The Influence of Fresh and Weathered Rock Foliation on the Stability of the Monte Seco Tunnel

Abstract

The Monte Seco tunnel (MST) is one of several old unlined tunnels constructed for Brazilian railways in the 1950s, and the MST still receives intense train traffic (primarily for iron ore transportation). The MST was constructed in a fractured gneissic rock mass, which has potential instability problems associated with gravity-driven block falls (at low stress confinements) defined by three fracture sets and the metamorphic foliation. Previous geological and geotechnical surveys at the MST site have included basic geomechanical classifications from outcrops and drill core specimens, detailed terrestrial laser scanning (TLS) mapping of foliation and fracture planes, geoelectrical imaging and laboratory tests. These surveys discovered two sections of the tunnel (referred to herein as MS1 and MS2) with major potential for instability problems (i.e., poor rock mass qualities). In this paper, the 3D discrete element method (DEM) was used to assess the potential stability problems in these sections with particular interest on the role of the rock foliation strength on the current stability state of these sections. Three instability indicators were developed and monitored during and after the DEM simulations: the total failed block volume (FBV), the average displacement of the tunnel face (AD), and the percentage of slipping contacts near the tunnel face (SC). The weathering effects were considered in two different scenarios: the occurrence of isolated weathered foliation planes (WFPs) and the general weathering advance through potentially weathered regions. In the latter scenario, the percentage of weathered contacts (WC) increased progressively. The overall results indicated that fresh foliation planes ensured the current tunnel stability due to the moderate mica content (M_a) in such geological structures. Thus, underestimating the strength of foliation planes causes unrealistic instability conditions in the tunnel. However, the weathering advance on fractures and foliation planes can trigger important instability problems over time.

1 Introduction

The Monte Seco tunnel (MST) was constructed in 1950s for a Brazilian railway, currently responsible for the transportation of most iron ore produced in southeastern Brazil. Most of these tunnels are located at shallow depths (less than 200 m), constructed in hard rock masses (granites and gneiss rocks) and do not have bolt or liner support systems along the majority of their lengths. In the past few years, new safety requirements have been implemented, and some of these tunnels, including the MST, showed the need for advanced stability analyses using modern tools, such as terrestrial remote sensing, discrete element modeling, and geophysical prospecting. In this scenario, the MST became a laboratory tunnel that is currently being used by the GeoInfraUSP group for multiple rock mechanics and engineering geology purposes, including terrestrial laser scanning (TLS) mapping and analyses (Cacciari and Futai 2016, 2017), geophysical prospecting and weathering advance studies (Monticelli 2019).

The MST was constructed in a fractured gneissic rock mass, which has potential instability problems associated with gravity-driven block falls at shallow depths (low stress confinements). These blocks are defined by different geological structures on the rock mass, including shear fractures, sheet joints and the gneissic banding and foliation. Considering the aforementioned geological fabric and low stress conditions, discrete models are preferred for performing tunnel stability analyses because they simulate the mechanisms of block falls, creating discontinuity-controlled overbreak patterns similar to those observed in situ. The 2D and 3D versions of the discrete element method (DEM) (Cundall 1988; Hart et al. 1988) are often used for tunnel stability analyses (Bhasin and Hoeg 1998; Ferrero et al. 2004; Vardakos et al. 2007; Solak 2009; Fekete et al. 2010; Wu and Kulatilake 2012; Fekete and Diederichs 2013; Oliveira and Diederichs 2017; Bahrani and Hadjigeorgiou 2018; He et al. 2018; Merlini et al. 2018).

The International Society for Rock Mechanics (ISRM 1978) defined discontinuity as “the general term for any mechanical discontinuity in a rock mass having zero or low tensile strength”. In practical rock mechanics, discontinuity sets are often generalized as joint sets, regardless of the type and genesis of each geological structure. In these cases, it is usual to assume friction-based models (linear and nonlinear) to represent the mechanical behavior of discontinuities, ignoring any cohesion or tensile strength. It is important to note that the ISRM definition uses the term “mechanical discontinuity”, which are discontinuities formed by mechanical processes, such as tectonism. Therefore, before ignoring any cohesion or tensile strength values, two aspects should be taken into account:

• 1. Incipient rock bridges can provide considerable tensile strength and cohesion to nonpersistent fractures. Thus, the geomechanical model must consider fractures as finite-size planes within the rock mass.

• 2. Geological structures characterized by mineralogical distribution and alignment on the rocks, such as foliation, schistosity, bedding planes, and banding contacts, are not “mechanical discontinuities”, and these structures can have considerable tensile strength and cohesion due to connection forces within mineralogical contacts. For practical rock engineering applications in blocky rock masses, such geological structures were defined as “intrablock”, whereas fractures and joints were defined as “interblock” structures (Day et al. 2017).

The first aspect listed above has been widely discussed in the literature. Usually, discontinuity analysis is used to define the probability distribution of discontinuity sizes on discrete fracture networks (DFNs). The second aspect listed above has not been discussed much in the literature, and the particular mechanical properties of such intrablock structures are often ignored. Rock foliation, for example, is a type of intrablock structure characterized by the alignment of minerals along planes during metamorphism. In this case, it is predictable that the contents of mineral types will directly affect the strength of such geological structures.

Gneiss rocks, for example, are both heterogeneous (due to the different mafic and felsic bands) and anisotropic (due to the orientation of the metamorphic foliation). Cacciari and Futai (2019) showed the importance of the mica content in the foliation planes on the shear and tensile strength of a biotite gneiss. These authors verified that, even for foliation planes with 90% surface area covered by biotite, the tensile strength and inherent shear strength (cohesion) are not negligible, especially under low stress confinements.

In this paper, the 3D DEM is used to assess the stability sate of the MST. The geological–geotechnical investigations on the MST have included basic geomechanical classifications from outcrops and drill core specimens, detailed TLS mapping of fractures and foliation, geoelectrical imaging and laboratory tests. These investigations have revealed two sections of the MST with major potential for instability problems due to the following characteristics: the existence of a shear zone of high fracture intensity with evidence of weathering and the existence of an extremely shallow section of moderate fracture intensity with evidence of weathering. These sections were modeled using a coupled TLS-DFN-DEM approach with particular interest on the role of the rock foliation strength on the actual stability state of these sections. Moreover, different weathering scenarios were simulated based on the observations from the aforementioned geological and geotechnical investigations.

2 DNF-DEM Modeling Methodology

Cacciari and Futai (2017) developed a coupled TLS-DFN modeling methodology for creating continuous DFNs (C-DFNs) from TLS mapping of fractures along tunnels. This methodology is based on full orientation, trace length and position mapping on TLS point clouds and automatic application of window sampling methods to obtain the probability distributions of fracture geometrical parameters and create C-DFNs.

The flowchart in Fig. 1 summarizes the aforementioned methodology, which starts with TLS mapping of orientations, trace lengths, and endpoint positions apparent in the tunnel (I). Next, discontinuity analyses by window sampling methods are performed continuously and automatically along the tunnel to obtain the probability density functions (PDFs) of diameters and orientations (II). A 3DEC-Fish (Itasca 2014) code uses the discontinuity analysis results to generate DFNs and continuously calculate the mean volumetric intensity (P₃₂) along the tunnel (III). Finally, the continuous P₃₂ and the PDFs of the diameters and orientations are used to create the C-DFNs (IV). This process is performed separately for each fracture set (for more details, see Cacciari and Futai 2017).

Fig. 1

Flowchart of the methodology developed by Cacciari and Futai (2017) used herein to create the C-DFNs of the MST

After obtaining the C-DFNs, DEM models were created by the 3DEC cutting logic, which selects and separately cuts only the blocks in contact with each discontinuity (from the largest to the smallest). The rock foliation was assumed to be persistent because it may be inappropriate to estimate a mean trace length (and diameter) from TLS images in this case, considering the genesis of such geological structures (Cacciari and Futai 2016, 2017). Moreover, the orientation and spacing were considered deterministic for foliation planes, based on mean linear frequencies and attitudes measured from the exposed areas of these planes in the TLS point cloud (Cacciari and Futai 2016, 2017). It is reasonable to assume that the foliation planes with measurable areas at the tunnel face are the weakest planes exposed after the excavation process. Therefore, the cutting process started with the foliation planes, followed by the C-DFNs according to each disc-shaped fracture diameter. The bedrock and surface topographies are also included in the DEM models.

2.1 Initial Under- and Over-Break Condition

Drilling and blasting cause excavation damage to tunnels, leading to irregular under- and overbreak geometry. In several cases (such as the MST), the drilling and blasting design is unknown, making it difficult to estimate the extent of the excavation damage zone and the actual damage to the rock mass in terms of mechanical parameter degradation. In this case, it is not possible to create initial over- and underbreak conditions in the DEM models similar to the real tunnel by degrading mechanical parameters of foliation, fractures, and intact rock obtained in laboratory tests. Therefore, an alternative method is proposed to establish the initial under- and overbreak conditions based on removing blocks inside a range defined by the real tunnel boundary. This methodology is described as follows:

• 1. import the tunnel digital model as a triangular mesh into 3DEC (Fig. 2a);

• 2. create microscopic disc-shaped planes inside each triangle of the tunnel mesh (the discs must have the same orientation as the triangles and should not be larger than the triangle) (Fig. 2b);

• 3. cut the blocks touching the discs and group the blocks inside the tunnel boundary (Fig. 2c).

Fig. 2

Computational process used to create initial under- and overbreak conditions in DEM models of tunnels

The final appearance of the DEM model is exemplified in Fig. 2d, wherein the geometry is almost identical to that in the TLS digital model. The same method can be applied to any type of surface, such as natural slopes and open pits.

It is important to note that this methodology reproduces the actual irregular geometry of the tunnel, which modifies the stress distributions along the excavation boundary. However, the extent of the damage inside the rock mass caused by drilling and blasting remains unknown. It is important to note that the regularly designed shape (horseshoe, circular, etc.) for tunnels in blocky rock masses under low stress conditions (such as the MST) is hardly achieved after drilling and blasting. Thus, the DEM simulation of such cases should not start with the designed excavation geometries because the stress arching effect associated with such regular shapes can affect the results of DEM simulations.

3 Case Study: Monte Seco Tunnel

The MST is located in Espirito Santo State in southeastern Brazil (Fig. 3) and is part of the Vitória-Minas Railway, which is responsible for most of the iron ore transportation in the country. The tunnel was excavated from gneiss rocks of the Nova Venécia Complex in the northern portion of the Mantiqueira Province, which is part of the Araçuaí orogenic belt. The local structural fabric is composed of four discontinuity sets: gneissic foliation (parallel to the gneissic banding), shear fractures (F1 and F2), and sheet joints (F3). The rock is a paragneiss composed of quartz, plagioclase, alkaline feldspar, biotite, cordierite, hypersthene, and garnet (from the highest to the lowest content).

Fig. 3

Locations of MS1 and MS2 in the MST and the important geotechnical investigations at the tunnel site (Cacciari and Futai 2017)

The MST has been used as a model for some rock mechanics studies, including TLS mapping (Cacciari and Futai 2016), DFN-DEM modeling (Cacciari and Futai 2017), laboratory tests, and geophysical and drilling borehole surveys. More recently, a conceptual model for the weathering advance through foliation and fractures into the tunnel has been developed by correlating multiple regional and local geological aspects with geoelectrical imaging profiles and TLS mapping (Moticelli 2019). In this case, two sections of the tunnel (named MS1 and MS2) showed potential for instability problems. Figure 3 shows the geographic locations of MS1 and MS2 in the MST and the positions of the geoelectrical imaging profiles and drilling boreholes. Next, the important aspects of MS1 and MS2 are described in detail.

MS1: This section crosses an F2 shear zone, corresponding to a high total P₃₂ (F1 + F2 + F3) along the tunnel (Fig. 4). The overburden of MS1 varies from 30 to 20 m, and the bedrock dips steeply in the ENE direction. The bedrock was defined by an association of drilling boreholes and geoelectrical imaging profiles. Both bedrock and surface geometries are simplified in the final DEM model to avoid errors caused by undesired convex blocks and excessive construction planes, which affect the DFN block cutting and mesh distribution inside the model.

Fig. 4

P₃₂ distribution along the MST (Cacciari and Futai 2017) and the locations of MS1 and MS2

The MS1 shear zone was identified in both TLS mapping and geoelectrical imaging profiles. Figure 4 shows the continuous P₃₂ along the tunnel obtained by Cacciari and Fitai (2017), indicating that P₃₂ of F2 abruptly increases between 110 and 140 m, where the F2 shear zone and MS1 are located. Figure 5 shows the location of MS1 on the geoelectrical imaging profile of line 2 (positioned above the tunnel axis) (Fig. 3), which is inside the high conductivity anomaly generated by the water flow through the F2 shear zone towards the tunnel. Figure 5b shows the TLS trace and orientation mapping of the tunnel region containing the F2 shear zone and MS1. Figure 6a shows the wet and dripping rock face on the east wall and roof of the MS1-TLS point cloud.

Fig. 5

Geological aspects of MS1 and MS2: a geoelectrical imaging profile of line 2 positioned above the tunnel axis (Monticelli 2019); b TLS traces and orientation of the tunnel region containing MS1; c and TLS traces and orientation of the tunnel region containing MS2. Note that Sn represents the foliation planes

Fig. 6

TLS point clouds of a MS1 and b MS2, indicating the wet and dripping rock faces (white dashed lines)

Figure 7a, b show the final DEM model of MS1 (5 m long), indicating the C-DFN used to create the F2 shear zone. In this case, the rock mass above and below the F2 shear zone was modeled using mean fracture parameters instead of using a unique larger DFN domain, which results in an excessively complex model and low computational performance. The thickness of the shear zone (in the NNW-SSE direction) was estimated as the maximum perpendicular distance of the traces mapped on the roof of the tunnel.

Fig. 7

a, b DFN used to create the F2 shear zone and the final DEM model of MS1. c, d DFN used to create the entire model and the final DEM model of MS2

MS2: This section is located 20 m ahead of the south entrance of the tunnel after the end of the structural concrete liner, which was most likely used to support the soil and soil–rock transition at the beginning of the excavation. From Fig. 4, MS2 shows a small P₃₂ peak, but this peak is not much different from the other regions of the tunnel (e.g., 150–160 m and 250–260 m). However, MS2 is particularly interesting because it is an extremely shallow and wet portion of the tunnel that exhibits potential for advanced weathering processes. Figure 5c shows the TLS trace and orientation mapping of the tunnel region containing MS2. Figure 6b shows the wet and dripping rock face on the roof of the MS2 TLS point cloud. Figure 7a, b show the final DEM model of MS2 (5 m long). As P₃₂ is moderate and there is no specific shear zone in this section, a large C-DFN domain was used to cut the blocks in the entire MS2-DEM model.

During field work, both MS1 and MS2 were classified with the rock mass rating (RMR₁₄) (Celada et al. 2014), the rock mass quality (Q) (Barton et al. 1974) and the geological strength index (GSI) (Marinos and Hoek 2000), which was recently updated by Schlotfeldt and Carter (2018); the results are shown in Table 1. The ranges of each rock mass classification system are determined by the extreme weathering conditions found on the MST. In Q and GSI, the weathering conditions are determined by the J_a parameter (Barton et al. 1974), whereas in RMR₁₄, the weathering effects are determined by the joint conditions and alterability index (I_d2). The P₃₂ values obtained by Caccairi and Futai (2017) were used to estimate the GSI, according to the methodology proposed by Schlotfeldt and Carter (2018).

Table 1 Summary of the rock mass classification ranges of MS1 and MS2 for extreme weathering conditions

It is important to note that the MST was constructed in the 1950s before the development of these classification systems. Moreover, there are no documents available with details of the MST design methods and criteria, including drill and blast planning, previous geological surveys, and excavation front mapping and characterization. The only indirect information pertaining to the excavation method is the drill and blast borehole marks, which indicate that they did not follow a systematic arrangement. In addition to differences in the RMR₁₄ and Q values of MS1 and MS2, both sections have the same general class (III for RMR₁₄ and fair or poor for Q), which shows the lack of sensitivity of such methods for moderate differences in fracture intensities.

3.1 Mechanical Properties of Intact Rock, Foliation and Fracture Planes

In this study, the discontinuities are considered discrete planes that are mechanically described by the Coulomb-slip joint model available in 3DEC, which is defined by the tensile strength (σ_t), cohesion (c) and friction angle (φ). The uniaxial compressive strength of the intact rock (without foliation-controlled failure) varies from 100 to 200 MPa. Due to the low stress conditions at shallow depths and the relative high uniaxial compressive strength, intact rock failure is ignored, and the linear-elastic model is used for both intact rock and soil materials. As the foliation is considered a set of discrete and full-persistent planes, the elastic parameters—Young’s modulus (E) and Poisson’s ratio (ν)—of the intact rock were taken from uniaxial compression tests perpendicular to the foliation planes (data not published). The values used in all DEM analyses were E = 48 GPa and ν = 0.2 for the intact rock (from laboratory tests) and E = 0.48 GPa and ν = 0.2 for the residual gneissic soil (inferred).

3.1.1 Mechanical Properties of the Fresh Gneissic Foliation and Banding Planes

Gneissic foliation is a planar geological structure formed by the alignment of minerals along recrystallization planes during metamorphism. Monticeli (2019) performed several petrological analyses and defined three petrographic facies to the gneissic rock at MST, with the main characteristics summarized in in Table 2 and Fig. 8. B1 and B2 are foliated facies, while B3 is massive (non-foliated). The differentiation between B1 and B2 is only due to grain size, with B1 predominantly fine-grained and B2 fine- to medium-grained. In the MST, the foliation is parallel to the gneissic banding and well defined in B1 and B2 facies. This gneiss is characterized by abrupt transitions creating biotite-rich contact planes exhibiting low shear and tensile strength. Figure 8a, b shows examples of a rock block and a drill core specimen containing this structure. The biotite content in B1 and B2, quantified by micrographic analysis of thin sections perpendicular to the foliation planes (Fig. 8c), is low to moderate (Table 2). However, in this work, the biotite content is analyzed directly on failed foliation and banding contact planes subject to tension and shear tests.

Table 2 Main characteristics of the petrographic facies of the gneissic rock at MST site

Fig. 8

a Gneiss block with a marked biotite-rich banding contact. b 100 mm diameter core highlighting the foliated and massive (non-foliated) bandings and the biotite-rich contact between bands. c Micrography of a foliated band (B2) indicating the principal minerals

The biotite content plays an important role in the shear and tensile strengths of gneissic foliation. Cacciari and Futai (2019) performed an extensive laboratory campaign with a biotite gneiss from the Ana Matos tunnel (also part of the Vitória-Minas Railway) and obtained a strong correlation between the shear and tensile strengths and the percentage of biotite area (M_a) after failure of the foliation planes. Moreover, these authors obtained a 3D strength envelope defined by Eqs. 1 and 2, wherein M_a is an independent variable.

$$({\sigma }_{\mathrm{t}},c \mathrm{or} \, \varphi )={\beta }_{\mathrm{t},\mathrm{ c},\varphi }/(1+{{(\alpha }_{\mathrm{t},\mathrm{ c},\varphi }{M}_{\mathrm{a}})}^{{n}_{\mathrm{t},\mathrm{ c},\varphi }})$$

(1)

$${\sigma }_{\mathrm{s}}={\sigma }_{n}\mathrm{tan} \, \varphi +c$$

(2)

Equation 1 describes the variation in the tensile strength (σ_t), cohesion (c) and friction angle (φ) with respect to M_a, using the equivalent values for α, β and n (subscripts t, c and φ, respectively). Equation 2 is the Mohr–Coulomb shear strength criteria, and σ_t is the tension cut-off. In their case, the parameters in Eq. 1 were ${\beta }_{\mathrm{t}}$= 4.70 MPa, ${\alpha }_{\mathrm{t}}$= 0.022 and ${n}_{\mathrm{t}}$= 3.42; ${\beta }_{\mathrm{c}}$= 9.10 MPa, ${\alpha }_{\mathrm{c}}$= 0.022 and ${n}_{\mathrm{t}}$= 4.08; and ${\beta }_{\varphi }$= 56.80 MPa, ${\alpha }_{\varphi }$= 0.0113 and ${n}_{\varphi }$= 2.83. Note that ${\beta }_{\mathrm{t},\mathrm{ c},\varphi }$ represent the equivalent σ_t, c and φ for M_a = 0% (null mica content).

A series of pull-off tests (POTs) were performed on rock blocks from the MST. The POT was recently introduced to rock mechanics applications, which consists of pulling a metal disc attached to a partial core drilled against a flat rock surface (Cacciari and Futai 2018). All POTs were performed perpendicular to the foliation/banding planes to obtain the tensile strength values and estimate M_a. The same methodology used by Caccari and Futai (2018,2019) was applied herein, including the POT devices and image analyses for M_a quantification. More details on the POT and M_a can be found in these aforementioned works.

Figure 9 shows the POT results from the MST gneiss plotted with the results obtained by Cacciari and Futai (2019) for biotite gneiss. The same tendency of both results indicates that M_a can also be used to predict the tensile strength of foliation planes on the MST gneiss (Eq. 1 with subscript t). However, M_a = 61% and M_a = 21% had the highest and lowest biotite contents, respectively (I and II highlighted in Fig. 9). Specimen II in Fig. 9 represents the lowest tensile strength from biotite-rich contacts, as indicated in Fig. 8a, b.

Four direct shear tests (DSTs) were performed with specimens taken from the biotite-rich contact (Fig. 8) and isolated inside a 1-cm-thick shear zone (Fig. 10). The two-stage testing method (Cacciari and Futai 2019) was used to allow M_a quantification before causing major shear damage to the banding contact surface. The first stage (the peak stage) is the DST of the intact foliation plane (intrablock), which ends after capturing the complete stain softening behavior of the shear stress vs. shear displacement curve (red lines in Fig. 10a–d). The second stage (the postpeak stage) consists of the DST of the open foliation plane (OFP) created after the peak stage (black lines in Fig. 10a–d). In the postpeak stage, the DST ends after achieving a total shear displacement equivalent to 10% of the specimen length in the shear direction. It is important to note that a foliation plane can become a OFP after previous imposed stresses, both by shear or tension. OFP represents the critical condition for a fresh foliation plane with certain mica content, with complete loss of mineral connections, cohesion and tensile strength.

Fig. 9

POTs from MST gneiss plotted with POTs from biotite gneiss

The DSTs were performed under constant normal load boundary conditions with normal stress values of 0.5, 1.5, 3.0, and 5.0 MPa. The M_a = 60% and M_a = 70% lines in Fig. 10e are particular cases of the 3D shear envelope defined by Cacciari and Futai (2019) for a biotite gneiss (Eqs. 1 and 2). The MST specimens showed good agreement with these envelopes within the shear strength range corresponding to 60 < M_a < 70%. The mean shear stiffness (K_s) of the peak and postpeak stages were 6.1 GPa/m and 1.6 GPa/m, respectively. Considering the good agreement between the MST gneiss and the biotite gneiss obtained by both POTs and DSTs, the 3D strength envelope (Eqs. 1 and 2) is suitable to represent the strength of the foliation planes on the MST gneiss. Details of the laboratory results and analysis used to develop the 3D strength envelope for foliation planes with different mica contents (M_a) can be found in the work referenced above.

3.1.2 Mechanical Properties of the Fracture Sets

The mechanical properties of the F1, F2 and F3 fracture sets were determined empirically using the joint roughness coefficient (JRC), the joint compressive strength (JCS) and the residual friction angle (φ_r) from Barton and Choubey (1977). The JRC was assessed in field outcrops and drill core specimens with manual 30-cm and 10-cm profilometers (Barton’s comb), respectively. Additionally, 3D plane amplitudes from well-exposed fracture planes were measured via TLS point clouds and converted to JRC values using Barton’s chart (Monticeli et al. 2015). JCS and φ_r values were obtained by Monticelli (2019) using empirical correlations between the Schmidt hammer rebound and uniaxial compressive strength of fresh and weathered cylindrical core specimens. As the JRC values were noticeably different among fracture sets, a single envelope was used for all these structures. The mean and standard deviation of JRC, JCS and φ_r for the fracture sets were 9.7 (2.3), 105 MPa (24 MPa) and 25.5° (2.1°), respectively.

For the fracture sets (F1, F2 and F3), the Coulomb-slip envelopes were defined by linearizing the Barton-Bandis envelopes, following the secant-line method suggested by Prassetyo et al. (2017), which results in null cohesion and tensile strength for such geological structures. The linearization method resulted in an equivalent secant friction angle of 40°. The shear stiffness of OFPs in Fig. 10 (1.6 GPa/m) was also used for the fracture sets. For both fractures and foliation planes, the normal stiffness (K_n) was calculated as K_n = 10 Ks, according to the tendency observed by Bandis et al. (1983). Considering that OFPs and fractures have similar mechanical behavior (friction-based with null cohesion and tensile strength), the φ_r of fractures was also used to characterize the postpeak behavior of OFPs.

3.1.3 Mechanical Properties of Weathered Fracture and Foliation Planes

Monticelli (2019) described the weathering effects on the MST site that affected the individual discontinuity planes on the drill core specimens. As noted by the author, isolated discontinuities, including fracture and foliation planes, show advanced weathering grades, but the tunnel rock face does not show significant weathering effects on the rock matrix. Foliation planes with advanced weathering grades split on the drill cores, indicating a lack of tensile strength and cohesion in such conditions. Figure 11a shows the variations in φ_r with respect to porosity (η) for foliation, F1 and F2 planes. The φ_r values of weathered foliation and fracture planes decrease substantially with increasing η. Moreover, the F2 and foliation planes had more advanced weathering grades than the F1 planes, indicating that the former had lower φ_r values. Figure 11b shows the foliation specimen with the highest η and lowest φ_r. Figure 11c shows a micrograph taken from this specimen, perpendicular to the foliation plane, indicating that the weathering path may reach substantial distances (e.g., over 5 mm). Weathered minerals have characteristic colors and textures (see example highlighted in yellow in Fig. 11c), which are the result of cordierite grains replaced by pinite, chlorite, iron oxides and hydroxides and fissures filled by carbonate and clay (Monticelli 2019).

Fig. 10

a–d DSTs of MST specimens, including the M_a estimates (red lines and black curves are the peak and postpeak DSTs, respectively). e Peak shear strength values of the MST specimens plotted with the specific envelopes from Cacciari and Futai (2019) (color figure online)

In this work, the discontinuity weathering is simulated only in extreme conditions, wherein φ_r = 20° for all discontinuity sets (foliation and fractures); these conditions represent the intermediate value of the total φ_r range from the drill core specimens. Considering that the Coulomb-slip model is linear, to simulate such extreme weathering conditions, the φ_r was directly used in the model without considering any influences of weathered JRC or JCS parameters that would increase the equivalent friction angle obtained by the secant-line method (Prassetyo et al. 2017).

4 DFN-DEM Results

Next, DFN-DEM analyses show the influence of rock foliation on MST stability, including the mechanical characteristics presented in Sect. 3.1.1. The in situ stresses were included in 3DEC using the surface topography (INSITU TOPOGRAPHY command) and the intact rock unit weight (26.5 kN/m³) to calculate the vertical stresses along depth. The horizontal stresses in both x and y directions were considered equal to the vertical stresses along the depth (K₀ = 1.0). Although in situ stress measurements were not available, the regional geology and tectonics do not suggest the occurrence of extremely high or low horizontal/vertical stress ratio. Moreover, other works using DEM models showed that the influence of K₀ values between 0.5 and 1.2 is secondary to the tunnel deformation and stability compared to the effects of geometrical parameters (orientation, size, and intensity) (Vardakos et al. 2007; Solak 2009).

All mechanical parameters of foliation and fractures used in the following DEM analyses are summarized in Table 3. Case a represents the unweathered OFPs and fractures; cases b–g represent the intact foliation planes with different M_a values (particular cases of the 3D strength envelope from Cacciari and Futai (2019)); and case h represents the foliation and fracture planes with advanced weathering grade. A single case (from a to h) was used for the foliation planes in each DEM model simulation.

Table 3 Coulomb-slip parameters of the foliation and fracture planes used in the DEM analyses: M_a (percentage of mica area); K_s (shear stiffness); K_n (normal stiffness); σ_t (tensile strength); c (cohesion); φ_p (peak friction angle); φ_r (residual friction angle); OFP (open foliation plane); WFP (weathered foliation plane); F1, F2 and F3 (fracture sets); and WFR (weathered fracture)

The main parameter used to analyze the DEM results was the total failed block volume (FBV), obtained by a Fish function that calculates the sum of block volumes for three different displacement magnitude thresholds (D > 0.1, D > 0.05 and D > 0.01 m). Additionally, a Fish function computed the average displacement of the tunnel face (AD) and the total number of slipping contacts (SC) near the tunnel face while stepping to monitor the excavation behavior during the analyses. In these cases, the Fish function found the grid-points of the blocks on the tunnel face and contacts 0.25 m from the tunnel face (TLS digital model in Fig. 2b) and computed AD and SC, respectively. Considering that the MST is a small-size tunnel (approximately 5 m wide and 6 m high) and the lack of information on the excavation method used in 1950s, the tunnel was fully excavated in a single step, followed by the calculation of AD and SC while stepping, until the end of each analysis. All DEM models stopped running after 100 × 10³ calculation steps (approximately 10 h for MS1 and 6 h for MS2 models).

4.1 Effects of Fresh Foliation on the MST Stability

The gneissic foliation planes have cohesion and tensile strength, which vary with respect to the biotite content (M_a). Thus, using friction-based models for these structures can significantly underestimate the actual stability condition of the rock mass. To demonstrate this problem, the DEM models in Fig. 7 were ran using the 3D peak shear strength envelope described by Eqs. 1 and 2, in which M_a is an independent variable (as the normal stress). The case a in Table 3 was used for OFP, F1, F2 and F3, and the cases b to g were used for foliation planes with different mica contents.

Figure 12 shows the FBV results obtained for MS1 and MS2. Four FBV zones were defined: zone I represents released block volumes higher than 10² m³, which is associated with global instability problems; zone II represents released block volumes between 10 and 10² m³, which is associated with large instabilities around the excavation; zone III represents released block volumes between 1 and 10 m³, which is associated with intermediate instabilities around the excavation; and zone IV represents released block volumes lower than 1 m³, which is associated with small block releases and generally stable conditions.

Fig. 11

Modified from Monticelli (2019)

a Residual friction angles of discontinuities decreasing with increasing porosity due to weathering. b Foliation specimens with advanced watering grade, and c a micrograph taken perpendicular to the foliation wall indicating weathered minerals (highlighted in yellow). (color figure online)

Figure 13 shows examples of the results in Fig. 12a for MS1. The potential instability problems of this section are clearly controlled by the F2 shear zone. DEM models with OFP (null cohesion and tensile strength) and M_a = 100% (Table 3) showed a global failure pattern with extremely high FBV values for displacements higher than 0.1 m. It is important to note that the failure reaches the bedrock, suggesting that daylight collapse could occur for such low foliation strengths. As M_a increases, the tunnel becomes more stable. For M_a = 90%, major discontinuity-controlled failure occurred surrounding the excavation. For M_a = 60%, only the east wall showed a significant discontinuity-controlled failure. For M_a = 50% or less, only isolated failures of small blocks occurred on the east wall.

Fig. 12

Variation in the FBV values of a MS1 and b MS2 with respect to M_a for different displacement magnitude thresholds (D > 0.01, 0.05 and 0.1 m): (I) global instability zone, (II) large instability zone, (III) intermediate instability zone, and (IV) stable zone

Figure 14 shows examples of the results in Fig. 12b for MS2. The potential instability problems of MS2 are controlled by the foliation planes, as the fracture intensity is much lower than in MS1 (Fig. 4). As MS2 is extremely shallow, the low cohesion and tensile strength values are sufficient to maintain the tunnel stability. The mechanical parameters of OFP (null cohesion and tensile strength) triggered global failure patterns by shear failure of persistent foliation planes on the west wall of the tunnel. For M_a = 90%, only the east wall showed a significant discontinuity-controlled failure. For M_a = 80% or less, the tunnel shows stable conditions with isolated failures of small blocks on the east wall and roof.

Fig. 13

Examples of MS1 DEM results for different foliation plane conditions (DEM models facing south)

The FBV values from different displacement magnitude thresholds (D > 0.1, D > 0.05 and D > 0.01 m) indicate the homogeneity of the block velocities in the models. In unstable conditions (zones I, II and III), close FBV values indicate the existence of defined unstable regions in the model (defined masses of blocks moving with similar velocity). In stable conditions (zone IV), close FBV values indicate general stability (lack of significant movement). On the other hand, outlying FBV values indicate heterogeneous distributions of block movements (masses of blocks moving with different velocities in the models).

Figure 15a shows the calculated variations in AD from OFPs (condition I) and M_a = 60% (conditions I and II) for MS1. Conditions II and III in this figure show slight changes in AD after removing free falling blocks with D > 0.01 m, which corroborates the stable conditions observed above by the FBV for foliation planes with such mica content (Fig. 12a). Figure 15b shows the calculated variations in AD from OFPs (condition IV), M_a = 80% (conditions V and VI) and M_a = 60% (conditions VII and VIII) for MS2. For M_a = 80%, AD continued to increase due to small blocks free falling from the tunnel roof (condition V in Fig. 15). After removing blocks with D > 0.01 (condition VI in Fig. 15), AD was in agreement with the stable conditions observed for M_a = 80% by the low FBV values (Fig. 12b). MS2 with M_a = 60% showed inexpressive AD during the entire analysis, before and after removing blocks with D > 0.01 m (conditions VII and VIII).

Fig. 14

Examples of MS2 DEM results for different foliation plane conditions (DEM models facing north)

Figure 15c shows the SC monitored for MS1 and MS2 using OFPs and M_a = 60% (cases a and f in Table 3). For all cases, the SC starts with higher values and decreases rapidly, reaching a relative stability after 20 × 10³ calculation steps. These results indicate that a characteristic instability pattern is achieved after 100 × 10³ calculation steps. Note that SC is considerably higher and much more unstable for OFPs than for M_a = 60%, which indicates that only a few blocks near the tunnel are in motion during the analyses in the second case. For MS1 with M_a = 60%, SC decreases drastically after removing blocks with D > 0.01 (condition III in Fig. 15a, c), reaching an SC value similar to that from MS2 under the same conditions (condition VIII in Fig. 15b, c). Figure 15d shows the slipping contacts surrounding the excavation boundary for MS1 (conditions I and II) and MS2 (conditions IV and VII). Note that only the slipping contacts 0.25 m from the excavation boundary were used to calculate SC.

The DSTs in Fig. 10 indicated M_a values closer to 60%; however, these specimens represent the worst-case (such as the biotite-rich contact in Fig. 8) observed on the MST gneiss. The POT results (Fig. 9) corroborate this statement, as 61% was the lowest estimated M_a. In addition to the block failures observed on the east wall of the MST for M_a = 60%, after removing blocks with D > 0.01 m, the AD decreased to 0.0035 m (Fig. 15a), and the SC decreased to 0.3%, indicating stable conditions. Therefore, the mechanical parameters associated with M_a = 60% (case f in Table 3) can be considered representative of actual stable conditions in the MST without support systems.

Despite the stable conditions verified above for the M_a values correspondent to the MST reality, the possible weathering effects noted in Sect. 4.1.3 were not included. In the following sections, a parametric study is presented considering the weathering effects in different scenarios.

4.2 Weathering Effects on Foliation and Fractures

In this section, a parametric study is performed considering possible weathering distributions on the rock mass. As indicated in Sect. 3.1.3, the weathering advanced through foliation and fractures on the MST and did not affect the intact rock; however, it drastically decreases the strength of individual foliation planes. Advanced weathering conditions in foliation planes can cause complete loss of cohesion and tensile strength, which can be critical to the tunnel stability special on such low condiment conditions (shallow depths).

Next, the effects of advanced wreathing in foliation planes is assessed via DEM analysis of MS1 and MS2 are evaluated in two different ways: the effects of isolated and persistently weathered foliation planes (WFPs) on the stability of the tunnel and the effect of a percentage of weathered planes (including foliation and fractures) distributed on a defined weathered domain.

4.2.1 Effects of Isolated Weathered Foliation Planes

Field surveys, drill cores and inspections inside the MST showed evidence of isolated foliation planes in advanced weathering conditions. These structures have high porosity (Fig. 11); thus, they contribute significantly to the water inflow on the MST (Fig. 6).

Considering the aforementioned evidence, a single WFP with critical mechanical properties associated with advanced weathering was inserted at different positions in the MS1 and MS2 models. The parameters in case h (Table 3) were attributed to the WFPs, and the parameters in cases f and a were attributed to the remaining foliation and fracture planes, respectively (Table 3). Figure 16 shows the position of each WFP in MS1 and MS2 and the respective FBV results of each simulation. Figure 17 shows examples of these results indicating the position of the WFP and the magnitude of block displacements.

Fig. 15

AD calculated while stepping a MS1 (DEM models facing south) and b MS2 (DEM models facing north). c SC calculated while stepping of MS1 and MS2 for the OFP and M_a = 60% cases. d Current slipping contacts at the end of the analysis for the OFP and M_a = 60% cases. I–III and IV–VIII indicate different DEM conditions of AD and SC for MS1 and MS2, respectively

Fig. 16

Location and the respective FBV results of each WFP in (a and b) MS1 and (c and d) MS2 for different displacement magnitude thresholds (D > 0.01; 0.05 and 0.1 m): (I) global instability zone, (II) large instability zone, (III) intermediate instability zone, and (IV) stable zone. Note that the MS1 DEM models face south and the MS2 DEM models face north

In MS1, WPF 09, which is near the top-east corner of the tunnel (Fig. 16a), caused major instability problems with large failure surrounding the excavation (Figs. 16b, 17a). Above WFP 09, WFPs 10–13 did not cause significant block failures, and the final stability state was similar to that in the case of M_a = 60% without WFPs (Figs. 12a, 13). Below WFP 09, WFPs 08 and 07 also caused large local instabilities (FBV values inside zone II); however, WFPs near the top-west corner (WFPs 03–06) did not trigger unstable conditions in the tunnel. WFPs 01 and 02, which are near the bottom-west corner, caused intermediate to large unstable conditions (FBV values between zones III and II). Therefore, a single WFP could cause significant instability in MS1 (inside zone II) if it is located near the top-east or the bottom-west corners of the tunnel; however, the first case is much more critical. It is important to highlight that the water inflow occurs through the F2 shear zone in MS1, and the top-east corner of the tunnel is constantly wet and dripping (Fig. 6a).

Considering the FBV values in Fig. 16, MS2 is less affected by isolated WFPs than MS1; however, MS2 showed expressive FBV values for WFPs 01 and 06, which are located near the bottom-west and top-east corner of the tunnel, respectively (Figs. 16d, 17b). These WFPs triggered intermediate to large block failures (FBV values between zones III and II) on the walls but triggered general failures around the excavation, such as the WFP 09 in MS1.

Both MS1 and MS2 showed important instability problems associated with WFPs crossing the rock mass near the top and bottom corners of the tunnel. In this case, it is interesting to verify the consequences of two WFPs in such positions. Figure 18a, b show the DEM results of MS1 with WFPs 02 and 09 and MS2 with WFPs 01 and 06, respectively. Both cases indicated major failures (FBV values higher than all cases in Fig. 16), which would compromise the integrity of the tunnel. However, in MS2, only two parallel WFPs in such positions, among foliation planes of high strength (M_a = 60%), would be necessary to trigger the same conditions observed for OFP (null cohesion and tensile strength for all foliation planes in the DEM model) in Fig. 14.

Fig. 17

DEM simulations with WFPs in different positions of a MS1 and b MS2. Note that the MS1 DEM models face south and the MS2 DEM models face north

4.2.2 General Weathering Advance

The evidence of weathering at the MST site indicates the occurrence of isolated planes (including foliation and fracture planes) of advanced weathering grades rather than a general weathering advance through all discontinuities in the rock mass. Nevertheless, it is interesting to assess the effects of a progressive weathering advance on potentially weathered regions in MS1 and MS2. The following analyses verify the effects of the weathering advance, affecting both foliation and fracture planes. In MS1, potentially weathered region was defined by the F2 shear zone, which is responsible for the water inflow towards the tunnel. In MS2, this region was defined by field inspections and TLS images, which showed wet rock faces and water dripping on the roof of the tunnel (Fig. 6b). In this case, the water is likely seeping from the west slope and top surface towards the tunnel through the F1 and foliation planes, as F2 has lower intensity in this section and dips west. Figure 19 shows the potentially weathered regions defined in MS1 and MS2.

Fig. 18

DEM models of MS1 and MS2 containing two WFPs at critical positions. Note that the MS1 DEM model faces south and the MS2 DEM model faces north

The weathering advance was modeled in 3DEC using a Fish code that selects block contacts and changes their mechanical properties to the same weathered properties used in the analyses presented above (case h in Table 3). The selection process was random, and the percentage of weathered contacts (WC) was used to stop the process. WC is calculated as the sum of the selected contact areas (green contacts in Fig. 19) divided by the sum of all contact areas on the potentially weathered regions (green and blue contacts in Fig. 19) of MS1 and MS2. The increase in WC is a simplified interpretation of the general weathering advance in these regions, which decreases the rock mass quality surrounding the excavation. Note that WC is equivalent to the weathered percentage of P₃₂ on the potentially weathered regions (total discontinuity area per rock mass volume).

Figure 20 shows the FBV values for WC values ranging from 10 to 90%, and Fig. 21 shows examples of graphical DEM results. For MS1 (Figs. 20a, 21a), the increase in WC caused a progressive increase in FBV. MS1 exhibited substantial local instability problems (zone II) for WC > 50%, and global instability problems for WC > 80%. MS2 exhibited local instability problems (between zones III/II) only for WC > 90%; thus, 10% of unweathered foliation and fracture planes was sufficient to avoid global instability problems in this case (Figs. 20b, 21b).

Fig. 19

Potentially weathered regions defined for MS1 and MS2 with WC = 50%. Green contacts are weathered foliation and fracture planes; the blue contacts are untethered and inside the potentially weathered regions; and the red contacts are untethered and outside the potentially weathered regions. Note that the MS1 and MS2 DEM models face north

Fig. 20

FBV results of each WC in a MS1 and b MS2 for different displacement magnitude thresholds (D > 0.01, 0.05, and 0.1 m): (I) global instability zone, (II) large instability zone, (III) intermediate instability zone, and (IV) stable zone

Fig. 21

Examples of DEM simulations with different WC values for a MS1 and b MS2. Note that the MS1 DEM model faces south and the MS2 DEM model faces north

Interestingly, isolated WFPs 07, 08, and 09 (Fig. 17a) and WC = 60% (Fig. 21a) trigger similar failure patterns and magnitudes in MS1. However, from geotechnical–geological surveys and site observations, isolated WFPs are more likely to occur than general weathering distributions of such magnitudes. However, the weathering advance can cause major instability problems in both cases.

MS2 showed stable conditions for most simulations, including WFP and WC. Due to extremely low confinements, for WC = 90%, the remaining untethered foliation planes (less than 10%) with M_a = 60% avoided global instability problems. On the other hand, the low confinement was unfavorable in the critical cases of isolated WFPs with null cohesion and tensile strength (Fig. 18b).

5 Discussion

This work is based on the assumption that DEM analysis with a fixed DFN (fixed geometrical parameters) can be representative of the overall rock mass condition. Moreover, the actual tunnel geometry is built in the model (Sect. 2.1); thus, representative stable conditions for MS1 and MS2 should not have failures along the foliation planes leading to additional overbreaks. As the DFN generation is stochastic, the fractures on the DEM tunnel face are not identical (in size, position, and orientation) to the real fractures mapped via TLS on MS1 and MS2. Therefore, small block failures cannot be associated with actual unstable conditions, while major failures of block sets can.

There is no specific parameter to verify the stability state of tunnel models in 3DEC. Monitoring the parameters introduced herein (FBV, AD, and SC), along with the total unbalanced forces of the models, one can indicate stable or unstable conditions in the tunnel. Unstable models with a high volume of moving blocks show high and oscillatory unbalanced forces, whereas stable models with a low volume of moving blocks show steady and low unbalanced forces. For example, after removing the small volume of free falling blocks from MS1 (M_a = 60% in Fig. 15a) and MS2 (M_a = 80% in Fig. 15a), the total unbalanced forces were steady at 22.9 N and 93 N, respectively, and AD stopped increasing. On extremely unstable models, such as the OFP cases (Figs. 13, 14), the total unbalanced forces oscillated from 10⁴ to 10⁵ N.

From the results in Fig. 15c, d, 100 × 10³ calculation steps were sufficient to define the failure pattern in these models. Increasing the number of calculation steps would increase the amount of time to complete the analysis without resulting in additional relevant information. On the other hand, a lower number of calculation steps would decrease the final displacement of the failed blocks, which would not highlight the failed zones in the models. Considering that SC and AD indicated 100 × 10³ calculation steps suitable to obtain representative stability patterns, hereafter only the FBV will be used to analyze the numerical results.

As mentioned before, both MS1 and MS2 sections do not have any kind of support systems. The RMR₁₄, Q and GSI values of these sections (Table 1) suggest that some support system should have been applied during tunnel construction; however, these methods were developed after the excavation period, and the excavation methods adopted at the time (if there were any specific methods) are unknown.

The fact that the MST stands stable without apparent major stability problems indicates that the traditional empirical classification methods in Table 1 overlook certain important characteristics of the rock mass that are favorable to tunnel stability. The results presented in Sect. 4.1 indicate that foliation plays an important role in the stability of the tunnel; thus, ignoring the inherent cohesion and tensile strength of such geological structures creates unrealistic instability conditions. It is interesting to note that null cohesion and tensile strength (OFP) triggered global unstable conditions for both MS1 and MS2. In this case, there is an agreement between the numerical results with the general classification results in Table 1, which would recommend immediate support installation on these sections of the tunnel. The discontinuity description in these classification systems considers the roughness and weathering conditions but starts from the assumption that discontinuities have null tensile strength (ISRM 1978).

In practical geological mapping, the exposed foliation planes are commonly described as a “joint set”, with the same classification parameters used for different structures, such as fractures and sheet joints, which is conservative because it underestimates the real shear and tensile strengths of such geological structures. This fact becomes evident after reassessing old tunnels (such as the MST) constructed before the development of the most popular rock mass classification systems. It is important to note that the classification systems are not wrong, as they should be conservative. However, using these classification systems as definitive empirical design methods causes direct consequences on the support system design.

The weathering scenarios simulated in Sect. 4.2 indicate that advanced weathering conditions can trigger major instability problems to the tunnel. The evidence of weathering at the MST site indicates the occurrence of isolated planes, including foliation and fracture planes, of advanced weathering grades (such as simulated in Sect. 4.2.1) rather than a general weathering advance through all foliation and fracture planes in the rock mass (such as simulated by Sect. 4.2.2). Although all geological structures are affected by weathering, the complete loss of cohesion and tensile strength in foliation planes caused by advanced weathering scenarios (from f to h in Table 3) is much more critical to the tunnel stability than the reduction of friction angle in fracture planes (from a to h in Table 3) due to the low confinements (shallow depths) at the MST.

Currently, model-scale WFPs in such critical grade (case h in Table 3) may not exist; however, there are two strong pieces of evidence causing concerns regarding this issue: the drill cores showed isolated laboratory-scale WFPs of equal or worse strength conditions than those used in the analyses presented above; In addition, water is constantly inflowing through foliations and fractures on these sections of the MST. Moreover, weathering is a dynamic process that evolves over time, progressively decreasing the mechanical properties of foliation and fracture planes. Therefore, model-scale WFPs close to reaching such critical weathering grades can exist and cause unexpected instability problems in the future.

6 Conclusions

The following summary and conclusions can be provided for the study conducted:

• 1. The MST is an old tunnel with intense train traffic that is important for iron ore transportation on the Vitória-Minas Railway. The tunnel was constructed in the 1950s in a gneissic rock mass and contains four discontinuity sets, including fractures (F1, F2 and F3) and metamorphic foliation. Regardless of 5 m of structural concrete in each portal, the MST does not have any kind of support system and has remained stable since its excavation.

• 2. The rock mass classifications in Table 1 indicated moderate (RMR₁₄ and GSI) to poor (Q) rock mass qualities for MS1 and MS2. This result agrees with the DEM results, ignoring the inherent cohesion and tensile strength of foliation planes. However, this assumption is unrealistic and substantially underestimates the rock mass quality. The laboratory tests and DEM results indicated that M_a = 60% (or lower) is representative of the actual tunnel conditions; thus, the fresh foliation planes on the MST gneissic rock mass can explain the current stable conditions of the tunnel.

• 3. Even though the MST is currently stable, the evidence of weathering advances on MS1 and MS2 pointed to the need for DEM analyses considering this issue. From the DEM results, isolated WFPs can cause significant instability problems, especially in MS1. Moreover, two WFPs in critical positions could cause global instabilities in both MS1 and MS2. The increase in WC caused progressive instability problems in MS1, which became critical for WC > 50%. MS2 was stable in intense weathering conditions represented by WC. In this section, only WC = 90% caused relevant instability problems in the tunnel. However, even in such weathering conditions, a few fresh foliation contacts (e.g., 10%) with expressive cohesion and tensile strength (M_a = 60%) guaranteed global tunnel stability.

• 4. In practical rock mechanics applications, discontinuity sets are often treated as joint sets, regardless of the type and genesis of each geological structure, and friction-based models (linear and nonlinear) are assumed to represent the mechanical behavior of such discontinuity sets. The case study in this paper indicated that more attention should be given to understanding the mechanical behavior of intrablock structures, such as metamorphic foliation, as these structures play an important role in the stability of engineering structures such as the MST.