities including K2, K5, K6 and K7 are marked. Stereographic representation of the discontinuities identified in this outcrop is also included. (b) Stereographic representation of the discontinuities identified in the most representative outcrops. The ID and location of each outcrop is included up above each plot and in the geological map (Fig. 2), respectively. (c) View of the geometrical arrangement of different sets of discontinuities. (d) Stereographic representation of different sets of discontinuities from field data collection. Discontinuities were classified into seven main sets, including K1 and K2 related to bedding

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Table 2 Detailed characteristics of the different sets of discontinuities. The Joint Roughness Coefficient (JRC) was estimated by comparing the appearance of a discontinuity surface with standard profiles, while wall compressive strength (JCS) was estimated by the Schmidt rebound hammer
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K1 and K2. Orientation varies according to the geometry of the folds as follow: K1 (limb 1), 233 ± 40º / 51 ± 20º and K2 (limb 2), 57 ± 11º / 65 ± 08º (Figs. 5c and 8; Table 2). These set are easily identified all along the outcrops, on the contrary not all the outcrops contains both sets and sometimes K1 and K2 could be confused with K5 an K7 set, respectively. The spacing between discontinuities varies from 20 to 25 cm and the aperture from 0 (very tight) to 3 cm (very wide), some of the planes are filled by dry sandy, silty or clayey material. The wall roughness in large scale (10 m) was characterized as rough undulating, while the roughness in terms of JRC was visually selected as 6–8 and 4–6 for K1 and K2, respectively. The wall strength values obtained using the Schmidt rebound hammer is 48 and 49 MPa for K1 and K2, respectively (Table 2).

K3 (related to shear discontinuities due to folding). As well as K1 and K2, this set is easily identified, the spacing between discontinuities varies from 30 to < 100 cm while the aperture is 0 cm (very tight). The roughness in terms of JRC is 14–16 and the wall strength is 80 MPa (Table 2).

K4 (related to shear discontinuities due to folding). This set is not easily identified in all of the outcrops, the spacing between discontinuities varies from 50 to < 100 cm while the aperture is < 0.5 cm (very tight). The roughness in terms of JRC is 8–10 and the wall strength is 78 MPa (Table 2).

K5 and K7 present very similar characteristics (related to tensile discontinuities due to folding). The trace of these sets is nearly parallel to the trace of limbs. The spacing between discontinuities is < 100 cm while the aperture is < 1 cm, some of the planes are filled by silty material. The roughness in terms of JRC is 4–6 and the wall strength is 48 MPa (Table 2).

K6 (related to shear discontinuities due to folding). The trace of this set is perpendicular to the trace of limbs. The spacing between discontinuities is < 20 cm while the aperture is < 0.5 cm (very tight). The roughness in terms of JRC is 2–4 and the wall strength is 82 MPa (Table 2).

In general terms and based on the identified number of sets of discontinuities and their characteristics, as not weathered or altered and closely spaced but not well interlocked, the rock masses in the area could be described as moderately blocky.

Semi-automatic extraction of the discontinuity planes of Tetela outcrop

The Tetela outcrop is located on a limb of a fold, characterized by vertical axial plane (Fig. 9a). In fact, the fold shows the typical characteristics of plunging upright fold. Figure 9b shows the axial surface, fold crest and some vertical strata. Figure 9c shows the Tetela outcrop, where section A is extracted. The stereographic plots of discontinuity orientation extracted from the 3D point cloud data of Tetela outcrop (Fig. 9d-g), suggests the presence of a total of six discontinuity sets: the bedding sequence represented by K1 set, well exposed in Section A (Fig. 9c, K1 form the slope); K3, K4 and K6 sets related to shear discontinuities due to folding; and K5 and K7 related to tensile stress due to folding. As described in previous paragraph K7 presents similar direction of K1 and is not well recognized or could be mis grouped in outcrop scale, on the contrary and according to the UAV photogrammetry analyses, K7 set (Fig. 9e-g) is identified and could be associated to the hinge of fold. In fact, the direction of K7 set in the region depends on the geometry of each fold, on the plunge of hinge line and the dip of axial surface.

Fig. 9
figure 9

(a) general panoramic view of the study area reconstructed by the digital elevation model. Red rectangle indicates the location of section “A”. (b) local panoramic view of the study area. Panoramic view is perpendicularly oriented to the exposed area of the Tetela outcrop. Location of section “A” is indicated by a white circle. Note: the set colors of discontinuities are randomly assigned. (c) Point cloud of Tetela outcrop. Red rectangle indicates the location of section “A”. (d) point cloud of Section “A”. (e) Cluster identification on Tetela outcrop, Section “A”. Color of clusters do not match color of discontinuities sets. (f) point cloud of Tetela outcrop, where the most representative plane of each set of discontinuities are included. (g) Stereographic representation of seven different sets of discontinuities. Stroke colors and the Id of each set were assigned according to field data collection

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Basic assessment of the properties of rock masses by Rock Mass Rating scheme

The purpose of this section is to illustrate and highlight the main geomechanical characteristics of the rock masses of the region based on an exemplification of a rock mass classification. Detailed laboratory and field survey data (e.g. Uniaxial Compressive Strength; geometrical characteristics of the discontinuities) have allowed us to obtain a good example of the applicability of this classification. The quality of a representative rock mass has been expressed as a numerical value, not corrected, or adjusted for the effect of orientation of the discontinuity with respect to any engineering work (e.g. tunneling, stability of excavation). As briefly described in 3.4, the RMR scheme uses five different parameters which according to our data could be described as follow:

1) strength of the intact rock material. As could be observed in Table 1; Fig. 7a-d all samples show high values of strength, in fact very high values of strength [> 160 MPa] of the same units has been reported in other studies (Weydt et al. 2020) (Table 3).

Table 3 Geomechanical parameters of intact rock and rock discontinuities (see also Table 2). Parameters of rock mass classification RMR system
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2) Rock quality designation (RQD). It was obtaining by the volumetric joint count Jv = 15 from the spacings (which are K1 = 0.25 m, K3 = 0.30 m, K4 = 0.50 m, K5 = 1 m, and K6 = 0.20 m) and a simple correlation RQD = 115 − 3.3 Jv = 65.5% (Table 3);

3) spacing of discontinuities. According to the information recollected in field survey, included in Sect. 4.2, and Table 2, the structure of rock masses could be considered as moderately blocky to blocky with good surface condition, interlocked, folded with multi-faced angular blocks formed by the six different sets of discontinuities.

4) condition of discontinuities. this parameter includes two different descriptions: K1 and K2 sets exhibit very smooth and sometimes highly polished and slightly weathered surfaces planes, while K3 to K6 sets exhibit slightly rough and tightly closed and unweathered surfaces planes (Table 3).

5) groundwater conditions. The general condition of almost all discontinuities plane surfaces is damp to completely dry (Table 3).

According to previous description and those included in Table 3, the calculated basic RMR for case 1 is 75 and for case 2 is 55. Case 1 falls in rock class B which indicates the rock mass is of good quality, with associated cohesion and rock mass friction angle values between 330 and 400 KPa and 35 to 45º, respectively. Case 2 falls in rock class C which indicates the rock mass is of fair quality, with associated cohesion and rock mass friction angle values between 200 and 300 KPa and 25 to 35º, respectively.

Discussions

The validation of the proposed coded written in python language was done by extracting four clear different planes from the 3D point cloud of Case 3 (Validation Model-Ciclovia), composed by approximately 200,000 points, all of them with values of the RGB colour, X, Y, Z coordinates, and the normal vectors coordinates. As shown in Fig. 10, the four different planes mapped by using the code, were compared with those measured directly in the field with an azimuth graduation compass-clinometer. In general, the rock mass is affected by three almost vertical discontinuity planes (K1, K2, and K4) and one almost horizonal (K3). As observed in the stereographic plot included in Fig. 10a, the manual measures of each vertical discontinuity plane show same strike direction, but different dip direction depending on the measurement location. In addition, the four-representative discontinuity planes, colored in Fig. 10a and b, were chosen because they are accessible and clearly visible for UAV survey. The differences in dip direction (∆/DD) and dip angle (∆/DA), as well as the value of dihedral angle between planes (Da) suggest that both methods give similar results. As shown in Fig. 10c the high value of DD, DA, and Da, is 2.44, 2.39, and 2.8º, respectively. These differences between values are acceptable if we consider the next points: (1) the precision obtained for field collection of discontinuity orientations by a compass-clinometer is from 2 to 5°. (2) the manual measurement is frequently influenced by the local characteristics of the plane surfaces as the roughness in centimetric scale and the waviness in metric scale. In fact, the dip angle of K3 set varies from 15 to 30º. (3) the manual measurements are limited to the exposed and inaccessible parts of the outcrops. (4) more representative measurement of discontinuity orientation can be obtained based on an average value of the entire surface (K1 plane is composed by 108,542 points).

Fig. 10
figure 10

(a) general panoramic view of Case 3 Validation Model-Ciclovia. Stereographic representation of the four sets of discontinuities is included. (b) 3D Point cloud of Case 3 Validation Model-Ciclovia (Cluster identification). The most representative plane of each set of discontinuities are identified. (c) Comparison of discontinuity orientations values using the proposed code written in Python language with the manual field survey.Abbreviations are: ∆/DD = differences in dip direction, ∆/DA = differences in dip angle, Da = value of dihedral angle between planes

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Validation of our method also consisted in applying our proposed method into a road cut slope localized in Ouray, Colorado, USA, proposed as a standard by Lato et al. (2013) and used as benchmark by Riquelme et al. (2014), Chen et al. (2016), and Kong et al., (2020). The Table 4, constructed according to Kong et al. (2020), includes a comparison of orientation values of ten selected randomly planes of Ouray model, using the proposed method and those mentioned previously. As shown in Table 4 all values of the average deviation of dip direction and dip angle is less than 2.9º. In fact, the values of the average deviation of our proposed method are 1.7 and 2.1º, respectively. These differences could indicate that our method is reliable, it provides accurate values, and it could be reproducible. In general, these differences in values could be insignificant if we consider the advantages of using automatic methods including the reduction of time in data collection.

Table 4 Comparison of orientation results obtained by different methods of ten selected randomly planes of the road cut slope of Ouray, Colorado, USA, proposed as a standard by Lato et al. (2013)
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Conclusions

The results indicate that physical and mechanical properties of rock specimens and discontinuities together with outcrop information are very important to assign suitable properties to large rock units. In fact, the products of a future evaluation, or analyses of our laboratory measurements, including the development of empirical relations needed for the construction of any geomechanical model. In turn, our exhaustive and accurate work done in the field, where a lot of data were collected has allowed to underline the importance of using the proposed code written in python language, for example: different set of discontinuities, including those related to shear and tensile due to folding were identified by plotting the collected data of each single outcrops, particularly K7 with almost same direction to K2 and K1 are not well recognized in all the outcrops, on the contrary the great amount of data extracted from UAV photogrammetry of Tetela case (3D point of detailed survey is composed by 1,940,189 points) has allowed to identify or ungroup two sets of fractures with similar direction but different dip (K2 limb 2, K7), which had originally been gotten mixed up or grouped together as a single set (K2 limb 2). In fact, the construction, and analyses of 3D point cloud of different outcrops, including Acp2 and Acb14 were useful for visualized the spatial variation of folds geometries, particularly the variation of orientation of limbs (K1 and K2) and its relationship with some other discontinuities as K5 and K7.

Code validation was done correctly, the use of a proposed and previously used model for different authors indicates that it works as expected. One of the benefits of the proposed code is that it has been written in python language, which is free and open source, is easy to comprehend and has a huge array of third-party packages, libraries, and frameworks that facilitate the development process.

This work represents the basis for creating a workflow related to the characterization and evaluation of rock mass condition with special emphasis on defining fracture pattern parameters. Future works includes the automatic obtaining of other geomechanical parameters as the length of each plane of discontinuity and the size and shape of blocks formed by the arrangement of plane sets. Finally, to facilitate the understanding and use of the here exposed methodology and that derived from future works, we have the purpose of building a detailed technical document that integrates, step by step, the explanation of the use of each part of the code, including the measurements of the block sizes and shapes.