Preliminary Assessment of Badajo Cave (Segovia, Spain) Stability Using Empirical, Numerical and Remote Techniques

Badajo cave is a shallow cavity (hemispherical rock shelter) located in the valley of Clamores River (Segovia city, Central Spain). This small canyon carved in Cretaceous dolostones has numerous geosites, as well as a rich archaeological and historical heritage. There are dozens of rock outcrops in the valley’s cliffs and slopes, on both banks, where various types of sedimentary rocks can be easily recognized and differentiated, especially carbonates (dolostones and limestones), and mixed carbonate-detrital (dolomitic sandstones, calcareous silts, marls). The cave was formed by karstic and gravitational processes within a mixed dolomitic sandstones and limestones, and it has an important archaeological interest. This study proposes a preliminary stability analyses of the cave applying: (i) empirical approaches based on geomechanical classifications using Barton’s Q Index, Rock Mass Rating (RMR) and the recently created Cave Geomechanical Index (CGI); (ii) three-dimensional model generated with the remote photogrammetric technique Structure from Motion (SfM) to allow acquisition of data to complete values collected in the geomechanical station, and to create the numerical model of the critical sections of the cave; and (iii) numerical simulations using a 2D model based on the generalized Hoek and Brown failure criterion and a 3D wedge analysis. The results of the analysis show that the cave is stable, although it presents some places with small problems (falls of slabs and blocks) that deserve monitoring. Furthermore, the evaluation by the geomechanical classification Q and the corresponding abacus of cave stability indicates that it is located in the “transition” zone where attention is required. In addition, SfM photogrammetric technique makes possible to generate a geometric 3D model that allowed the acquisition of data that were difficult to take in situ. The geotechnical parameters obtained from the different methods complement each other, resulting in a more realistic engineering representation of the subsurface environment. As a conclusion, a graph showing the two empirical methodologies (Barton’s Q Index and CGI), and some recommendation for a future analysis are given.


Introduction
The stability of caves and underground spaces is a relevant issue in the field of engineering because these spaces can induce serious environmental hazards.Therefore, it is very important to investigate and evaluate their stability to identify areas that may result in risks and, also, to prevent accidents [1].The assessment of the stability of caves is similar to those of underground mining excavations, it is very 1295 (2024) 012011 IOP Publishing doi:10.1088/1755-1315/1295/1/012011 2 often performed with the use of rock mass classification taking into account local geology, geometry and technology (this last factor only in mining cases).One of the first methods to investigate the stability of caves is the empirical analysis through geomechanical classifications, in particular by means of the Barton's Q index [2] and Bieniawaski's Rock Mass Rating (RMR) [3] or using the recently proposed Cave Geomechanical Index (CGI) [7].To calculate these index, structural data collection plays a very important role, either by traditional measurements in field or using photogrammetry techniques like Structure from Motion (SfM) [8], which has shown a great potential to complete the data, especially to identify families of discontinuities in higher zones not physically accessible or where there is a risk of falling rock blocks.In this work, a preliminary stability analysis of a case study is presented, of a shallow cavity −hemispherical rock shelter− named Badajo cave.This cave is located in the valley of Clamores River in Segovia city (central Spain).This small canyon carved in Cretaceous dolostones has numerous geosites, as well as a rich archaeological and historical heritage.There are dozens of rock outcrops in the valley's cliffs and slopes, on both banks, where various types of sedimentary rocks can be easily recognized and differentiated, especially carbonates (dolostones and limestones), and mixed carbonatedetrital (dolomitic sandstones, calcareous silts, marls).The cave was formed by karstic and gravitational processes within a mixed dolomitic sandstones and limestones, and it has an important archaeological interest.The cave is around 20 m length and 22 m width and its height is approximately 9 m.The aim of this work is to analyse the stability of the cave, applying an empirical approach based on the geomechanical classifications Q Index, RMR and the CGI.Also, from a 3D point cloud generated with SfM, a 2D numerical modelling analysis −based on the generalized Hoek and Brown failure criterion− and a 3D wedge analysis are carried out.

Geomechanical Stations and Rock Mass Classifications
The stability of underground spaces can be initially evaluated using rock mass classification systems.The Q index (Barton, 1974) and the Rock Mass Rating (RMR) (Bieniawski, 1973) are the most widely used.The Q index, developed in the Norwegian Geotechnical Institute in 1974, assign a score to each rock mass domain, and increases in value with rock mass quality.Its variation is not linear (unlike the RMR), but exponential, and ranges between Q = 0.001 for very poor rock mass and Q = 1000 for an excellent rock mass.The Q index can be obtained from the following equation: where RQD (in %) is the Rock Quality Designation index, Jn is the joint number coefficient, Jr is the joint roughness coefficient, Ja is the joint alteration number, Jw is the water reduction factor, and SRF is the Stress Reduction Factor, which depends on the stress state of the rock surrounding the tunnel.The Rock Mass Rating (RMR) is the sum of the values assigned to the following parameters: unconfined compressive strength of intact rock, RQD, spacing of discontinuities, condition of discontinuities, ground water conditions and orientation of discontinuities and it ranges between RMR = 0 for very poor and RMR = 100 for very good rock quality.There are several modifications of RMR (Bieniawski, 1973) applied to slopes and mining, but in this case only the modification for caves will be analysed.This research is based on the Q index and Rock Mass Rating (RMR) to assess the stability of the cave.However, to validate the results, the study is completed with the Cave Geomechanical Index (CGI).The CGI is a recent major factor developed by Brandi and collaborators in iron caves of Brazil [7].CGI is considered the first cave-specific geomechanical -rock mass-classification and it can be obtained from the following equation: where: αRMR is the assigned value to the rock mass classification, β HR corresponds to the hydraulic radius, γ CS to the roof shape, and δ CT to the roof thickness.The CGI range from 0, that corresponds to the worst quality rock, to 100, and it propose 5 categories considering the susceptibility to structural instability of the spans.In this work, studies are based on a geomechanical station conducted in situ, to determine the rock mass parameters such as RMR, Q index, GSI and joints parameters, improving the collected data by means of SfM.

Photogrammetry SfM
SfM is low-cost remote technique, that enables extracting, from a pair or a set of images, the 3D geometry of a scene.The process to extract 3D information are based on the principles of stereoscopic vision (using only two photographs) or on modern 3D reconstruction techniques using automatic correlation algorithms of images [8,14].
In the field campaign, 230 photographs were taken at Badajo cave with a low-cost amateur digital Nikon camera, from a different angles and positions (see Figure 2).For orientation and scaling of the 3D point cloud, an orientation template has been used [13].This template contains 5 Ground Control Points and 2 axes (x, y), orientating the Y axis to the north using a compass.For the reconstruction of the 3D point cloud, the sofware Agisoft Metashape [15] has been used.One main limitation of photogrammetry, specifically Structure from Motion (SFM), in caves and underground excavations is the lack of sufficient lighting and visibility.In environments with low light conditions or limited visibility, capturing highquality images for accurate 3D reconstructions becomes challenging.Caves often have uneven and complex surfaces, making it difficult to obtain clear and well-illuminated photographs from all necessary angles.Additionally, the computation time for processing large sets of high-resolution images in SFM can be a significant constraint.Creating detailed 3D models from numerous images demands substantial computational power and time.However, this methodology has proven significant utility and acceptable results.

Extraction of discontinuities
In addition to rock mass classification systems, a proper analysis of discontinuities is an important key to assess the stability of caves [6,8].These discontinuities (joints, faults, strata or veins) are represented by dip angle and dip direction.The most common method for measuring orientation is by compass.This method presents limitations as it requires physical access of engineers to the location, which is frequently not possible since the cave or part of it is inaccessible or unsafe.As an alternative to manual data collection with compass, the analysis can be carried out from 3D point clouds using the software Cloudcompare [8].

Numerical modeling and wedge analysis
The numerical modelling performed in this study involves stress-strain analysis, using the boundary element software Examine2D which can simulate stress and strength in rock masses.The aim is to obtain a safety factor (which is related to the strength factor) and maximum displacements to compare them to the degree of stability obtained through the rock mass classifications and empirical approaches [9].In this case we are not going to analyse any supporting measures, the strength factor will only be used to state the safety factor and to know the extension of the overstress rock mass.
The input data to use in the numerical analysis were determined from the geomechanical stations, employing Rocdata software (Rocscience) to calculate rock mass parameters.The geometry of the cave was obtained with SfM while the stress initial condition was determined from the depth of the cave and the density of the rock.
Considering the Hoek and Brown failure criteria, the parameters used for rock mass were those obtained from the field geomechanical stations.However, this boundary analysis has a limitation since the material is considered as continuous medium which is not true (fractured rock).Therefore, an additional analysis based on blocks theory was carried out using the software UNWEDGE (Rocscience), for identification of potential blocks or wedges that can slide or fall.

Cave model as 3D point cloud and discontinuities extraction
Discontinuity sets were determined by different methods: (i) with a manual compass in the field (Figure 3a); and (ii) from the 3D point cloud using Cloudcompare software by two procedures: a) selection of points groups from a discontinuity and fitting a plane by the least square method (Figure 3b); and b) semi-automatically (Figure 3c).The results of these methods are presented in Figures 4a and 4c, whereas the result of combining these methods are illustrated in Figure 4c. Figure 4a shows 37 poles obtained manually with a compass in the field and 4 main sets (J1, J2, J3, J4), and Figure 4b

Empirical analysis and stability Q-graph
Table 1 presents the Q index outcome of the cave, based on our preliminary analysis.The main characteristics of parameters such as Rock Quality Designation (RQD%), the Joint set number (Jn), the Joint roughness number (Jr), the Joint alteration number (Ja), the Joint Water reduction factor (Jw), and the Stress Reduction Factor (SRF) are summarized in Table 1.Finally, Table 3 illustrates the cave geomechanical index CGI parameters and their corresponding observed values.In this case, the parameters are: α RMR the assigned value to the rock mass classification, β HR to the hydraulic radius, CS the roof shape, and δ CT the roof thickness.The results of the emprical analysis Q index and CGI are ploted in Figure 5 to evaluate the stability of the cave.

Numerical analysis 3.3.1 Stress strain analysis
A numerical simulation is carried out using the boundary elements method with the Examine2D software.An average section of the cave located between the middle and the entrance has been modelled from the 3d point cloud generated with SfM.The boundary conditions of the model are fixed nodes at 3 times the width of the cave.Lithostatic stresses and the worst-case scenario for the stress distribution coefficient (K0 = 1) have been considered -therefore, ℎ = v.Table 3 lists the input parameters employed in the numerical model.

Wedge analysis
An additional analysis based on blocks theory has been carried out using the software UNWEDGE (Rocscience).A combinatorial analysis of the 4 main sets (J1, J2, J3, J4) has been done.As classification criteria for combinations, safety factor and wedge size have been considered.The input parameters are summarized in Table 3, assuming a 150 NE orientation for the cave.

Figure 1 .
Figure 1.Location and geological context of Badajo cave.
shows 50 poles obtained from the 3D point cloud.It is clear that more values are shown for the joint J2 and J3. Figure 8c shows a combination of poles obtained with compass and with 3D point cloud.The combination of data improves considerably the original stereogram obtained via compass.Finally, the 4 main sets are J1: 325/82, J2:252/84, J3:070/31 and J4:240/11.

Figure 4 .
Figure 4. Pole concentration stereogram: (a) data obtained via compass; (b) data obtained from 3D point cloud in CloudCompare; (c) combination of data (a) and (b)

Figure 4
Figure4shows the results of the numerical model.As shown, total displacements are negligible.The stresses around the cavity are small and there are only stress concentrations in the right wall close to the cave roof, keeping the cavity in a stable elastic regime.However, some unstable blocks are visible at the entrance.There is no minimum safety factor stablished for caves in Spanish legislation.In this case the strength factor around the cave varies from 2 to 3, but with very local values below 1.Those low values are not relevant meaning that there is a stress concentration in certain angles.

Table 1 .
Geomechanical parameters of the Q index.

Table 3 .
Determination of CGI from the geomechanical station.