3D Numerical Analysis for Failure and Deformation Assessment of the Waterway Tunnel, Wabe Hydropower Project, Central Ethiopia

3D Numerical Analysis for Failure and Deformation Assessment of the Waterway Tunnel, Wabe Hydropower Project, Central Ethiopia | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article 3D Numerical Analysis for Failure and Deformation Assessment of the Waterway Tunnel, Wabe Hydropower Project, Central Ethiopia Mesay Kassaw, Bayisa Regassa, Tarun Raghuvanshi, Mamo Methe This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3956277/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract In designing suitable support systems and ensuring safe excavation of a tunnel, deformation and block failure assessment around the opening is a crucial aspect of tunneling. In this study, a distinct element modeling approach was employed to evaluate the distribution of failed blocks, failure modes, and displacements of the tunnels to gain insight into support recommendations for the Wabe Hydropower project in central Ethiopia. For this purpose, three representative numerical models were developed considering different rock mass along the tunnel alignment. Subsequently, the influence region classification technique was introduced and the models were systematically classified into three distinct regions. This technique enabled the consideration of blocky rock mass as discontinuum through the direct inclusion of field-measured joints with average spacings of 0.2, 0.56, and 1.2 m into a region surrounding the tunnel opening. The simulation results indicated that tunnels in closely jointed rock mass behave anisotropically, with failed blocks following the joint inclinations of N253/72 and N035/79 and exhibiting a tensile failure mode. Tunneling in the fault zone induced a shear failure mode, with a significant distribution of failed blocks aligned in the maximum principal stress direction. However, under low horizontal in-situ stress, both shear and tensile failure could exist, tensile failure affecting the roof and floor. Furthermore, tunnels in closely jointed rock mass are primarily influenced by horizontal displacement, whereas tunneling in fault zones led to both greater horizontal and vertical convergences, with horizontal displacement being more significant. Finally, the obtained results were used to propose support recommendations. Block failure Displacement Distinct element method Tunneling Wabe Hydropower Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Introduction Model testing and numerical analysis are two broad approaches that are generally used to investigate tunnel deformation and failure mechanisms (Jia and Tang 2008 ; Lohar et al. 2023 ). Numerical techniques are being developed to provide a more thorough understanding of challenging underground excavation problems (Marinos et al. 2007 ). Compared with other methods (e.g., physical modeling methods, empirical methods, and other closed-form solutions), numerical techniques have been proven to be a suitable tool for challenging conditions, such as the presence of discontinuities, the existence of high in-situ stresses, and the tunnel system layout (Jia and Tang 2008 ; Kulatilake et al. 2013 ; Wang et al. 2012 ). Furthermore, three-dimensional (3D) modeling is necessary when the aforementioned challenging conditions cannot be adequately simplified on a single plane (Xing et al. 2018 ) and when it is important to consider the actual stress path that is caused by excavation (Cai 2008 ). The two most prevalent 3D numerical approaches in rock engineering are the continuum and discontinuum models (Raghuvanshi 2019 ). Discontinuum modeling tools (Discrete Element Methods) enable to treat the rock mass as a discontinuum or equivalent continuum medium. When a rock mass is strongly jointed with no preferred failure direction, it is appropriate to treat it as an equivalent continuum (Eberhardt 2012 ). Several studies have used this assumption (e.g., Xing et al. 2017 , 2018 ; Shreedharan and Kulatilake 2016 ). The rock mass properties can thus be obtained by scaling down the intact rock properties using several empirical relations (Hoek and Brown 1997 ; Barla and Barla 2000 ). However, if it is believed that the presence of discontinuities may significantly contribute to the instability of the structure in the rock mass, an explicit representation of the discontinuities is required (Regassa et al. 2018 ; Itasca 2016). As a result, models could be able to account for assessing the rock mass anisotropy, failure modes, and large deformations (Marinos et al. 2007 ; Hao and Azzam 2005 ; Huang et al. 2013 ). Discrete Element Methods (DEM) are considered suitable tools for the stability analysis of underground structures; however, they require accurate input data on the properties of rock mass (Marinos et al. 2007 ). Furthermore, data on the nature and orientation of discontinuities govern the directional effects that arise from the deformability and stability of the rock mass, together with the effects of intact rock properties (Wang et al. 2012 ). As a result, it is generally essential to include the 3D effects of the discontinuities during the modeling process. An approach forwarded by Kulatilake et al. ( 1993 ) is being followed to include joints in models when the number of joints is quite large (e.g., Wang et al. 2012 ; Wu and Kulatilake 2012 ). In this method, the first invariant of the fracture tensor is a combined measure of fracture size and intensity. Thus, by preserving the same orientation, increasing the fracture size, and reducing the fracture intensity to maintain the first invariant of the fracture tensor, a comparable fracture system can be generated. In Ethiopia, during the Gilgel Gibe I, II, and III hydropower development projects, tunnel collapse issues and support problems commonly and repeatedly occurred. These problems were primarily attributed to unexpected failure and unpredicted deformation conditions that were encountered during the construction stage, and it was realized that employing the Discrete Element Method (DEM) would have anticipated adverse conditions and possibly would have provided adequate mitigation measures prior to the occurrence of such problems (Kidane and Engida 2010). In this regard, previous researchers (e.g., Macklin et al. 2012 ) have demonstrated the value of the DEM modeling technique in the prediction and mitigation of such problems prior to the commencement of projects. The tunnel at the Wabe Hydropower Project in Central Ethiopia is situated in a similar geological and hydrological setup as that of Gilgel Gibe I, II, and III; however, the designers have not employed DEM to simulate the tunnel excavation processes. Current investigations have been limited to topographical suitability assessments, slope stability evaluations based on the old Norwegian rule of thumb, and the kinematic checks conducted through exposed joints in slope sections (ECDSWC 2019 ; Dumesso 2020). Consequently, proceeding solely with these investigations for a tunneling program may likely result in unforeseen stability issues and other challenging conditions related to rock support. Thus, a comprehensive understanding of the deformation, failure distribution, and possible mechanisms involved in the project area is crucial for the design of appropriate support systems and may equally be important for ensuring safe excavations. This study aims to assess the distribution and mode of failure of the failed blocks, and displacement at various parts of the tunnel under study in the Wabe Hydropower Project. The proposed tunnel with a diameter of 5 m could encounter four Geotechnical units at different depths. To model the different geotechnical units, the 3DEC distinct element code (Itasca 2016) was utilized and three representative numerical models were developed. Thus, Model I represents Upper basalt with N253/72, N046/81, and N329/82 oriented joint sets of 0.2 m spacing (GU1) alongside an inclined fault zone (GU4) at 90 m depth. Models II and III represent Middle basalt with N157/80, N035/79, and N202/69 oriented joint sets of 0.56 m spacing (GU2) at ca. 190 m depth and Lower basalts N022/86, N231/81, and N078/78 oriented joint sets of 1.2 m spacing (GU3) at ca. 356 m depth, respectively. Thereafter, the influence region classification technique was introduced and models were systematically classified into three distinct regions of influence. This classification method allowed for the direct inclusion of a large number of joints, as measured in the field, into the area surrounding the tunnel openings. Subsequent stress analyses were performed to assess the distribution and failure mode of the failed blocks, as well as the displacement of the tunnel; these findings are discussed to gain valuable insights into future rock mass support recommendations. The Project Area Description of the Area The Wabe Hydropower project area lies in the upstream catchment of the Omo-Gibe River Basin, located in the country's southwestern region adjacent to Kenya and the South Sudan international border. The study area is located approximately 161 km from Addis Ababa in central Ethiopia. The entire project area, which includes a reservoir area of approximately 15.06 km 2 and a 17.215 km long tunnel system, is situated at the transition between the northwestern plateau and the southwestern plateau volcanites. Geographically, the proposed tunnel alignment runs between UTM Zone 37 N coordinates; 368389mE, 911141mN (intake) and 351568mE, 909698mN (outlet) (Fig. 1 ). Geology and Engineering Geology The entire project area is located along the Main Ethiopian Rift (MER) margin, which is a tectonically active continental rift margin with numerous parallel-stepping faults (Ebinger et al. 1993 ). The Precambrian crystalline basement, Eocene to Miocene volcanic rocks, Quaternary lacustrine deposits, alluvial sediments, and volcanic flows make up the regional geology of the area (Davidson and Rex 1983 ). At the proposed Wabe Hydropower Project site detailed surface and subsurface geological mapping has been carried out up to an offset of 500 m from the tunnel alignment and using boreholes along the alignment by the Ethiopian Construction Design and Supervision Works Corporation (ECDSWC 2019 ). The major lithologies are: The Upper basaltic formation, this unit is ca. 84.5 m thick and consists of aphanitic and phyric (the phenocrysts are dominantly composed of Plagioclase) basalts predominantly. At places, basalts are found interbedded with thin layers of welded tuff, and ca. 18.6 m thick volcano-clastic sediments composed of tuffaceous deposits with minor clastic sediments separating them from the underlying basalt. The middle basaltic formation, this unit is ca. 380.5 m thick, phyric (the phenocrysts are dominantly composed of Plagioclase) basalt with subordinate amygdaloidal (calcite-filled) basalt. It is characterized by the common presence of calcite veins and volcanic breccia. A 60.8 m thick, BH 16 and BH 15, ignimbrite unit separated it from the underlying lower Basalt. The Lower basalt, this unit is fresh, massive phyric basalt exposed in the river bed of the Wabe River. It is primarily composed of plagioclase phenocrysts, with lesser amounts of olivine and pyroxene. Additionally, vesicles in this unit make up approximately 18–30% of its volume. This unit seldomly appears interlaying with gray to green sub-volcanic rocks of 1.2 to 2.5 m thickness. The geological cross-section along the tunnel alignment with boreholes is presented in Fig. 2 . A general engineering geologic description of each Geotechnical unit (GU) is presented in Table 1 . For the pre-assumed blocky rock mass, the orientations of 387 discontinuity were recorded—140 in GU1, 164 in GU2, and 83 in GU3. Subsequently, by applying lower-hemisphere and equal-area projections, their orientations were deduced using the DIPS v 6.0 software package (Rocscience 2016); as a result, the three most dominant joints were identified. The determined dominant joint sets in these rock mass are presented in Table 1 and their corresponding stereo-net projections are presented in Fig. 3 . Table 1 General engineering geological description of various units present along the tunnel alignment Geotechnical units Formation General engineering geologic description Identified joint sets GU1 Upper Basalt This rock mass is very blocky and of good to excellent quality. Joints within this rock mass are 0.2 m spaced on average, and moderately to slightly weathered with no infillings. 1N 253/72 2N 046/81 3N 329/82 GU2 Middle Basalt This rock mass is very blocky and disturbed, with a fair to good quality. Joints within this rock mass are 0.56 m spaced on average, highly to moderately weathered with no or occasional clay infillings. 1N 157/80 2N 035/79 3N 202/69 GU3 Lower Basalt This rock mass is blocky and of excellent quality. Joints inside this rock mass are 1.2 m spaced on average, with some rough joints, and no visible weathering effect or infillings. 1N 022/86 2N 231/81 3N 078/78 GU4 Fault zone This rock mass is poorly interlocked, heavily broken, and of very poor quality. - Materials and Methods Estimation of the Engineering Properties of Rocks The basic geological strength index (GSI) chart provided by Hoek and Marinos ( 2000 ) has been used to obtain the respective ratings. The surface and structural conditions of the discontinuities within each Geotechnical unit were assessed in the field, and the range of GSI values was determined, as presented in Table 2 . Laboratory test results for both Young’s modulus ( \({E}_{i}\) ) and strength ( \({\sigma }_{ci}\) ) of intact rock were also available. Estimation of the Engineering Properties of the Rock Mass Modulus of Deformation The empirical equation provided by Hoek and Diederichs ( 2006 ) was used to compute the modulus of deformation values for each Geotechnical unit: \({E}_{rm}={E}_{i}\left(0.02+\frac{1-D/2}{1+{e}^{\left(\left(60+15D-GSI\right)/11\right)}}\right)\) ……..Eq. 1 where \({E}_{i}\) is the Young’s modulus of the intact rocks; The disturbance factor (D) due to blast damage and stress relaxation was set to 0 and GSI is the Geological Strength Index. Table 2 Rock mass and intact rock mechanical properties, and GSI distributions Geotech. Units \({E}_{i}\) γ GSI Distribution E rm Eq. (1) Maximum Mean Minimum Max. Mean Min. (GPa) (KN/m 3 ) (GPa) GU1 72.4 25.9 58 51 45 34.37 23.61 16.19 GU2 54.5 24.7 50 41 32 16.74 9.316 5.052 GU3 70.0 28.6 70 62 55 51.29 39.57 28.58 GU4 2.0 23.2 30 25 20 0.163 0.119 0.091 Note: Ei - Young’s modulus of the intact rocks; γ - unit weight of the rock; GSI – Geological Strength Index and E rm - modulus of deformation of the rock mass Hoek–Brown Parameters The parameters that define the rock mass strength characteristics (Hoek-Brown material constants; \(s\) , \(a\) , and \({m}_{b}\) ) were calculated by using GSI and D values. Empirical equations ( Eqs. 2, 3, and 4 ) , which were first introduced by Hoek ( 1994 ) and Hoek et al. ( 1995 ), were used. \(\frac{{m}_{b}}{{m}_{i}}= exp\left(\frac{GSI-100}{28-14D}\right)\) …….. Eq. 2 \(s=exp\left(\frac{GSI-100}{9-3D}\right)\) …….. Eq. 3 \(a=\frac{1}{2}+\frac{1}{6}\left({e}^{-GSI/15}- {e}^{-20/3}\right)\) …….. Eq. 4 where s, a, and mb are the Hoek-Brown material constants, D is the disturbance factor, GSI is the Geological Strength Index, mi is the material constant for intact rock, and for basalt, it was taken as 25 (from the table proposed by Marinos and Hoek ( 2000 )). Following the determination of the Hoek-Brown material constants using Eqs. 5, 6, and 7, the Mohr-Coulomb friction angle ( ϕ ), tensile strength ( \({\sigma }_{t}\) ), and cohesion ( \(c\) ) of the Geotechnical units were estimated. \(\varphi = \left[\frac{6a{m}_{b}{\left(s+ {m}_{b}{\sigma }_{3n}\right)}^{a-1}}{2\left(1+a\right)\left(2+a\right)+6a{m}_{b}{\left(s+ {m}_{b}{\sigma }_{3n}\right)}^{a-1}}\right]\) …….. Eq. 5 \(c= \frac{{\sigma }_{ci}\left[\left(1+2a\right)s+ \left(1-a\right){m}_{b}{\sigma }_{3n}\right]{\left(s+ {m}_{b}{\sigma }_{3n}\right)}^{a-1}}{\left(1+a\right)\left(1+2a\right)\sqrt{1+ \left(6a{m}_{b}{\left(s+ {m}_{b}{\sigma }_{3n}\right)}^{a-1}\right)/\left(1+a\right)\left(1+2a\right)}}\) …….. Eq. 6 \({\sigma }_{t}= \frac{s.{\sigma }_{ci}}{{m}_{b}}\) …….. Eq. 7 where \({\sigma }_{3n}= \frac{{{\sigma }^{{\prime }}}_{3max}}{{\sigma }_{ci}}\) ; \({{\sigma }^{{\prime }}}_{3max}\) is the highest limit of confining stress considered in the link between the Hoek-Brown and the Mohr-Coulomb criterion. For deep tunnels, Hoek et al. ( 2002 ) have provided guidelines; thus, values from 1 to 5.6 MPa were taken. Poisson’s ratio There are few available empirical equations for estimating Poisson’s ratio ( \({V}_{rm}\) ) of the rock masses. Using the \({m}_{i}\) and GSI , Vasarhelyi ( 2009 ) provided a suitable alternative empirical equation whenever the Poisson’s ratio of the intact rock ( \({V}_{i}\) ) is not available, as follows: \({V}_{rm}= -0.002GSI-0.003{m}_{i}+0.457\) …….. Eq. 8 The computed Mohr-Coulomb material constants, shear strength parameters, and Poisson’s ratio values for each Geotechnical unit using a mean GSI value are given in Table 3 . Table 3 Rock mass parameters and material constants for the average GSI values. Geotechnical Units Depth (m) Shear Strength Parameters Poisson’s ratio ( \({V}_{rm})\) Material constants Cohesion (C) Friction angle ( ϕ) Tensile strength ( \({\sigma }_{t})\) A S mb (MPa) ( 0 ) (MPa) Eq. 6 Eq. 5 Eq. 7 Eq. 8 Eq. 2 Eq. 3 Eq. 4 GU1 90 1.69 65.3 0.29 0.28 0.51 0.01 4.84 GU2 190 1.42 57.6 0.08 0.30 0.51 0.002 3.15 GU3 356 3.98 58.7 0.46 0.26 0.50 0.015 6.44 GU4 90 0.2 35.7 0.001 0.33 0.53 0.0002 1.72 Estimation of the Engineering Properties of Joints In the present study, an effort was made to determine the shear strength characteristics of joints for blocky rock mass, however, as already stated Geotechnical unit GU4 was considered as an equivalent continuum medium. Due to the non-availability of rock core through joints, for design purposes, initial estimations can be carried out using empirical approaches (Sharma et al. 1999 ). Therefore, the following empirical law of friction provided by Barton ( 1973 ) was utilized: \(\left(\frac{ \tau }{{\sigma }_{n}}\right) = {\varphi }_{b}+JRC \left(\frac{JCS}{{\sigma }_{n}}\right)\) …….. Eq. 9 where \(JCS\) is the compressive strength of the joint surface, which may equal 1/4th of the uniaxial compressive strength of the intact rock ( \(\frac{{\sigma }_{ci}}{4}\) ) (Sharma et al., 1999 ). \({\varphi }_{b}\) and \(JRC\) are the basic friction angle and Joint roughness coefficient of the joints, respectively, and their respective values were obtained from the standard Table 1 proposed by Barton and Choubey (1977), to be on the safer side the lower boundary values were taken. Further, the dry and wet \({\varphi }_{b}\) values were determined based on the groundwater condition at the site. An effort was also made to compute the minimum normal stress acting on the surface of the joints by using the following relation: \({\varphi }_{b}+JRC\left(\frac{JCS}{{\sigma }_{n}}\right) = {70}^{0}\) …….. Eq. 10 where \({\varphi }_{b}\) is the basic friction angle, JRC - Joint roughness coefficient, \(JCS\) is the compressive strength of the joint surface, and \({\sigma }_{n}-\) normal stress acting on the surface of the joints. In addition to the shear strength parameters of the joints, their stiffness is required as an input for the numerical model. The normal (K n ) and shear stiffness (K s ) of joints can typically be determined through laboratory tests by using the guidelines suggested by Kulatilake et al. ( 2016 ). However, in the absence of laboratory tests, Kulatilake et al. ( 2016 ) proposed that the joint normal and shear stiffnesses are linear functions of the applied normal stress ( \({\sigma }_{n}\) ). As discussed, the normal stiffness, in GPa/m, can be approximated to be between 10 and 20 times the applied normal stress, expressed in MPa. Similarly, the shear stiffness expressed in GPa/m can be estimated to be 0.65–2.15 times that of the applied normal stress expressed in MPa. The approximated joint parameters and computed stiffness values for each Geotechnical unit are listed in Table 4 . Back–analysis for Some Parameters To determine some of the intact rock properties, a back-analysis procedure was performed. For this purpose, the available estimated rock mass mechanical properties of the corresponding rock mass were utilized. Several published studies have compared the properties of rock masses and intact rocks, and a summary of these studies is presented as follows: Owing to the presence of discontinuities, Kulatilake et al. ( 2004 ) proposed that the Poisson’s ratio of the rock mass may increase by 21% in comparison to that of intact rock; Huang et al. ( 2017 ) determined that the tensile strength of the rock mass, as estimated from the Hoek and Brown criterion is approximately 24 to 35% of the tensile strength of the intact rock. Specifically, Wu and Kulatilake ( 2012 ) concluded that the tensile strength of the rock mass can reach approximately 35% of tensile strength intact rock; and Further, Shreedharan & Kulatilake ( 2016 ) indicated that the estimated cohesion value of the rock mass may be between 35 to 45% of that of the intact rock’s cohesion value. Table 4 Useful joint parameters in each Geotechnical unit Discontinuity type \({\varphi }_{b}\) \(JRC\) \({\sigma }_{ci}\) \(JCS\) \({\sigma }_{n}\) Eq. 10 \(\left(\frac{ \tau }{{\sigma }_{n}}\right)\) K n K s ( 0 ) (MPa) (MPa) (MPa) ( 0 ) (GPa/m) (GPa/m) Joints 1* 35 2 207.0 51.7 1.63 38.0 10* \({\sigma }_{n}\) 2.15* \({\sigma }_{n}\) Joints 2 31 2 155.6 38.9 1.23 34.0 10* \({\sigma }_{n}\) 2.15* \({\sigma }_{n}\) Joints 3 31 4 200.0 50.0 8.88 34.0 10* \({\sigma }_{n}\) 2.15* \({\sigma }_{n}\) \({\varphi }_{b}\) - basic friction angle, JRC - Joint roughness coefficient, \({\sigma }_{ci}\) – intact uniaxial compressive strength \(JCS\) is the compressive strength of the joint surface, \({\sigma }_{n}-\) normal stress acting on the surface of the joints, K n - normal stiffness, and K s - shear stiffness * 1,2, and 3 indicate joints within the GU1, GU2, and GU3 units, respectively Based on the aforementioned discussion, in this study, the tensile strength of the intact rock and cohesion values were set to 2.3 times that of the corresponding rock mass values. The values for Poisson’s ratio of intact rock were set to be 0.83 times that of the Poisson’s ratio values of the rock mass. However, the angle of the internal friction for intact rock was directly taken from the corresponding rock mass values, as recommended by Kulatilake et al. ( 2004 ) and Shreedharan and Kulatilake ( 2016 ). The estimated results are presented in Table 5 . Development of the Numerical Models In the present study, the 3DEC version 5.2 software package (Itasca 2016) was employed to simulate and perform the stress–strain analyses. The length, width, and height of the selected cubes were 50 m × 50 m × 50 m, respectively. The origin of the models (0, 0, 0) was made to be at the center of the cubes. The models were prepared to be -25 to 25 long along the x– and y–axes and − 25 to 25 tall along the z–axis (Fig. 4 ). Furthermore, the positive x– and y–axes of Models I and II coincided with the southeast (SE) and northeast (NE) directions of the field conditions, respectively, whereas the positive x– and y–axes of Model III coincided with the southwest (SW) and southeast (SE) directions. The z–axis represents the vertical direction in all the models. Table 5 The back-analyzed results obtained for intact rocks of each Geotechnical unit Rock mass Properties Values Geotechnical Units Multiplying factor Intact rock Values Cohesion ( MPa ) 1.69 GU1 3.89 1.42 GU2 2.3 3.27 3.98 GU3 9.16 0.2 GU4 0.46 Friction angle ( 0 ) 65.3 GU1 65.3 57.6 GU2 1 57.6 58.7 GU3 58.7 35.7 GU4 35.7 Poisson’s ratio 0.28 GU1 0.232 0.30 GU2 0.83 0.249 0.26 GU3 0.214 0.33 GU4 0.276 Tensile strength ( MPa ) 0.29 GU1 0.67 0.08 GU2 2.3 0.18 0.46 GU3 1.06 0.001 GU4 0.002 The proposed circular tunnel geometry with a diameter of 5 m was used. Three models were constructed by considering the representative Geotechnical units along the proposed tunnel alignment. Figures 1 and 2 were used to locate the modeled areas. Accordingly, Model I represents the area around chainage 0 + 600 (Fig. 2 ), and the coordinate of 368000 mE, and 911027.9 mN (Fig. 1 ). This model comprises the GU1 and GU4 units. Model II was chosen around chainage 10 + 800, and the coordinate of 364173.4 mE, and 909885.6 mN. This model includes only the GU2 unit. Similarly, Model III was chosen around chainage 15 + 600, and coordinate of 353721.4 mE, and 909170.3 mN. This model is composed of only the GU3 unit. In Model I, the GU4 unit was set to be 30 m thick (from y = -15 to 15 in the model), inclined and planar with an approximate dip direction of N64 o E and a dip of 79 o . Furthermore, only those discontinuities expected have a greater influence on the mechanical response of the model should be included (Chen and Zhu 2022 ; Itasca 2016). Therefore, for modeling purposes, it was assumed that the recorded dominant joint sets were considered to have a greater influence on the mechanical response of the rock mass under the applied in-situ stress conditions. In addition, in Model I the contacts between the fault zone GU4 and GU1 Geotechnical unit are marked by the presence of discontinuity interfaces (Fig. 4 a); thus, these planes were also considered a set of discontinuities. Instead of employing the joint inclusion approach of Kulatilake et al. ( 1993 ), the spacings of the discontinuity, measured in the field around the opening, were directly incorporated. Thus, the cubes were systematically divided into three distinct regions of influence, as shown in Fig. 2 d. The region around the tunnel opening (Region 1) contains the field–measured spacing of the joints as well as their orientations, as indicated in Table 6 . For the other two regions (Regions 2 and 3), the spacings were increased systematically, but the orientations remained the same as those of the field–measured values (Table 6 ). Further, the Coulomb slip constitutive model was used to represent the behavior of the joint and discontinuity interfaces. The values of the mechanical properties of the various discontinuities present in the different Geotechnical units and the discontinuity interfaces used in the Models are presented in Table 7 . The joints considered in the Models were assumed to be smooth and open with occasional infillings; therefore, their cohesion and tensile strength were taken as 0 MPa (Wang et al. 2012 ; Xing et al. 2017 , 2018 ). Furthermore, these joints were initially kept elastic to avoid movement during cycling and achieve gravitational equilibrium (Itasca 2020). In the case of fictitious joints that appeared during the initial preparation of representative models, i.e., during region classification, the TUNNEL command in 3DEC was used to avoid undesired effects due to artificial joints. Since the discontinuity interfaces were assumed to be well-bonded surfaces, their mechanical parameters ( E i , C , ϕ, and \({V}_{r}\) ) were first estimated by averaging the values between the two units — GU1 and GU4. Later, some of these parameters ( E i , and \({V}_{r}\) ) were put into empirical relations provided by Kulatilake et al. ( 1992 ), where the average values of 0.01 and 2.5 were assigned to Eq. (11) and Eq. (12), respectively. Such average values were commonly used previously by Xing et al. ( 2017 , 2018 ), Kulatilake et al. ( 1992 ), and Kulatilake et al. ( 1993 ). Table 6 Joint orientations and spacings within respective regions in the Models Regions in the Model Model number Joint sets Discontinuity Orientations Original mean spacing The mean spacing used The thickness of the regions Dip direction Dip ( 0 ) ( 0 ) (m) (m) (m) 1 N 253 72 I 2 N 046 81 0.2 4.0 3 N 329 82 1 N 157 80 Region 3 II 2 N 035 79 0.56 4.0 9.0 3 N 202 69 1 N 022 86 III 2 N 231 81 1.2 4.0 3 N 078 78 1 N 253 72 I 2 N 046 81 0.2 2.0 7.5 3 N 329 82 1 N 157 80 Region 2 II 2 N 035 79 0.56 2.0 8.5 3 N 202 69 1 N 022 86 III 2 N 231 81 1.2 1.2 7.5 3 N 078 78 1 N 253 72 I 2 N 046 81 0.2 0.40 6.0 3 N 329 82 1 N 157 80 Region 1 II 2 N 035 79 0.56 0.60 5.0 3 N 202 69 1 N 022 86 III 2 N 231 81 1.2 1.2 6.0 3 N 078 78 The shear modulus ( \({G}_{r})\) of the intact rock (blocks) can be obtained from Young’s modulus and Poisson’s ratio. \(\frac{{G}_{r}}{Ks} =0.008-0.012\) (GPa/m) …….. Eq. 11 \(\frac{Kn}{Ks}=2-3\) (GPa/m) …….. Eq. 12 where Ks and Kn are the joint shear and normal stiffnesses, respectively. Table 7 Values of the mechanical properties of various discontinuities, present in different Geotechnical units and the interfaces, used in the Models Discontinuity type Normal stiffness Shear stiffness Friction angle Cohesion Tensile strength (GPa/m) (GPa/m) ( 0 ) (MPa) (MPa) Joints in GU1 16.3 3.51 38.0 0 0 Joints in GU2 12.3 2.65 34.0 0 0 Joints in GU3 88.8 19.1 34.0 0 0 Interfaces between GU1 and GU4 4010.5 1604.2 50.5 2.1 0.34 The values used to represent the intact rock mechanical properties in the models are presented in Table 8 . For intact rock the built–in constitutive model used was Mohr–Coulomb plasticity model. These blocks were treated as deformable blocks. For the Models, depending on the region of influence, different mesh sizes were implemented. The inner-most region (Region 1), which corresponds to the volume of the rock mass surrounding the opening, was zoned using the constant-strain elements of a finer edge length. In contrast, the outer regions (Regions 2 and 3) were zoned with coarser edge lengths. Table 8 Values of the mechanical properties of intact rock in various Geotechnical units used in the Models Geotechnical unit Density Bulk modulus Shear modulus Friction Cohesion Tensile strength (kg/m 3 ) (GPa) (GPa) ( 0 ) (MPa) (MPa) GU1 2590 44.27 29.37 65.3 3.75 0.67 GU2 2450 35.95 21.81 57.6 3.29 0.19 GU3 2860 40.81 28.83 58.7 9.15 1.06 GU4 2320 0.10 0.050 35.7 0.46 0.002 The center points of the tunnels in Models I, II, and III were located at depths of ca. 90, 190, and 356 m below the ground surface, respectively. By taking an average density of 2700 kg/m 3 for the overburden lithology, the vertical stress (ZZ–stress in 3DEC) that was applied on the top of the Model has values equal to 1.8, 4.5, and 8.9 MPa for Models I, II, and III, respectively. Due to the nonavailability of measured in-situ horizontal stress in the area, deformation and stress analyses were carried out by utilizing the lower and upper bound Ko values [0.5, 2.0]. According to Hoek et al. ( 2005 ) for design purposes, these assigned lower and upper bound values of K 0 can be considered reasonable, particularly for areas where no in-situ stress measurements are available. Further, the fixed boundary was set to the base of the Models. For the other four faces of the cubes, first, depth-dependent increasing stress boundary conditions were applied. Then, to preserve the prescribed stresses and restrict the motion of the failed blocks, velocity boundary conditions were provided after the stress boundary conditions affected the same boundary corners. Figure 5 a illustrates the boundary conditions that were used during the modeling process. Simulating exact field excavation during modeling by 3DEC software is almost impossible because of its complexity (Shreedharan and Kulatilake 2016 ). However, during the present study attempts were made to simulate the excavation sequence. For this purpose, the rock mass to be excavated was divided into different blocks. The divided blocks were subsequently grouped into different excavation advance steps (Fig. 5 b). Therefore, in the present study, the circular tunnels were presumed to be numerically excavated in six advance steps (Fig. 5 b) by considering the full-face tunneling method. This process may help to monitor the trend of the rock mass deformation and the stress redistribution possibly caused by stepwise excavation rather than excavating the entire length of the tunnel (50 m) at once. Results and Discussion The present study was carried out performing stress analyses through three models that were considered representative of four different types of rock mass at different depths, utilizing a range of Ko [0.5, 2.0] as recommended by Hoek et al. ( 2005 ). We evaluated the displacement, failure mode, and distribution of failed blocks in different parts of the tunnel under investigation through comparing the results from various cases, thereby gaining valuable insights for rock mass support recommendations. A comprehensive examination of graphic output, on a case-by-case basis, was performed. It should be noted that all the representative figures and values obtained were taken on the y = 0 plane, except for the case of the GU1 unit in Model I, where the results were taken on the y = -23 plane. Conventionally, in 3DEC, negative values of stress and deformation indicate compression conditions. Validation Using Basic Numerical Modeling Results It is a commonly followed practice to validate numerical models using basic models before utilizing them for any subsequent analyses (e.g., Shreedharan and Kulatilake 2016 ; Wang et al. 2012 ; Feng et a. 2019). For the present study, the basic models, which do not consider joints, were assessed basically for validation purposes. The interfaces between Geotechnical units GU1 and GU4 were included as they were considered as well bonded with higher mechanical properties. Before the tunnel excavation, the applied input vertical in-situ stress of the models was assessed and it was observed that the vertical in-situ stress increased linearly from the top to the bottom of the model, and the top and bottom far-field ZZ–stress perfectly coincided with the prescribed and expected stresses at the model boundaries. After performing the validation before excavation, using the same models the next validation process was carried out following the tunnel excavation. Under this, the validation was performed using the XX– and ZZ–stress distributions. Figure 6 shows the symmetric XX– and ZZ–stress distributions for each model. As shown in Fig. 6 a–c, all the XX–stress distributions are minimum around the sidewalls and they peak around the roof and floor of the tunnels. On the other hand, in Fig. 6 d–f, the ZZ–stress showed minimum stress distributions around the roof and floor, and, as expected they peaked around the sidewalls. As stated by Shreedharan and Kulatilake ( 2016 ), when subjected to excavation, the two sidewalls of the opening experienced greater compressive ZZ–stress than did the roof and floor of the opening. Meanwhile, the roof and floor of the opening experience higher compressive XX–stress as compared to the sidewalls. To summarize, the unexcavated models demonstrated consistency between the far-field ZZ-stress in the prepared models and the empirically calculated results at the model boundary. And, the XX – and ZZ – stress distributions surrounding the excavated openings were consistent with expectations that the stresses redistribute as a result of vertical and horizontal stress adjustment through the ground arching mechanism following the removal of materials (Chen et al. 2011 ). Therefore, all these results are in confirmation with the previous findings (e.g., Xing et al. 2017 ; Li et al. 2018c ; Feng et al. 2019 ) indicating that the applied inputs are transferred correctly to the models. This may further be noticed in later sections 4.2 and 4.3 (deformation and stress analyses where the applied inputs are transferred correctly to the models). The Distribution and Failure Mode of Failed Blocks of the Tunnels In the present study, by varying Ko from 0.5 to 2.0, an attempt was made to study the possible distribution and mode of failure of failed blocks in each tunnel. Thus, as suggested by Shreedharan and Kulatilake ( 2016 ), the considered failed blocks were those that had reached their residual strength in the past or the present (now), either in shear or tension. The representative figures for the failure zone in the tunnels of each Geotechnical unit are shown in Figs. 7 , 8 , and 10 . From these figures, in the legend section, the suffixes ‘p’ and ‘n’ in shear-p, shear-n, tension-p, and tension-n represent ‘past’ and ‘now’, respectively. The corresponding interpretation is that regions in the rock mass that are occupied by shear-p or shear-n have experienced shear failure in the past or now. Similarly, the regions in the rock mass occupied by tension-p or tension-n have experienced tension failure in the past or the present (now). After excavation in the GU1 unit (treated as a discontinuum medium), the failure of blocks may initiate around the roof and the floor of the tunnel; however, blocks on the left sidewall and the right haunch of the tunnel may remain undetached (Fig. 7 a). With increasing Ko (Fig. 7 b), failures around the tunnel periphery may become more intense, and the joint set, i.e., Join set 1, around the right shoulder may act as the line of detachment. This tendency may become more obvious for a Ko value equal to 2.0 (Fig. 7 c). Similarly, in the GU2 unit (also treated as a discontinuum medium) failed blocks may initially appeared everywhere around the periphery of the tunnel (Fig. 7 d). With increasing Ko (Fig. 7 e), the failed blocks in the roof and floor generally tend to follow a preferential direction imposed by the orientation of Joint Set 2, and the blocks on the left shoulder and the right haunch of the tunnels may remain undetached. With a further increase in the value of Ko (Fig. 7 f), the tendency of blocks to fail along the orientation of this joint set became obvious around the tunnel opening, and this phenomenon may further intensify in areas that were previously undetached. The failed blocks in this rock mass suffered from tensile failure; however, a minor number of blocks in the GU2 unit were likely to undergo shear failure at a Ko value equal to 2.0. For both rock mass, a large number of discontinuities were superimposed—three closely spaced joint sets in each of the rock mass under different stress conditions—and it was observed that the distribution of the failure zone in these rock mass was affected by the presence of particular joint sets. Consequently, joint set 1 in the GU1 unit and joint set 2 in the GU2 unit provided an anisotropic nature to their corresponding rock mass mostly when the value of Ko was greater than or equal to 1.0. Therefore, the assumption of modeling the anisotropy of these rock mass by superimposing a large number of discontinuities in the models is worthwhile and may be provided results that can compare well with more traditional anisotropic solutions (cf., Marinos et al. 2007 ). Moreover, considering these joint sets in the area would provide more efficient support measures (Ghorbani et al. 2020 ; Jia and Tang 2008 ). After the excavation in the GU3 unit (Fig. 8 a), it was observed that small block detachments occurred around the left and the right haunches of the tunnel. With increasing Ko (Fig. 8 b), the left sidewall of the tunnel experienced local failure, while the remaining portions of the tunnel exhibited relatively higher stability. With a further increase in the value of Ko (Fig. 8 c), local failures began to emerge around the left and the right haunches of the tunnel. This may be ascribed to the redistribution and concentration of the maximum principal stress around the haunches of the tunnel due to material heterogeneity, which is similar to the findings of Xing et al. ( 2017 ) and Feng et al. ( 2019 ). Despite these failures, the right shoulder and roof of the tunnel achieved a stable state as the maximum principal stress concentration around these areas was reduced significantly. According to the observations of Xing et al. ( 2017 ), even if Ko is higher, large deformation cannot be observed at locations around openings that are far from areas of maximum principal stress concentration. In this tunnel, the failed blocks underwent tensile failure across all the cases. To gain insight into the cause, a block-size assessment was carried out using 3DEC as it is proven accurate and reliable means to estimate rock block volume (Koulibaly et al. 2023 ), and the volumes of 68 blocks around Region 1 (Fig. 9 b) were recorded. However, 13 blocks had to be excluded from the analysis because they were significantly influenced by the boundaries of the region. By examining the moving average curve (Fig. 9 a), it was observed that approximately 75% of the blocks are of large and very large block volumes. As a result, these blocks could have enhanced the stability of this rock mass. Furthermore, compared with tunnels running through the GU1 and GU2 units, it is observed that the results almost align with the suggestion of Yeung and Leong ( 1997 ) as deeper tunnels tend to exhibit greater stability because of their better confinement, provided that the intact rock is hard, and the tunnel depth is relatively deeper. However, it is important to note that this type of tunnel could cause local failures as they are subjected to higher stress levels (Yeung and Leong 1997 ), and the joints are of higher dip angle (Feng et al. 2019 ). After excavation in the GU4 unit (treated as an equivalent continuum medium), the failed blocks may have appeared around the tunnel periphery. The thickness of the failure zone is different, i.e., it is much thicker around the sidewalls than the roof and the floor (Fig. 10 a). With an increase in Ko (Fig. 10 c), the zone of the failed block around the tunnel periphery became more uniformly distributed in terms of thickness. With a further increase in the value of Ko (Fig. 10 e), thicker failure zones appeared around the roof and the floor of the tunnel. It is important to note that this change in the thickness direction of the failure zone is associated with the rotation direction of the maximum principal stress (Figs. 10 b, d, and f). Furthermore, it is evident that at a value of Ko equal to 0.5, the sidewalls experienced shear failure, and tension failures were more common on the roof and the floor of the tunnel. As the value of Ko is increased further (Ko = 2.0), a significant number of failed blocks may primarily exhibit shear failures. However, the failed blocks located in the immediate vicinity of the sidewalls may appear to suffer from tensile failure. This significant change in the failure mode may also be explained by the fact that as the maximum principal stress appears on the sidewalls, stress relaxation occurs on the roof and the floor, and vice versa. This stress relaxation phenomenon may lead the blocks to experience increased tensile stresses and fail in tension failure (Yang et al. 2017 ). Meanwhile, the concentration of stress in the other part of the tunnel may lead to higher shear stresses and subsequent shear failures in the blocks located in that area. The observed change in failure mode in the GU4 unit tunnel, as indicated by 3D models, is consistent with a similar phenomenon observed in the horseshoe-shaped tunnel studied by Hao et al. ( 2022 ) using 2D models. As a result, understanding the status of failed blocks for specific parts of the tunnel may help in designing support systems that can control and contain the specific failure mechanism and may possibly prevent collapse (Yang et al. 2017 ). Displacements of Tunnel Opening Under Varying Lateral In-Situ Stress The displacements of the roof, floor, and sidewalls of the tunnels that run through four different Geotechnical units were studied using a range of Ko values (from 0.5 to 2.0). Figure 11 shows the displacement results for the four tunnels, represented by the different color of lines, and in the legend section ‘SW’ stands for ‘sidewall’. The Z-displacements of the roof and floor in the GU1, GU2, and GU3 units (Fig. 11 a) exhibited a gradual reduction and eventually became insignificant as the Ko value increased from 0.5 to 2.0. However, as can be seen, the Z–displacement lines of the floor and roof of the GU4 unit exhibited three significant changes with increasing Ko: (i) a linear decrement from 0.5 to 1.0, (ii) a slight increment from 1.0 to 1.5, and (iii) a steeper increment from 1.5 to 2.0. During the initial phase, the reduction in vertical deformation was accompanied by an increase in horizontal deformation as Ko was increased to 1.0, representing a lower level of stress concentration stage (Feng et al. 2019 ) and the occurrence of localized failure (Zhao et al. 2020 ). The next stage was characterized by an increase in both deformations as Ko was increased to 1.5. At this stage, a significant amount of released strain energy must exist to the roof and floor of the tunnel as higher Ko was applied (Feng et al. 2019 ), which could be the reason why the increase in horizontal stress induced the increase in vertical deformation. In the last stage, there was a substantial increase in horizontal deformation along with a rapid increase in vertical deformation. This indicates that the rock mass was still in the strain energy release phase. However, at this stage, the released energy could have been of a greater magnitude, considering the significant increase in both deformations. This finding aligns with the findings of Feng et al. ( 2019 ), who reported that increasing Ko beyond 1.0 leads to more strain energy release. In another instance, Fig. 11 b shows that most of the X–displacements on the sidewalls of each tunnel increase linearly from Ko = 0.5 to 2.0. The only exception is X–displacement on the sidewalls of GU3, which remained comparatively unchanged, and it depicted a decrement from Ko = 0.75 to 1.5. For the tunnel in the GU4 unit (represented by green and brown colors), which represents a fault zone, both the vertical (Z–displacement) and horizontal (X–displacement) convergences exhibited significantly greater values than did the other three tunnels. As Ko increases from 0.5 to 2.0, a relative shift in convergence from a higher vertical to a higher horizontal convergence is observed. Hence, the horizontal convergence increases gradually, eventually surpassing the vertical convergence at Ko = 1.25. With a subsequent increase in Ko from 1.0 to 2.0, both convergences experienced a considerable rise, with the horizontal convergence surpassing the vertical convergence. For example, at Ko = 2.0, the horizontal convergence almost tripled (2.9 to 7.5 cm) and the vertical convergence increased by 47% (3.4 to 5.0 cm). This shows that the strain energy released to the roof and floor of the tunnel was lower than that released to the sidewalls because the applied horizontal stress was higher than the vertical stress, which is consistent with the findings of Yang et al. ( 2017 ) and Xing et al. ( 2017 ). Similarly, for the GU2 unit (represented by red and yellow colors), the horizontal convergence exceeded the vertical convergence beyond Ko = 0.75; however, for the GU1 unit (represented by black and purple colors), the horizontal convergence exceeded the vertical convergence across all the cases, which can be attributed to the nonuniform distribution of the stress field (Fan et al. 2020 ). These observed exceedances in convergence could provide valuable insight into decision-making, particularly for optimized support placement under the right field stress conditions (Basarir et al. 2005 ; Xing et al. 2017 ). Conclusion To ensure the safe excavation of a tunnel and design appropriate support systems, it is crucial to assess the deformation and potential block failure around the tunnel opening. In the present study, a systematic failure and deformation assessment of the waterway tunnel of the Wabe Hydropower Project in central Ethiopia was conducted using a 3D discontinuum numerical model called 3DEC. The proposed 5 m diameter tunnel under study is planned through four different geotechnical units. Each of these geotechnical units was modeled under three numerical models, considering locations where the tunnel encounters different Geotechnical units. Thus, Model I represents Upper basalt with N253/72, N046/81, and N329/82 joint sets of 0.2 m spacing (GU1) alongside an inclined 30 m thick fault zone (GU4) at 90 m depth. Models II and III represent Middle basalt with N157/80, N035/79, and N202/69 joint sets of 0.56 m spacing (GU2) at 190 m depth and Lower basalts N 022/86, N 231/81, and N 078/78 joint sets of 1.2 m spacing (GU3) at 356 m depth, respectively. The distribution of failure zones around the tunnels was studied through stress analyses, which involved varying Ko values between 0.5 and 2.0. The modeling results revealed that the presence of particular joint sets had a noticeable impact on the distribution of failed blocks, more obvious when Ko > 1.0. The failed blocks in tunnels under the GU1 and GU2 units did distribute along a direction imposed by the joint sets with inclinations of N253/72 and N035/79, respectively. This suggests that these joint sets could induce anisotropic conditions in their corresponding rock mass during tunneling. Owing to better confinement, the presence of large and very large blocks around the opening, and the presence of high-angle dipping joints, the tunnel in the GU3 unit is stable with some local failures around the tunnel periphery. For tunnels in the GU4 unit, a significant concentration of failed blocks occurs in association with the maximum principal stress direction, despite the occurrence of failures throughout the tunnel periphery. The possible mode of failure in these tunnels was assessed and observed that all blocky rock mass along the alignment — the GU1, GU2, and GU3 units — underwent tensile failure without any change in the mode of failure in all the cases. As a result, it can be expected that tunneling in these rock mass could cause blocks to fail in a tensile mode of failure. Tunneling in the GU4 unit (the fault zone) caused dominant blocks to fail in a shear mode of failure, however both shear and tensile modes of failure could coexist. At Ko = 0.5, the sidewalls experienced shear failure, and tension failures were more common on the roof and the floor. Subsequent increase in Ko to 1.0 resulted in a significant number of failed blocks primarily exhibited shear failures, however, the failed blocks near the sidewalls appeared to suffer from tensile failure. In this case, determining the mode of failure at the particular locations should be made based on the specific site conditions encountered. Furthermore, stress analyses were conducted to investigate the possible vertical and horizontal displacements of the tunnels. The simulation results indicated that tunnels in the GU4 unit, increasing Ko led to a gradual increase in the horizontal displacement and an initial decrease, followed by a gradual increase and a subsequent rapid increase in the vertical displacement. In other blocky rock masses, the vertical displacement gradually decreased, whereas most horizontal displacements increased linearly with higher Ko values, except for the GU3 unit —which remained unaffected. It can be concluded that tunneling in the fault zone could lead to greater horizontal and vertical convergences, with horizontal displacement exceeding vertical displacement. However, tunnels in the GU1 and GU2 units could primarily be affected by horizontal displacement rather than vertical one. The present study has shed a light on the necessity of a support system design for controlling large displacements, specific types of failure modes, and directional failures in the GU1, GU2, and GU4 units. As a result, when designing support measures, it is crucial to consider the anisotropic behavior of the rock mass in the GU1 and GU2 units. This implies that support systems should be oriented intersecting the joint sets with inclinations of N253/72 in the GU1 unit and N035/79 in the GU2 unit. In addition, the simulation results clearly demonstrate that if Ko is less than 1.0 in the tunnels through the GU4 unit, there is a need for longer and dense support systems at sidewalls, targeting the shear mode of failure, whereas shorter and dense support systems at roof and floor, targeting tensile mode of failure. On the other hand, if Ko exceeds 1.0, longer and dense support systems at the roof and floor are required, targeting the shear mode of failure mechanisms, whereas shorter and dense support systems at the sidewalls, targeting the tensile mode of failure. Generally, it is expected that by incorporating these recommendations, a comprehensive and effective rock mass support strategy can be implemented during the construction of these tunnels. Declarations Conflict of Interest On behalf of all authors, the corresponding author states that there is no conflict of interest. Author Contribution Material preparation, data collection and analysis were performed by Mesay and Bayisa. The first draft of the manuscript was written by Mesay and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript. Acknowledgments This study was funded by the School of Earth Sciences of Addis Ababa University. We also extend our utmost gratitude to the Ethiopian Ministry of Water and Energy for their invaluable support in providing the data for this study. Data Availability Data sets and written commands generated during the current study are available from the corresponding author upon reasonable request. References Barla G, Barla M (2000) Continuum and discontinuum modeling in tunnel engineering. Min Geol Pet Eng Bull. 12:45–57. https://hrcak.srce.hr/file/8108 . Barton N (1973) Review of a new shear strength criteria for rock joints. Eng. Geol. 7: 287–330. https://doi.org/10.1016/0013-7952(73)90013-6 . 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Rock Mech Rock Eng 49:1903–1922. https://doi.org/10.1007/s00603-015-0885-9 . Vasarhelyi B (2009) A POSSIBLE METHOD FOR ESTIMATING THE POISSON’S RATE VALUES OF THE ROCK MASS. Acta Geod. Geoph. Hung., Vol. 44(3), pp. 313–322. https://doi.org/10.1556/AGeod.44.2009.3.4 . Wang X, Kulatilake PHSW, Song WD (2012) Stability investigations around a mine tunnel through three-dimensional discontinuum and continuum stress analyses. Tunn Undergr Space Technol 32:98–112. https://doi.org/10.1016/j.tust.2012.06.003 . Wu Q, Kulatilake PHSW (2012) REV and its properties on fracture system and mechanical properties, and an orthotropic constitutive model for a jointed rock mass in a dam site in China. Int J Comput Geotech 43:124–142. https://doi.org/10.1016/j.compgeo.2012.02.010 . Xing Y, Kulatilake PHSW, Sandbak LA (2017) Rock mass stability investigation around tunnels in an underground mine in USA. Geotech Geol Eng 35:45–67. https://doi.org/10.1007/s10706-016-0084-9 . Xing Y, Kulatilake PHSW, Sandbak LA (2018) Effect of rock mass and discontinuity mechanical properties and delayed rock supporting on tunnel stability in an underground mine. Engineering Geology, 238, 62–75. https://doi.org/10.1016/j.enggeo.2018.03.010 . Yang SQ, Chen M, Jing HW, Chen KF, Meng B (2017) A case study on large deformation failure mechanism of deep soft rock roadway in Xin'An coal mine, China. Engineering Geology, 217, 89–101. https://doi.org/10.1016/j.enggeo.2016.12.012 . Yeung MR, Leong LL (1997) Effects of joint attributes on tunnel stability. International Journal of Rock Mechanics and Mining Sciences, 34(3–4), 348-1. https://doi.org/10.1016/S1365-1609(97)00286-4 . Zhao H, Liu C, Huang G, Yu B, Liu Y, Song Z (2020) Experimental investigation on rockburst process and failure characteristics in trapezoidal tunnel under different lateral stresses. Construction and Building Materials, 259, 119530. https://doi.org/10.1016/j.conbuildmat.2020.119530 . 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Kassaw","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA/klEQVRIiWNgGAWjYDAD9gYg8YGNGcQ2IEaDAQPPAQYGxhkILQS1QbQw8xCjRbe9/eFnHoY/cjzsvQ8/25RZJzawN2+TYKj4g1OL2ZkzxtI8DAbGPDzHjaVzzqUnNvAcK5NgOIPbFrMbOQwgLYn7JdIYpHPbDic2SOSYSTC24dFy//nj30At9T3yz5h/W4K0yL8BavmHzxYGM5AtCTwSbGzSjGBbeIBaGvBoOZNjZjnHwNiwhyeNzbLnXLpxG09asUXCMWPcWo4ff3zjTYWcPA/7MeYbP8qsZfvZD2+88aFGDqcWEGDiQXYFG4hIwKsBGOk/CCgYBaNgFIyCEQ4ArNlKJt3JAwAAAAAASUVORK5CYII=","orcid":"","institution":"School of Earth Sciences, Addis Ababa University","correspondingAuthor":true,"prefix":"","firstName":"Mesay","middleName":"","lastName":"Kassaw","suffix":""},{"id":273673584,"identity":"942001e7-4b5a-45f2-a889-1575c485829e","order_by":1,"name":"Bayisa Regassa","email":"","orcid":"","institution":"School of Earth Sciences, Addis Ababa University","correspondingAuthor":false,"prefix":"","firstName":"Bayisa","middleName":"","lastName":"Regassa","suffix":""},{"id":273673585,"identity":"9592fc1b-d9d8-4fbb-ba53-a5eaaf0fd839","order_by":2,"name":"Tarun Raghuvanshi","email":"","orcid":"","institution":"Civil Engineering Department, Graphic Era Hill University","correspondingAuthor":false,"prefix":"","firstName":"Tarun","middleName":"","lastName":"Raghuvanshi","suffix":""},{"id":273673586,"identity":"73dc7251-c611-49b1-a472-c2cc729fe825","order_by":3,"name":"Mamo Methe","email":"","orcid":"","institution":"School of Earth Sciences, Addis Ababa University","correspondingAuthor":false,"prefix":"","firstName":"Mamo","middleName":"","lastName":"Methe","suffix":""}],"badges":[],"createdAt":"2024-02-14 14:08:30","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-3956277/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3956277/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":51410927,"identity":"cf4cda99-d21e-47fd-8271-4edc69187059","added_by":"auto","created_at":"2024-02-21 05:04:21","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":207422,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eLocation map of the project area\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"image1.png","url":"https://assets-eu.researchsquare.com/files/rs-3956277/v1/3fb9587f2464189d42372333.png"},{"id":51410922,"identity":"2c28d25c-8b63-4837-a121-2442a16b7965","added_by":"auto","created_at":"2024-02-21 05:04:21","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":211090,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eThe geological cross-section along the proposed tunnel alignment\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"image2.png","url":"https://assets-eu.researchsquare.com/files/rs-3956277/v1/c4036d93a774cb7e0208d38f.png"},{"id":51410930,"identity":"9b6a495d-22f0-44f5-9abb-bc1b930d250a","added_by":"auto","created_at":"2024-02-21 05:04:22","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":1033374,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eDensity plot of discontinuity poles and attitudes of the dominant joint sets in (a) the GU1 unit, (b) the GU 2 unit, and (c) the GU3 unit\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"image3.png","url":"https://assets-eu.researchsquare.com/files/rs-3956277/v1/98c21c673d4a7633ed2a8eb9.png"},{"id":51411579,"identity":"2db52525-ff38-43fb-8fda-518f1475b583","added_by":"auto","created_at":"2024-02-21 05:12:21","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":717859,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eRepresentative numerical models of (a) Model I, (b) Model II,\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e(c) Model II, and (d) Considered different regions of influence\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"image4.png","url":"https://assets-eu.researchsquare.com/files/rs-3956277/v1/7ae76360dd7a9a527e905328.png"},{"id":51410923,"identity":"362ed5fa-90d6-42ee-81f6-5346a252cdd1","added_by":"auto","created_at":"2024-02-21 05:04:21","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":332517,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eIllustrations to represent the: (a) boundary condition and\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e(b) Sequences of excavations used during stress analyses\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"image5.png","url":"https://assets-eu.researchsquare.com/files/rs-3956277/v1/b0b4579a372d7d6142a26d44.png"},{"id":51410921,"identity":"e73aa853-ad31-4d76-a0c2-1a16a86cbd30","added_by":"auto","created_at":"2024-02-21 05:04:20","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":2498684,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eXX – and ZZ - Stress distributions (in Pa) after excavation for the basic models on the Y = 0 plane\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"image6.png","url":"https://assets-eu.researchsquare.com/files/rs-3956277/v1/0567f7a12ae8982a340ba10a.png"},{"id":51410925,"identity":"807897ce-0018-410a-a6f1-7558939a1dd0","added_by":"auto","created_at":"2024-02-21 05:04:21","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":2085185,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eFailed blocks’ status in GU1 and GU2 units at different Ko values\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"image7.png","url":"https://assets-eu.researchsquare.com/files/rs-3956277/v1/b7de7f64ed63e767faf10dc9.png"},{"id":51410931,"identity":"9f956092-57d3-4f10-8f45-25200b1681d4","added_by":"auto","created_at":"2024-02-21 05:04:22","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":908236,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eStatus of failed blocks in GU3 unit at different Ko values\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"image8.png","url":"https://assets-eu.researchsquare.com/files/rs-3956277/v1/646d3a1d397f36698a466658.png"},{"id":51411581,"identity":"314d1c7c-c660-47bb-9f15-e044dc28bf7c","added_by":"auto","created_at":"2024-02-21 05:12:21","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":355553,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eBlock-size assessment: (a) moving average curve and\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e(b) Blocks around the tunnel in the GU3 unit\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"image9.png","url":"https://assets-eu.researchsquare.com/files/rs-3956277/v1/df62af5a2d3200319888ed24.png"},{"id":51411580,"identity":"3cc31afa-7c52-46cf-a00c-939686109cc6","added_by":"auto","created_at":"2024-02-21 05:12:21","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":2318984,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eStatus of failed block in the GU4 unit (a, c, and e) and the rotation of\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003emaximum principal stress (b, d, and f) at different Ko values\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"image10.png","url":"https://assets-eu.researchsquare.com/files/rs-3956277/v1/bb94acd00daf42532437e221.png"},{"id":51410929,"identity":"698f37d9-5225-4018-9d80-839dfa7235e4","added_by":"auto","created_at":"2024-02-21 05:04:22","extension":"png","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":108266,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eDisplacements of different parts of the tunnel: (a) Z–displacement and (b) X–displacement\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"image11.png","url":"https://assets-eu.researchsquare.com/files/rs-3956277/v1/dacfeb7af8cab9d1b947c34f.png"},{"id":54245045,"identity":"4fad18c3-bbde-4d10-bc03-47b370792c30","added_by":"auto","created_at":"2024-04-07 14:38:02","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":12140705,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3956277/v1/9de2390f-c312-4cd3-9332-02efae652e8f.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"3D Numerical Analysis for Failure and Deformation Assessment of the Waterway Tunnel, Wabe Hydropower Project, Central Ethiopia","fulltext":[{"header":"Introduction","content":"\u003cp\u003eModel testing and numerical analysis are two broad approaches that are generally used to investigate tunnel deformation and failure mechanisms (Jia and Tang \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2008\u003c/span\u003e; Lohar et al. \u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). Numerical techniques are being developed to provide a more thorough understanding of challenging underground excavation problems (Marinos et al. \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e2007\u003c/span\u003e). Compared with other methods (e.g., physical modeling methods, empirical methods, and other closed-form solutions), numerical techniques have been proven to be a suitable tool for challenging conditions, such as the presence of discontinuities, the existence of high in-situ stresses, and the tunnel system layout (Jia and Tang \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2008\u003c/span\u003e; Kulatilake et al. \u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e2013\u003c/span\u003e; Wang et al. \u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e2012\u003c/span\u003e). Furthermore, three-dimensional (3D) modeling is necessary when the aforementioned challenging conditions cannot be adequately simplified on a single plane (Xing et al. \u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e2018\u003c/span\u003e) and when it is important to consider the actual stress path that is caused by excavation (Cai \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2008\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThe two most prevalent 3D numerical approaches in rock engineering are the continuum and discontinuum models (Raghuvanshi \u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). Discontinuum modeling tools (Discrete Element Methods) enable to treat the rock mass as a discontinuum or equivalent continuum medium. When a rock mass is strongly jointed with no preferred failure direction, it is appropriate to treat it as an equivalent continuum (Eberhardt \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2012\u003c/span\u003e). Several studies have used this assumption (e.g., Xing et al. \u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e2017\u003c/span\u003e, \u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Shreedharan and Kulatilake \u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e2016\u003c/span\u003e). The rock mass properties can thus be obtained by scaling down the intact rock properties using several empirical relations (Hoek and Brown \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e1997\u003c/span\u003e; Barla and Barla \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2000\u003c/span\u003e). However, if it is believed that the presence of discontinuities may significantly contribute to the instability of the structure in the rock mass, an explicit representation of the discontinuities is required (Regassa et al. \u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Itasca 2016). As a result, models could be able to account for assessing the rock mass anisotropy, failure modes, and large deformations (Marinos et al. \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e2007\u003c/span\u003e; Hao and Azzam \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2005\u003c/span\u003e; Huang et al. \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2013\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eDiscrete Element Methods (DEM) are considered suitable tools for the stability analysis of underground structures; however, they require accurate input data on the properties of rock mass (Marinos et al. \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e2007\u003c/span\u003e). Furthermore, data on the nature and orientation of discontinuities govern the directional effects that arise from the deformability and stability of the rock mass, together with the effects of intact rock properties (Wang et al. \u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e2012\u003c/span\u003e). As a result, it is generally essential to include the 3D effects of the discontinuities during the modeling process. An approach forwarded by Kulatilake et al. (\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e1993\u003c/span\u003e) is being followed to include joints in models when the number of joints is quite large (e.g., Wang et al. \u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e2012\u003c/span\u003e; Wu and Kulatilake \u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e2012\u003c/span\u003e). In this method, the first invariant of the fracture tensor is a combined measure of fracture size and intensity. Thus, by preserving the same orientation, increasing the fracture size, and reducing the fracture intensity to maintain the first invariant of the fracture tensor, a comparable fracture system can be generated.\u003c/p\u003e \u003cp\u003eIn Ethiopia, during the Gilgel Gibe I, II, and III hydropower development projects, tunnel collapse issues and support problems commonly and repeatedly occurred. These problems were primarily attributed to unexpected failure and unpredicted deformation conditions that were encountered during the construction stage, and it was realized that employing the Discrete Element Method (DEM) would have anticipated adverse conditions and possibly would have provided adequate mitigation measures prior to the occurrence of such problems (Kidane and Engida 2010). In this regard, previous researchers (e.g., Macklin et al. \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2012\u003c/span\u003e) have demonstrated the value of the DEM modeling technique in the prediction and mitigation of such problems prior to the commencement of projects. The tunnel at the Wabe Hydropower Project in Central Ethiopia is situated in a similar geological and hydrological setup as that of Gilgel Gibe I, II, and III; however, the designers have not employed DEM to simulate the tunnel excavation processes. Current investigations have been limited to topographical suitability assessments, slope stability evaluations based on the old Norwegian rule of thumb, and the kinematic checks conducted through exposed joints in slope sections (ECDSWC \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Dumesso 2020). Consequently, proceeding solely with these investigations for a tunneling program may likely result in unforeseen stability issues and other challenging conditions related to rock support. Thus, a comprehensive understanding of the deformation, failure distribution, and possible mechanisms involved in the project area is crucial for the design of appropriate support systems and may equally be important for ensuring safe excavations.\u003c/p\u003e \u003cp\u003eThis study aims to assess the distribution and mode of failure of the failed blocks, and displacement at various parts of the tunnel under study in the Wabe Hydropower Project. The proposed tunnel with a diameter of 5 m could encounter four Geotechnical units at different depths. To model the different geotechnical units, the \u003cem\u003e3DEC\u003c/em\u003e distinct element code (Itasca 2016) was utilized and three representative numerical models were developed. Thus, Model I represents Upper basalt with N253/72, N046/81, and N329/82 oriented joint sets of 0.2 m spacing (GU1) alongside an inclined fault zone (GU4) at 90 m depth. Models II and III represent Middle basalt with N157/80, N035/79, and N202/69 oriented joint sets of 0.56 m spacing (GU2) at ca. 190 m depth and Lower basalts N022/86, N231/81, and N078/78 oriented joint sets of 1.2 m spacing (GU3) at ca. 356 m depth, respectively. Thereafter, the influence region classification technique was introduced and models were systematically classified into three distinct regions of influence. This classification method allowed for the direct inclusion of a large number of joints, as measured in the field, into the area surrounding the tunnel openings. Subsequent stress analyses were performed to assess the distribution and failure mode of the failed blocks, as well as the displacement of the tunnel; these findings are discussed to gain valuable insights into future rock mass support recommendations.\u003c/p\u003e"},{"header":"The Project Area","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003eDescription of the Area\u003c/h2\u003e \u003cp\u003eThe Wabe Hydropower project area lies in the upstream catchment of the Omo-Gibe River Basin, located in the country's southwestern region adjacent to Kenya and the South Sudan international border. The study area is located approximately 161 km from Addis Ababa in central Ethiopia. The entire project area, which includes a reservoir area of approximately 15.06 km\u003csup\u003e2\u003c/sup\u003e and a 17.215 km long tunnel system, is situated at the transition between the northwestern plateau and the southwestern plateau volcanites. Geographically, the proposed tunnel alignment runs between UTM Zone 37 N coordinates; 368389mE, 911141mN (intake) and 351568mE, 909698mN (outlet) (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003eGeology and Engineering Geology\u003c/h2\u003e \u003cp\u003eThe entire project area is located along the Main Ethiopian Rift (MER) margin, which is a tectonically active continental rift margin with numerous parallel-stepping faults (Ebinger et al. \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e1993\u003c/span\u003e). The Precambrian crystalline basement, Eocene to Miocene volcanic rocks, Quaternary lacustrine deposits, alluvial sediments, and volcanic flows make up the regional geology of the area (Davidson and Rex \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e1983\u003c/span\u003e). At the proposed Wabe Hydropower Project site detailed surface and subsurface geological mapping has been carried out up to an offset of 500 m from the tunnel alignment and using boreholes along the alignment by the Ethiopian Construction Design and Supervision Works Corporation (ECDSWC \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). The major lithologies are: The Upper basaltic formation, this unit is ca. 84.5 m thick and consists of aphanitic and phyric (the phenocrysts are dominantly composed of Plagioclase) basalts predominantly. At places, basalts are found interbedded with thin layers of welded tuff, and ca. 18.6 m thick volcano-clastic sediments composed of tuffaceous deposits with minor clastic sediments separating them from the underlying basalt. The middle basaltic formation, this unit is ca. 380.5 m thick, phyric (the phenocrysts are dominantly composed of Plagioclase) basalt with subordinate amygdaloidal (calcite-filled) basalt. It is characterized by the common presence of calcite veins and volcanic breccia. A 60.8 m thick, BH 16 and BH 15, ignimbrite unit separated it from the underlying lower Basalt. The Lower basalt, this unit is fresh, massive phyric basalt exposed in the river bed of the Wabe River. It is primarily composed of plagioclase phenocrysts, with lesser amounts of olivine and pyroxene. Additionally, vesicles in this unit make up approximately 18\u0026ndash;30% of its volume. This unit seldomly appears interlaying with gray to green sub-volcanic rocks of 1.2 to 2.5 m thickness. The geological cross-section along the tunnel alignment with boreholes is presented in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e.\u003c/p\u003e \u003cp\u003eA general engineering geologic description of each Geotechnical unit (GU) is presented in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. For the pre-assumed blocky rock mass, the orientations of 387 discontinuity were recorded\u0026mdash;140 in GU1, 164 in GU2, and 83 in GU3. Subsequently, by applying lower-hemisphere and equal-area projections, their orientations were deduced using the DIPS v 6.0 software package (Rocscience 2016); as a result, the three most dominant joints were identified. The determined dominant joint sets in these rock mass are presented in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e and their corresponding stereo-net projections are presented in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eGeneral engineering geological description of various units present along the tunnel alignment\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"7\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGeotechnical units\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003eFormation\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c5\" namest=\"c4\"\u003e \u003cp\u003eGeneral engineering geologic description\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e \u003cp\u003eIdentified joint sets\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGU1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eUpper Basalt\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e \u003cp\u003eThis rock mass is very blocky and of good to excellent quality. Joints within this rock mass are 0.2 m spaced on average, and moderately to slightly weathered with no infillings.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e \u003cp\u003e1N 253/72\u003c/p\u003e \u003cp\u003e2N 046/81\u003c/p\u003e \u003cp\u003e3N 329/82\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"1\" nameend=\"c7\" namest=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGU2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMiddle Basalt\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e \u003cp\u003eThis rock mass is very blocky and disturbed, with a fair to good quality. Joints within this rock mass are 0.56 m spaced on average, highly to moderately weathered with no or occasional clay infillings.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e \u003cp\u003e1N 157/80\u003c/p\u003e \u003cp\u003e2N 035/79\u003c/p\u003e \u003cp\u003e3N 202/69\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"1\" nameend=\"c7\" namest=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGU3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eLower Basalt\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e \u003cp\u003eThis rock mass is blocky and of excellent quality. Joints inside this rock mass are 1.2 m spaced on average, with some rough joints, and no visible weathering effect or infillings.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e \u003cp\u003e1N 022/86\u003c/p\u003e \u003cp\u003e2N 231/81\u003c/p\u003e \u003cp\u003e3N 078/78\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"1\" nameend=\"c7\" namest=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGU4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eFault zone\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e \u003cp\u003eThis rock mass is poorly interlocked, heavily broken, and of very poor quality.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"1\" nameend=\"c7\" namest=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"Materials and Methods","content":"\u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003eEstimation of the Engineering Properties of Rocks\u003c/h2\u003e \u003cp\u003eThe basic geological strength index (GSI) chart provided by Hoek and Marinos (\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2000\u003c/span\u003e) has been used to obtain the respective ratings. The surface and structural conditions of the discontinuities within each Geotechnical unit were assessed in the field, and the range of GSI values was determined, as presented in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. Laboratory test results for both Young\u0026rsquo;s modulus (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({E}_{i}\\)\u003c/span\u003e\u003c/span\u003e) and strength (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\sigma }_{ci}\\)\u003c/span\u003e\u003c/span\u003e) of intact rock were also available.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003eEstimation of the Engineering Properties of the Rock Mass\u003c/h2\u003e \u003cdiv id=\"Sec8\" class=\"Section3\"\u003e \u003ch2\u003eModulus of Deformation\u003c/h2\u003e \u003cp\u003eThe empirical equation provided by Hoek and Diederichs (\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2006\u003c/span\u003e) was used to compute the modulus of deformation values for each Geotechnical unit:\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\({E}_{rm}={E}_{i}\\left(0.02+\\frac{1-D/2}{1+{e}^{\\left(\\left(60+15D-GSI\\right)/11\\right)}}\\right)\\)\u003c/span\u003e \u003c/span\u003e \u0026hellip;\u0026hellip;..Eq.\u0026nbsp;1\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({E}_{i}\\)\u003c/span\u003e\u003c/span\u003e is the Young\u0026rsquo;s modulus of the intact rocks; The disturbance factor (D) due to blast damage and stress relaxation was set to 0 and GSI is the Geological Strength Index.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eRock mass and intact rock mechanical properties, and GSI distributions\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"12\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c10\" colnum=\"10\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c11\" colnum=\"11\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c12\" colnum=\"12\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eGeotech. Units\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({E}_{i}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eγ\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"3\" nameend=\"c6\" namest=\"c4\"\u003e \u003cp\u003eGSI Distribution\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\" morerows=\"1\" rowspan=\"2\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colspan=\"5\" nameend=\"c12\" namest=\"c8\"\u003e \u003cp\u003e\u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003erm\u003c/em\u003e\u003c/sub\u003e Eq.\u0026nbsp;(1)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eMaximum\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eMean\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eMinimum\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003eMax.\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c10\" namest=\"c9\"\u003e \u003cp\u003eMean\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c12\" namest=\"c11\"\u003e \u003cp\u003eMin.\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e(GPa)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e(KN/m\u003csup\u003e3\u003c/sup\u003e)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colspan=\"5\" nameend=\"c12\" namest=\"c8\"\u003e \u003cp\u003e(GPa)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGU1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e72.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e25.9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e58\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e51\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e45\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c9\" namest=\"c8\"\u003e \u003cp\u003e34.37\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c11\" namest=\"c10\"\u003e \u003cp\u003e23.61\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e16.19\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGU2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e54.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e24.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e41\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e32\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c9\" namest=\"c8\"\u003e \u003cp\u003e16.74\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c11\" namest=\"c10\"\u003e \u003cp\u003e9.316\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e5.052\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGU3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e70.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e28.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e70\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e62\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e55\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c9\" namest=\"c8\"\u003e \u003cp\u003e51.29\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c11\" namest=\"c10\"\u003e \u003cp\u003e39.57\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e28.58\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGU4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e23.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c9\" namest=\"c8\"\u003e \u003cp\u003e0.163\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c11\" namest=\"c10\"\u003e \u003cp\u003e0.119\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e0.091\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"12\" nameend=\"c12\" namest=\"c1\"\u003e \u003cp\u003eNote: Ei - Young\u0026rsquo;s modulus of the intact rocks; γ - unit weight of the rock; GSI \u0026ndash; Geological Strength Index and E\u003csub\u003erm\u003c/sub\u003e - modulus of deformation of the rock mass\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003eHoek\u0026ndash;Brown Parameters\u003c/h2\u003e \u003cp\u003eThe parameters that define the rock mass strength characteristics (Hoek-Brown material constants; \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(s\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(a\\)\u003c/span\u003e\u003c/span\u003e, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({m}_{b}\\)\u003c/span\u003e\u003c/span\u003e) were calculated by using \u003cem\u003eGSI\u003c/em\u003e and D values. Empirical equations \u003cb\u003e(\u003c/b\u003eEqs.\u0026nbsp;2, 3, and 4\u003cb\u003e)\u003c/b\u003e, which were first introduced by Hoek (\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e1994\u003c/span\u003e) and Hoek et al. (\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e1995\u003c/span\u003e), were used.\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\frac{{m}_{b}}{{m}_{i}}= exp\\left(\\frac{GSI-100}{28-14D}\\right)\\)\u003c/span\u003e \u003c/span\u003e \u0026hellip;\u0026hellip;.. Eq.\u0026nbsp;2\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(s=exp\\left(\\frac{GSI-100}{9-3D}\\right)\\)\u003c/span\u003e \u003c/span\u003e \u0026hellip;\u0026hellip;.. Eq.\u0026nbsp;3\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(a=\\frac{1}{2}+\\frac{1}{6}\\left({e}^{-GSI/15}- {e}^{-20/3}\\right)\\)\u003c/span\u003e \u003c/span\u003e \u0026hellip;\u0026hellip;.. Eq.\u0026nbsp;4\u003c/p\u003e \u003cp\u003ewhere s, a, and mb are the Hoek-Brown material constants, D is the disturbance factor, GSI is the Geological Strength Index, mi is the material constant for intact rock, and for basalt, it was taken as 25 (from the table proposed by Marinos and Hoek (\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2000\u003c/span\u003e)).\u003c/p\u003e \u003cp\u003eFollowing the determination of the Hoek-Brown material constants using Eqs.\u0026nbsp;5, 6, and 7, the Mohr-Coulomb friction angle (\u003cem\u003eϕ\u003c/em\u003e), tensile strength (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\sigma }_{t}\\)\u003c/span\u003e\u003c/span\u003e), and cohesion (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(c\\)\u003c/span\u003e\u003c/span\u003e) of the Geotechnical units were estimated.\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\varphi = \\left[\\frac{6a{m}_{b}{\\left(s+ {m}_{b}{\\sigma }_{3n}\\right)}^{a-1}}{2\\left(1+a\\right)\\left(2+a\\right)+6a{m}_{b}{\\left(s+ {m}_{b}{\\sigma }_{3n}\\right)}^{a-1}}\\right]\\)\u003c/span\u003e \u003c/span\u003e \u0026hellip;\u0026hellip;.. Eq.\u0026nbsp;5\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(c= \\frac{{\\sigma }_{ci}\\left[\\left(1+2a\\right)s+ \\left(1-a\\right){m}_{b}{\\sigma }_{3n}\\right]{\\left(s+ {m}_{b}{\\sigma }_{3n}\\right)}^{a-1}}{\\left(1+a\\right)\\left(1+2a\\right)\\sqrt{1+ \\left(6a{m}_{b}{\\left(s+ {m}_{b}{\\sigma }_{3n}\\right)}^{a-1}\\right)/\\left(1+a\\right)\\left(1+2a\\right)}}\\)\u003c/span\u003e \u003c/span\u003e \u0026hellip;\u0026hellip;.. Eq.\u0026nbsp;6\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\({\\sigma }_{t}= \\frac{s.{\\sigma }_{ci}}{{m}_{b}}\\)\u003c/span\u003e \u003c/span\u003e \u0026hellip;\u0026hellip;.. Eq.\u0026nbsp;7\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\sigma }_{3n}= \\frac{{{\\sigma }^{{\\prime }}}_{3max}}{{\\sigma }_{ci}}\\)\u003c/span\u003e\u003c/span\u003e; \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({{\\sigma }^{{\\prime }}}_{3max}\\)\u003c/span\u003e\u003c/span\u003e is the highest limit of confining stress considered in the link between the Hoek-Brown and the Mohr-Coulomb criterion. For deep tunnels, Hoek et al. (\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2002\u003c/span\u003e) have provided guidelines; thus, values from 1 to 5.6 MPa were taken.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003ePoisson\u0026rsquo;s ratio\u003c/h2\u003e \u003cp\u003eThere are few available empirical equations for estimating Poisson\u0026rsquo;s ratio (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({V}_{rm}\\)\u003c/span\u003e\u003c/span\u003e) of the rock masses. Using the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({m}_{i}\\)\u003c/span\u003e\u003c/span\u003e and \u003cem\u003eGSI\u003c/em\u003e, Vasarhelyi (\u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e2009\u003c/span\u003e) provided a suitable alternative empirical equation whenever the Poisson\u0026rsquo;s ratio of the intact rock (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({V}_{i}\\)\u003c/span\u003e\u003c/span\u003e) is not available, as follows:\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\({V}_{rm}= -0.002GSI-0.003{m}_{i}+0.457\\)\u003c/span\u003e \u003c/span\u003e \u0026hellip;\u0026hellip;.. Eq.\u0026nbsp;8\u003c/p\u003e \u003cp\u003eThe computed Mohr-Coulomb material constants, shear strength parameters, and Poisson\u0026rsquo;s ratio values for each Geotechnical unit using a mean \u003cem\u003eGSI\u003c/em\u003e value are given in Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eRock mass parameters and material constants for the average GSI values.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"11\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c10\" colnum=\"10\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c11\" colnum=\"11\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003eGeotechnical\u003c/p\u003e \u003cp\u003eUnits\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003eDepth\u003c/p\u003e \u003cp\u003e(m)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"4\" nameend=\"c6\" namest=\"c3\"\u003e \u003cp\u003eShear Strength Parameters\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003ePoisson\u0026rsquo;s ratio\u003c/p\u003e \u003cp\u003e(\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({V}_{rm})\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"4\" nameend=\"c11\" namest=\"c8\"\u003e \u003cp\u003eMaterial constants\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e \u003cp\u003e\u003cb\u003eCohesion (C)\u003c/b\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003eFriction angle (\u003c/b\u003e\u003cem\u003eϕ)\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003eTensile strength (\u003c/b\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\sigma }_{t})\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c9\" namest=\"c8\"\u003e \u003cp\u003eA\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c10\"\u003e \u003cp\u003eS\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c11\"\u003e \u003cp\u003emb\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e(MPa)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c5\" namest=\"c4\"\u003e \u003cp\u003e(\u003csup\u003e0\u003c/sup\u003e)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003e(MPa)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c10\" namest=\"c9\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eEq.\u0026nbsp;6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c5\" namest=\"c4\"\u003e \u003cp\u003eEq.\u0026nbsp;5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eEq.\u0026nbsp;7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eEq.\u0026nbsp;8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eEq.\u0026nbsp;2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c10\" namest=\"c9\"\u003e \u003cp\u003eEq.\u0026nbsp;3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003eEq.\u0026nbsp;4\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGU1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e90\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.69\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c5\" namest=\"c4\"\u003e \u003cp\u003e65.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.29\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.28\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.51\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c10\" namest=\"c9\"\u003e \u003cp\u003e0.01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e4.84\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGU2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e190\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.42\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c5\" namest=\"c4\"\u003e \u003cp\u003e57.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.08\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.51\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c10\" namest=\"c9\"\u003e \u003cp\u003e0.002\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e3.15\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGU3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e356\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e3.98\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c5\" namest=\"c4\"\u003e \u003cp\u003e58.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.46\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.26\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c10\" namest=\"c9\"\u003e \u003cp\u003e0.015\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e6.44\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGU4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e90\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c5\" namest=\"c4\"\u003e \u003cp\u003e35.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.33\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.53\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c10\" namest=\"c9\"\u003e \u003cp\u003e0.0002\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e1.72\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003eEstimation of the Engineering Properties of Joints\u003c/h2\u003e \u003cp\u003eIn the present study, an effort was made to determine the shear strength characteristics of joints for blocky rock mass, however, as already stated Geotechnical unit GU4 was considered as an equivalent continuum medium. Due to the non-availability of rock core through joints, for design purposes, initial estimations can be carried out using empirical approaches (Sharma et al. \u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e1999\u003c/span\u003e). Therefore, the following empirical law of friction provided by Barton (\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e1973\u003c/span\u003e) was utilized:\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\left(\\frac{ \\tau }{{\\sigma }_{n}}\\right) = {\\varphi }_{b}+JRC \\left(\\frac{JCS}{{\\sigma }_{n}}\\right)\\)\u003c/span\u003e \u003c/span\u003e\u0026hellip;\u0026hellip;.. Eq.\u0026nbsp;9\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(JCS\\)\u003c/span\u003e\u003c/span\u003e is the compressive strength of the joint surface, which may equal 1/4th of the uniaxial compressive strength of the intact rock (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\frac{{\\sigma }_{ci}}{4}\\)\u003c/span\u003e\u003c/span\u003e) (Sharma et al., \u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e1999\u003c/span\u003e). \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\varphi }_{b}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(JRC\\)\u003c/span\u003e\u003c/span\u003e are the basic friction angle and Joint roughness coefficient of the joints, respectively, and their respective values were obtained from the standard Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e proposed by Barton and Choubey (1977), to be on the safer side the lower boundary values were taken. Further, the dry and wet \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\varphi }_{b}\\)\u003c/span\u003e\u003c/span\u003e values were determined based on the groundwater condition at the site.\u003c/p\u003e \u003cp\u003eAn effort was also made to compute the minimum normal stress acting on the surface of the joints by using the following relation:\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\({\\varphi }_{b}+JRC\\left(\\frac{JCS}{{\\sigma }_{n}}\\right) = {70}^{0}\\)\u003c/span\u003e \u003c/span\u003e \u0026hellip;\u0026hellip;.. Eq.\u0026nbsp;10\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\varphi }_{b}\\)\u003c/span\u003e\u003c/span\u003e is the basic friction angle, JRC - Joint roughness coefficient, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(JCS\\)\u003c/span\u003e\u003c/span\u003e is the compressive strength of the joint surface, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\sigma }_{n}-\\)\u003c/span\u003e\u003c/span\u003enormal stress acting on the surface of the joints.\u003c/p\u003e \u003cp\u003eIn addition to the shear strength parameters of the joints, their stiffness is required as an input for the numerical model. The normal (K\u003csub\u003en\u003c/sub\u003e) and shear stiffness (K\u003csub\u003es\u003c/sub\u003e) of joints can typically be determined through laboratory tests by using the guidelines suggested by Kulatilake et al. (\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e2016\u003c/span\u003e). However, in the absence of laboratory tests, Kulatilake et al. (\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e2016\u003c/span\u003e) proposed that the joint normal and shear stiffnesses are linear functions of the applied normal stress (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\sigma }_{n}\\)\u003c/span\u003e\u003c/span\u003e). As discussed, the normal stiffness, in GPa/m, can be approximated to be between 10 and 20 times the applied normal stress, expressed in MPa. Similarly, the shear stiffness expressed in GPa/m can be estimated to be 0.65\u0026ndash;2.15 times that of the applied normal stress expressed in MPa. The approximated joint parameters and computed stiffness values for each Geotechnical unit are listed in Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec12\" class=\"Section2\"\u003e \u003ch2\u003eBack\u0026ndash;analysis for Some Parameters\u003c/h2\u003e \u003cp\u003eTo determine some of the intact rock properties, a back-analysis procedure was performed. For this purpose, the available estimated rock mass mechanical properties of the corresponding rock mass were utilized. Several published studies have compared the properties of rock masses and intact rocks, and a summary of these studies is presented as follows:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eOwing to the presence of discontinuities, Kulatilake et al. (\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e2004\u003c/span\u003e) proposed that the Poisson\u0026rsquo;s ratio of the rock mass may increase by 21% in comparison to that of intact rock;\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eHuang et al. (\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2017\u003c/span\u003e) determined that the tensile strength of the rock mass, as estimated from the Hoek and Brown criterion is approximately 24 to 35% of the tensile strength of the intact rock. Specifically, Wu and Kulatilake (\u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e2012\u003c/span\u003e) concluded that the tensile strength of the rock mass can reach approximately 35% of tensile strength intact rock; and\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eFurther, Shreedharan \u0026amp; Kulatilake (\u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e2016\u003c/span\u003e) indicated that the estimated cohesion value of the rock mass may be between 35 to 45% of that of the intact rock\u0026rsquo;s cohesion value.\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eUseful joint parameters in each Geotechnical unit\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"9\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDiscontinuity type\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\varphi }_{b}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(JRC\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\sigma }_{ci}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(JCS\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\sigma }_{n}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003eEq.\u0026nbsp;10\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\left(\\frac{ \\tau }{{\\sigma }_{n}}\\right)\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003eK\u003csub\u003en\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c9\"\u003e \u003cp\u003eK\u003csub\u003es\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e( \u003csup\u003e0\u003c/sup\u003e )\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e(MPa)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e(MPa)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003e(MPa)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003e( \u003csup\u003e0\u003c/sup\u003e )\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003e(GPa/m)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c9\"\u003e \u003cp\u003e(GPa/m)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eJoints\u003csup\u003e1*\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e35\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e207.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e51.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1.63\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e38.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e10*\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\sigma }_{n}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e2.15*\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\sigma }_{n}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eJoints\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e31\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e155.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e38.9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1.23\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e34.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e10*\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\sigma }_{n}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e2.15*\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\sigma }_{n}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eJoints\u003csup\u003e3\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e31\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e200.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e50.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e8.88\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e34.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e10*\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\sigma }_{n}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e2.15*\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\sigma }_{n}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"9\" nameend=\"c9\" namest=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\varphi }_{b}\\)\u003c/span\u003e\u003c/span\u003e - basic friction angle, JRC - Joint roughness coefficient, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\sigma }_{ci}\\)\u003c/span\u003e\u003c/span\u003e \u0026ndash; intact uniaxial compressive strength \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(JCS\\)\u003c/span\u003e\u003c/span\u003e is the compressive strength of the joint surface, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\sigma }_{n}-\\)\u003c/span\u003e\u003c/span\u003enormal stress acting on the surface of the joints, K\u003csub\u003en\u003c/sub\u003e - normal stiffness, and K\u003csub\u003es\u003c/sub\u003e - shear stiffness\u003c/p\u003e \u003cp\u003e*\u003cem\u003e1,2, and 3 indicate joints within the GU1, GU2, and GU3 units, respectively\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eBased on the aforementioned discussion, in this study, the tensile strength of the intact rock and cohesion values were set to 2.3 times that of the corresponding rock mass values. The values for Poisson\u0026rsquo;s ratio of intact rock were set to be 0.83 times that of the Poisson\u0026rsquo;s ratio values of the rock mass. However, the angle of the internal friction for intact rock was directly taken from the corresponding rock mass values, as recommended by Kulatilake et al. (\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e2004\u003c/span\u003e) and Shreedharan and Kulatilake (\u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e2016\u003c/span\u003e). The estimated results are presented in Table\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec13\" class=\"Section2\"\u003e \u003ch2\u003eDevelopment of the Numerical Models\u003c/h2\u003e \u003cp\u003eIn the present study, the 3DEC version 5.2 software package (Itasca 2016) was employed to simulate and perform the stress\u0026ndash;strain analyses. The length, width, and height of the selected cubes were 50 m \u0026times; 50 m \u0026times; 50 m, respectively. The origin of the models (0, 0, 0) was made to be at the center of the cubes. The models were prepared to be -25 to 25 long along the x\u0026ndash; and y\u0026ndash;axes and \u0026minus;\u0026thinsp;25 to 25 tall along the z\u0026ndash;axis (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e). Furthermore, the positive x\u0026ndash; and y\u0026ndash;axes of Models I and II coincided with the southeast (SE) and northeast (NE) directions of the field conditions, respectively, whereas the positive x\u0026ndash; and y\u0026ndash;axes of Model III coincided with the southwest (SW) and southeast (SE) directions. The z\u0026ndash;axis represents the vertical direction in all the models.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab5\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eThe back-analyzed results obtained for intact rocks of each Geotechnical unit\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e \u003cp\u003eRock mass\u003c/p\u003e \u003cp\u003eProperties Values\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eGeotechnical Units\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eMultiplying factor\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eIntact rock\u003c/p\u003e \u003cp\u003eValues\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e\u003cem\u003eCohesion\u003c/em\u003e (\u003cb\u003eMPa\u003c/b\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.69\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eGU1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e3.89\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.42\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eGU2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e3.27\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e3.98\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eGU3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e9.16\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eGU4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.46\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e\u003cem\u003eFriction angle\u003c/em\u003e (\u003csup\u003e\u003cb\u003e0\u003c/b\u003e\u003c/sup\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e65.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eGU1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e65.3\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e57.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eGU2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e57.6\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e58.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eGU3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e58.7\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e35.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eGU4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e35.7\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e\u003cem\u003ePoisson\u0026rsquo;s ratio\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.28\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eGU1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.232\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eGU2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.83\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.249\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.26\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eGU3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.214\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.33\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eGU4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.276\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e\u003cem\u003eTensile strength\u003c/em\u003e\u003c/p\u003e \u003cp\u003e(\u003cb\u003eMPa\u003c/b\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.29\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eGU1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.67\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.08\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eGU2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.18\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.46\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eGU3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.06\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eGU4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.002\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cp\u003eThe proposed circular tunnel geometry with a diameter of 5 m was used. Three models were constructed by considering the representative Geotechnical units along the proposed tunnel alignment. Figures\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e and \u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e were used to locate the modeled areas. Accordingly, Model I represents the area around chainage 0\u0026thinsp;+\u0026thinsp;600 (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e), and the coordinate of 368000 mE, and 911027.9 mN (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). This model comprises the GU1 and GU4 units. Model II was chosen around chainage 10\u0026thinsp;+\u0026thinsp;800, and the coordinate of 364173.4 mE, and 909885.6 mN. This model includes only the GU2 unit. Similarly, Model III was chosen around chainage 15\u0026thinsp;+\u0026thinsp;600, and coordinate of 353721.4 mE, and 909170.3 mN. This model is composed of only the GU3 unit. In Model I, the GU4 unit was set to be 30 m thick (from y = -15 to 15 in the model), inclined and planar with an approximate dip direction of N64\u003csup\u003eo\u003c/sup\u003eE and a dip of 79\u003csup\u003eo\u003c/sup\u003e. Furthermore, only those discontinuities expected have a greater influence on the mechanical response of the model should be included (Chen and Zhu \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Itasca 2016). Therefore, for modeling purposes, it was assumed that the recorded dominant joint sets were considered to have a greater influence on the mechanical response of the rock mass under the applied in-situ stress conditions. In addition, in Model I the contacts between the fault zone GU4 and GU1 Geotechnical unit are marked by the presence of discontinuity interfaces (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ea); thus, these planes were also considered a set of discontinuities.\u003c/p\u003e \u003cp\u003eInstead of employing the joint inclusion approach of Kulatilake et al. (\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e1993\u003c/span\u003e), the spacings of the discontinuity, measured in the field around the opening, were directly incorporated. Thus, the cubes were systematically divided into three distinct regions of influence, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ed. The region around the tunnel opening (Region 1) contains the field\u0026ndash;measured spacing of the joints as well as their orientations, as indicated in Table\u0026nbsp;\u003cspan refid=\"Tab6\" class=\"InternalRef\"\u003e6\u003c/span\u003e. For the other two regions (Regions 2 and 3), the spacings were increased systematically, but the orientations remained the same as those of the field\u0026ndash;measured values (Table\u0026nbsp;\u003cspan refid=\"Tab6\" class=\"InternalRef\"\u003e6\u003c/span\u003e). Further, the Coulomb slip constitutive model was used to represent the behavior of the joint and discontinuity interfaces.\u003c/p\u003e \u003cp\u003eThe values of the mechanical properties of the various discontinuities present in the different Geotechnical units and the discontinuity interfaces used in the Models are presented in Table\u0026nbsp;\u003cspan refid=\"Tab7\" class=\"InternalRef\"\u003e7\u003c/span\u003e. The joints considered in the Models were assumed to be smooth and open with occasional infillings; therefore, their cohesion and tensile strength were taken as 0 MPa (Wang et al. \u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e2012\u003c/span\u003e; Xing et al. \u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e2017\u003c/span\u003e, \u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). Furthermore, these joints were initially kept elastic to avoid movement during cycling and achieve gravitational equilibrium (Itasca 2020). In the case of fictitious joints that appeared during the initial preparation of representative models, i.e., during region classification, the \u003cem\u003eTUNNEL\u003c/em\u003e command in 3DEC was used to avoid undesired effects due to artificial joints.\u003c/p\u003e \u003cp\u003eSince the discontinuity interfaces were assumed to be well-bonded surfaces, their mechanical parameters (\u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e, \u003cem\u003eC\u003c/em\u003e, \u003cem\u003eϕ, and\u003c/em\u003e \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({V}_{r}\\)\u003c/span\u003e\u003c/span\u003e) were first estimated by averaging the values between the two units \u0026mdash; GU1 and GU4. Later, some of these parameters (\u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e, \u003cem\u003eand\u003c/em\u003e \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({V}_{r}\\)\u003c/span\u003e\u003c/span\u003e) were put into empirical relations provided by Kulatilake et al. (\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e1992\u003c/span\u003e), where the average values of 0.01 and 2.5 were assigned to Eq.\u0026nbsp;(11) and Eq.\u0026nbsp;(12), respectively. Such average values were commonly used previously by Xing et al. (\u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e2017\u003c/span\u003e, \u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e2018\u003c/span\u003e), Kulatilake et al. (\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e1992\u003c/span\u003e), and Kulatilake et al. (\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e1993\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab6\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 6\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eJoint orientations and spacings within respective regions in the Models\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"8\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eRegions in the Model\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eModel number\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eJoint sets\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c5\" namest=\"c4\"\u003e \u003cp\u003eDiscontinuity Orientations\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eOriginal mean spacing\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eThe mean spacing used\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eThe thickness of the regions\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eDip direction\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eDip\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e(\u003c/b\u003e\u003csup\u003e\u003cb\u003e0\u003c/b\u003e\u003c/sup\u003e\u003cb\u003e)\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e(\u003c/b\u003e\u003csup\u003e\u003cb\u003e0\u003c/b\u003e\u003c/sup\u003e\u003cb\u003e)\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e(m)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e(m)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e(m)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eN 253\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e72\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eI\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eN 046\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e81\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e4.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eN 329\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e82\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eN 157\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e80\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRegion 3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eII\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eN 035\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e79\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.56\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e4.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e9.0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eN 202\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e69\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eN 022\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e86\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eIII\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eN 231\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e81\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e4.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eN 078\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e78\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eN 253\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e72\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eI\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eN 046\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e81\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e2.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e7.5\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eN 329\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e82\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eN 157\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e80\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRegion 2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eII\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eN 035\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e79\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.56\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e2.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e8.5\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eN 202\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e69\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eN 022\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e86\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eIII\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eN 231\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e81\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e1.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e7.5\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eN 078\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e78\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eN 253\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e72\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eI\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eN 046\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e81\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e6.0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eN 329\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e82\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eN 157\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e80\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRegion 1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eII\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eN 035\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e79\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.56\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.60\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e5.0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eN 202\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e69\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eN 022\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e86\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eIII\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eN 231\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e81\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e1.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e6.0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eN 078\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e78\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThe shear modulus (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({G}_{r})\\)\u003c/span\u003e\u003c/span\u003e of the intact rock (blocks) can be obtained from Young\u0026rsquo;s modulus and Poisson\u0026rsquo;s ratio.\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\frac{{G}_{r}}{Ks} =0.008-0.012\\)\u003c/span\u003e \u003c/span\u003e (GPa/m) \u0026hellip;\u0026hellip;.. Eq.\u0026nbsp;11\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\frac{Kn}{Ks}=2-3\\)\u003c/span\u003e \u003c/span\u003e (GPa/m) \u0026hellip;\u0026hellip;.. Eq.\u0026nbsp;12\u003c/p\u003e \u003cp\u003ewhere \u003cem\u003eKs\u003c/em\u003e and \u003cem\u003eKn\u003c/em\u003e are the joint shear and normal stiffnesses, respectively.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab7\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 7\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eValues of the mechanical properties of various discontinuities, present in different Geotechnical units and the interfaces, used in the Models\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDiscontinuity type\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNormal\u003c/p\u003e \u003cp\u003estiffness\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eShear stiffness\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eFriction angle\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eCohesion\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eTensile\u003c/p\u003e \u003cp\u003estrength\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e(GPa/m)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e(GPa/m)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e( \u003csup\u003e\u003cb\u003e0\u003c/b\u003e\u003c/sup\u003e )\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e(MPa)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e(MPa)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eJoints in GU1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e16.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e3.51\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e38.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eJoints in GU2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e12.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2.65\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e34.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eJoints in GU3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e88.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e19.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e34.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eInterfaces between GU1 and GU4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e4010.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1604.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e50.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e2.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.34\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThe values used to represent the intact rock mechanical properties in the models are presented in Table\u0026nbsp;\u003cspan refid=\"Tab8\" class=\"InternalRef\"\u003e8\u003c/span\u003e. For intact rock the built\u0026ndash;in constitutive model used was Mohr\u0026ndash;Coulomb plasticity model. These blocks were treated as deformable blocks. For the Models, depending on the region of influence, different mesh sizes were implemented. The inner-most region (Region 1), which corresponds to the volume of the rock mass surrounding the opening, was zoned using the constant-strain elements of a finer edge length. In contrast, the outer regions (Regions 2 and 3) were zoned with coarser edge lengths.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab8\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 8\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eValues of the mechanical properties of intact rock in various Geotechnical units used in the Models\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"7\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGeotechnical unit\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eDensity\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eBulk\u003c/p\u003e \u003cp\u003emodulus\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eShear\u003c/p\u003e \u003cp\u003emodulus\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eFriction\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eCohesion\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eTensile strength\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e(kg/m\u003csup\u003e3\u003c/sup\u003e)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e(GPa)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e(GPa)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e( \u003csup\u003e0\u003c/sup\u003e )\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003e(MPa)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003e(MPa)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGU1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2590\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e44.27\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e29.37\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e65.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e3.75\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.67\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGU2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2450\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e35.95\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e21.81\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e57.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e3.29\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.19\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGU3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2860\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e40.81\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e28.83\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e58.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e9.15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e1.06\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGU4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2320\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.050\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e35.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.46\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.002\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThe center points of the tunnels in Models I, II, and III were located at depths of ca. 90, 190, and 356 m below the ground surface, respectively. By taking an average density of 2700 kg/m\u003csup\u003e3\u003c/sup\u003e for the overburden lithology, the vertical stress (ZZ\u0026ndash;stress in 3DEC) that was applied on the top of the Model has values equal to 1.8, 4.5, and 8.9 MPa for Models I, II, and III, respectively. Due to the nonavailability of measured in-situ horizontal stress in the area, deformation and stress analyses were carried out by utilizing the lower and upper bound Ko values [0.5, 2.0]. According to Hoek et al. (\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2005\u003c/span\u003e) for design purposes, these assigned lower and upper bound values of K\u003csub\u003e0\u003c/sub\u003e can be considered reasonable, particularly for areas where no in-situ stress measurements are available. Further, the fixed boundary was set to the base of the Models. For the other four faces of the cubes, first, depth-dependent increasing stress boundary conditions were applied. Then, to preserve the prescribed stresses and restrict the motion of the failed blocks, velocity boundary conditions were provided after the stress boundary conditions affected the same boundary corners. Figure\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ea illustrates the boundary conditions that were used during the modeling process.\u003c/p\u003e \u003cp\u003eSimulating exact field excavation during modeling by 3DEC software is almost impossible because of its complexity (Shreedharan and Kulatilake \u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e2016\u003c/span\u003e). However, during the present study attempts were made to simulate the excavation sequence. For this purpose, the rock mass to be excavated was divided into different blocks. The divided blocks were subsequently grouped into different excavation advance steps (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003eb). Therefore, in the present study, the circular tunnels were presumed to be numerically excavated in six advance steps (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003eb) by considering the full-face tunneling method. This process may help to monitor the trend of the rock mass deformation and the stress redistribution possibly caused by stepwise excavation rather than excavating the entire length of the tunnel (50 m) at once.\u003c/p\u003e "},{"header":"Results and Discussion","content":"\u003cp\u003eThe present study was carried out performing stress analyses through three models that were considered representative of four different types of rock mass at different depths, utilizing a range of Ko [0.5, 2.0] as recommended by Hoek et al. (\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2005\u003c/span\u003e). We evaluated the displacement, failure mode, and distribution of failed blocks in different parts of the tunnel under investigation through comparing the results from various cases, thereby gaining valuable insights for rock mass support recommendations. A comprehensive examination of graphic output, on a case-by-case basis, was performed. It should be noted that all the representative figures and values obtained were taken on the y\u0026thinsp;=\u0026thinsp;0 plane, except for the case of the GU1 unit in Model I, where the results were taken on the y = -23 plane. Conventionally, in 3DEC, negative values of stress and deformation indicate compression conditions.\u003c/p\u003e \u003cdiv id=\"Sec17\" class=\"Section2\"\u003e \u003ch2\u003eValidation Using Basic Numerical Modeling Results\u003c/h2\u003e \u003cp\u003eIt is a commonly followed practice to validate numerical models using basic models before utilizing them for any subsequent analyses (e.g., Shreedharan and Kulatilake \u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e2016\u003c/span\u003e; Wang et al. \u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e2012\u003c/span\u003e; Feng et a. 2019). For the present study, the basic models, which do not consider joints, were assessed basically for validation purposes. The interfaces between Geotechnical units GU1 and GU4 were included as they were considered as well bonded with higher mechanical properties. Before the tunnel excavation, the applied input vertical in-situ stress of the models was assessed and it was observed that the vertical in-situ stress increased linearly from the top to the bottom of the model, and the top and bottom far-field ZZ\u0026ndash;stress perfectly coincided with the prescribed and expected stresses at the model boundaries.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eAfter performing the validation before excavation, using the same models the next validation process was carried out following the tunnel excavation. Under this, the validation was performed using the XX\u0026ndash; and ZZ\u0026ndash;stress distributions. Figure\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e shows the symmetric XX\u0026ndash; and ZZ\u0026ndash;stress distributions for each model. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003ea\u0026ndash;c, all the XX\u0026ndash;stress distributions are minimum around the sidewalls and they peak around the roof and floor of the tunnels. On the other hand, in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003ed\u0026ndash;f, the ZZ\u0026ndash;stress showed minimum stress distributions around the roof and floor, and, as expected they peaked around the sidewalls. As stated by Shreedharan and Kulatilake (\u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e2016\u003c/span\u003e), when subjected to excavation, the two sidewalls of the opening experienced greater compressive ZZ\u0026ndash;stress than did the roof and floor of the opening. Meanwhile, the roof and floor of the opening experience higher compressive XX\u0026ndash;stress as compared to the sidewalls.\u003c/p\u003e \u003cp\u003eTo summarize, the unexcavated models demonstrated consistency between the far-field ZZ-stress in the prepared models and the empirically calculated results at the model boundary. And, the XX \u0026ndash; and ZZ \u0026ndash; stress distributions surrounding the excavated openings were consistent with expectations that the stresses redistribute as a result of vertical and horizontal stress adjustment through the ground arching mechanism following the removal of materials (Chen et al. \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2011\u003c/span\u003e). Therefore, all these results are in confirmation with the previous findings (e.g., Xing et al. \u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e2017\u003c/span\u003e; Li et al. \u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e2018c\u003c/span\u003e; Feng et al. \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2019\u003c/span\u003e) indicating that the applied inputs are transferred correctly to the models. This may further be noticed in later sections 4.2 and 4.3 (deformation and stress analyses where the applied inputs are transferred correctly to the models).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec18\" class=\"Section2\"\u003e \u003ch2\u003eThe Distribution and Failure Mode of Failed Blocks of the Tunnels\u003c/h2\u003e \u003cp\u003eIn the present study, by varying Ko from 0.5 to 2.0, an attempt was made to study the possible distribution and mode of failure of failed blocks in each tunnel. Thus, as suggested by Shreedharan and Kulatilake (\u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e2016\u003c/span\u003e), the considered failed blocks were those that had reached their residual strength in the past or the present (now), either in shear or tension. The representative figures for the failure zone in the tunnels of each Geotechnical unit are shown in Figs.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e, \u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e, and \u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003e. From these figures, in the legend section, the suffixes \u0026lsquo;p\u0026rsquo; and \u0026lsquo;n\u0026rsquo; in shear-p, shear-n, tension-p, and tension-n represent \u0026lsquo;past\u0026rsquo; and \u0026lsquo;now\u0026rsquo;, respectively. The corresponding interpretation is that regions in the rock mass that are occupied by shear-p or shear-n have experienced shear failure in the past or now. Similarly, the regions in the rock mass occupied by tension-p or tension-n have experienced tension failure in the past or the present (now).\u003c/p\u003e \u003cp\u003eAfter excavation in the GU1 unit (treated as a discontinuum medium), the failure of blocks may initiate around the roof and the floor of the tunnel; however, blocks on the left sidewall and the right haunch of the tunnel may remain undetached (Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003ea). With increasing Ko (Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003eb), failures around the tunnel periphery may become more intense, and the joint set, i.e., Join set 1, around the right shoulder may act as the line of detachment. This tendency may become more obvious for a Ko value equal to 2.0 (Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003ec).\u003c/p\u003e \u003cp\u003eSimilarly, in the GU2 unit (also treated as a discontinuum medium) failed blocks may initially appeared everywhere around the periphery of the tunnel (Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003ed). With increasing Ko (Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003ee), the failed blocks in the roof and floor generally tend to follow a preferential direction imposed by the orientation of Joint Set 2, and the blocks on the left shoulder and the right haunch of the tunnels may remain undetached. With a further increase in the value of Ko (Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003ef), the tendency of blocks to fail along the orientation of this joint set became obvious around the tunnel opening, and this phenomenon may further intensify in areas that were previously undetached. The failed blocks in this rock mass suffered from tensile failure; however, a minor number of blocks in the GU2 unit were likely to undergo shear failure at a Ko value equal to 2.0.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFor both rock mass, a large number of discontinuities were superimposed\u0026mdash;three closely spaced joint sets in each of the rock mass under different stress conditions\u0026mdash;and it was observed that the distribution of the failure zone in these rock mass was affected by the presence of particular joint sets. Consequently, joint set 1 in the GU1 unit and joint set 2 in the GU2 unit provided an anisotropic nature to their corresponding rock mass mostly when the value of Ko was greater than or equal to 1.0. Therefore, the assumption of modeling the anisotropy of these rock mass by superimposing a large number of discontinuities in the models is worthwhile and may be provided results that can compare well with more traditional anisotropic solutions (cf., Marinos et al. \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e2007\u003c/span\u003e). Moreover, considering these joint sets in the area would provide more efficient support measures (Ghorbani et al. \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2020\u003c/span\u003e; Jia and Tang \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2008\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eAfter the excavation in the GU3 unit (Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003ea), it was observed that small block detachments occurred around the left and the right haunches of the tunnel. With increasing Ko (Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003eb), the left sidewall of the tunnel experienced local failure, while the remaining portions of the tunnel exhibited relatively higher stability. With a further increase in the value of Ko (Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003ec), local failures began to emerge around the left and the right haunches of the tunnel. This may be ascribed to the redistribution and concentration of the maximum principal stress around the haunches of the tunnel due to material heterogeneity, which is similar to the findings of Xing et al. (\u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e2017\u003c/span\u003e) and Feng et al. (\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). Despite these failures, the right shoulder and roof of the tunnel achieved a stable state as the maximum principal stress concentration around these areas was reduced significantly. According to the observations of Xing et al. (\u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e2017\u003c/span\u003e), even if Ko is higher, large deformation cannot be observed at locations around openings that are far from areas of maximum principal stress concentration. In this tunnel, the failed blocks underwent tensile failure across all the cases.\u003c/p\u003e \u003cp\u003eTo gain insight into the cause, a block-size assessment was carried out using 3DEC as it is proven accurate and reliable means to estimate rock block volume (Koulibaly et al. \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2023\u003c/span\u003e), and the volumes of 68 blocks around Region 1 (Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003eb) were recorded. However, 13 blocks had to be excluded from the analysis because they were significantly influenced by the boundaries of the region. By examining the moving average curve (Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003ea), it was observed that approximately 75% of the blocks are of large and very large block volumes. As a result, these blocks could have enhanced the stability of this rock mass. Furthermore, compared with tunnels running through the GU1 and GU2 units, it is observed that the results almost align with the suggestion of Yeung and Leong (\u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e1997\u003c/span\u003e) as deeper tunnels tend to exhibit greater stability because of their better confinement, provided that the intact rock is hard, and the tunnel depth is relatively deeper. However, it is important to note that this type of tunnel could cause local failures as they are subjected to higher stress levels (Yeung and Leong \u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e1997\u003c/span\u003e), and the joints are of higher dip angle (Feng et al. \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2019\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cp\u003eAfter excavation in the GU4 unit (treated as an equivalent continuum medium), the failed blocks may have appeared around the tunnel periphery. The thickness of the failure zone is different, i.e., it is much thicker around the sidewalls than the roof and the floor (Fig.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003ea). With an increase in Ko (Fig.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003ec), the zone of the failed block around the tunnel periphery became more uniformly distributed in terms of thickness. With a further increase in the value of Ko (Fig.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003ee), thicker failure zones appeared around the roof and the floor of the tunnel. It is important to note that this change in the thickness direction of the failure zone is associated with the rotation direction of the maximum principal stress (Figs.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003eb, d, and f).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cp\u003eFurthermore, it is evident that at a value of Ko equal to 0.5, the sidewalls experienced shear failure, and tension failures were more common on the roof and the floor of the tunnel. As the value of Ko is increased further (Ko\u0026thinsp;=\u0026thinsp;2.0), a significant number of failed blocks may primarily exhibit shear failures. However, the failed blocks located in the immediate vicinity of the sidewalls may appear to suffer from tensile failure. This significant change in the failure mode may also be explained by the fact that as the maximum principal stress appears on the sidewalls, stress relaxation occurs on the roof and the floor, and vice versa. This stress relaxation phenomenon may lead the blocks to experience increased tensile stresses and fail in tension failure (Yang et al. \u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e2017\u003c/span\u003e). Meanwhile, the concentration of stress in the other part of the tunnel may lead to higher shear stresses and subsequent shear failures in the blocks located in that area. The observed change in failure mode in the GU4 unit tunnel, as indicated by 3D models, is consistent with a similar phenomenon observed in the horseshoe-shaped tunnel studied by Hao et al. (\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2022\u003c/span\u003e) using 2D models. As a result, understanding the status of failed blocks for specific parts of the tunnel may help in designing support systems that can control and contain the specific failure mechanism and may possibly prevent collapse (Yang et al. \u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e2017\u003c/span\u003e).\u003c/p\u003e \u003cdiv id=\"Sec21\" class=\"Section3\"\u003e \u003ch2\u003eDisplacements of Tunnel Opening Under Varying Lateral In-Situ Stress\u003c/h2\u003e \u003cp\u003eThe displacements of the roof, floor, and sidewalls of the tunnels that run through four different Geotechnical units were studied using a range of Ko values (from 0.5 to 2.0). Figure\u0026nbsp;\u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e11\u003c/span\u003e shows the displacement results for the four tunnels, represented by the different color of lines, and in the legend section \u0026lsquo;SW\u0026rsquo; stands for \u0026lsquo;sidewall\u0026rsquo;.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe Z-displacements of the roof and floor in the GU1, GU2, and GU3 units (Fig.\u0026nbsp;\u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e11\u003c/span\u003ea) exhibited a gradual reduction and eventually became insignificant as the Ko value increased from 0.5 to 2.0. However, as can be seen, the Z\u0026ndash;displacement lines of the floor and roof of the GU4 unit exhibited three significant changes with increasing Ko: (i) a linear decrement from 0.5 to 1.0, (ii) a slight increment from 1.0 to 1.5, and (iii) a steeper increment from 1.5 to 2.0. During the initial phase, the reduction in vertical deformation was accompanied by an increase in horizontal deformation as Ko was increased to 1.0, representing a lower level of stress concentration stage (Feng et al. \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2019\u003c/span\u003e) and the occurrence of localized failure (Zhao et al. \u003cspan citationid=\"CR55\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). The next stage was characterized by an increase in both deformations as Ko was increased to 1.5. At this stage, a significant amount of released strain energy must exist to the roof and floor of the tunnel as higher Ko was applied (Feng et al. \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2019\u003c/span\u003e), which could be the reason why the increase in horizontal stress induced the increase in vertical deformation. In the last stage, there was a substantial increase in horizontal deformation along with a rapid increase in vertical deformation. This indicates that the rock mass was still in the strain energy release phase. However, at this stage, the released energy could have been of a greater magnitude, considering the significant increase in both deformations. This finding aligns with the findings of Feng et al. (\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2019\u003c/span\u003e), who reported that increasing Ko beyond 1.0 leads to more strain energy release. In another instance, Fig.\u0026nbsp;\u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e11\u003c/span\u003eb shows that most of the X\u0026ndash;displacements on the sidewalls of each tunnel increase linearly from Ko\u0026thinsp;=\u0026thinsp;0.5 to 2.0. The only exception is X\u0026ndash;displacement on the sidewalls of GU3, which remained comparatively unchanged, and it depicted a decrement from Ko\u0026thinsp;=\u0026thinsp;0.75 to 1.5.\u003c/p\u003e \u003cp\u003eFor the tunnel in the GU4 unit (represented by green and brown colors), which represents a fault zone, both the vertical (Z\u0026ndash;displacement) and horizontal (X\u0026ndash;displacement) convergences exhibited significantly greater values than did the other three tunnels. As Ko increases from 0.5 to 2.0, a relative shift in convergence from a higher vertical to a higher horizontal convergence is observed. Hence, the horizontal convergence increases gradually, eventually surpassing the vertical convergence at Ko\u0026thinsp;=\u0026thinsp;1.25. With a subsequent increase in Ko from 1.0 to 2.0, both convergences experienced a considerable rise, with the horizontal convergence surpassing the vertical convergence. For example, at Ko\u0026thinsp;=\u0026thinsp;2.0, the horizontal convergence almost tripled (2.9 to 7.5 cm) and the vertical convergence increased by 47% (3.4 to 5.0 cm). This shows that the strain energy released to the roof and floor of the tunnel was lower than that released to the sidewalls because the applied horizontal stress was higher than the vertical stress, which is consistent with the findings of Yang et al. (\u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e2017\u003c/span\u003e) and Xing et al. (\u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e2017\u003c/span\u003e). Similarly, for the GU2 unit (represented by red and yellow colors), the horizontal convergence exceeded the vertical convergence beyond Ko\u0026thinsp;=\u0026thinsp;0.75; however, for the GU1 unit (represented by black and purple colors), the horizontal convergence exceeded the vertical convergence across all the cases, which can be attributed to the nonuniform distribution of the stress field (Fan et al. \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). These observed exceedances in convergence could provide valuable insight into decision-making, particularly for optimized support placement under the right field stress conditions (Basarir et al. \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2005\u003c/span\u003e; Xing et al. \u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e2017\u003c/span\u003e).\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e"},{"header":"Conclusion","content":"\u003cp\u003eTo ensure the safe excavation of a tunnel and design appropriate support systems, it is crucial to assess the deformation and potential block failure around the tunnel opening. In the present study, a systematic failure and deformation assessment of the waterway tunnel of the Wabe Hydropower Project in central Ethiopia was conducted using a 3D discontinuum numerical model called 3DEC. The proposed 5 m diameter tunnel under study is planned through four different geotechnical units. Each of these geotechnical units was modeled under three numerical models, considering locations where the tunnel encounters different Geotechnical units. Thus, Model I represents Upper basalt with N253/72, N046/81, and N329/82 joint sets of 0.2 m spacing (GU1) alongside an inclined 30 m thick fault zone (GU4) at 90 m depth. Models II and III represent Middle basalt with N157/80, N035/79, and N202/69 joint sets of 0.56 m spacing (GU2) at 190 m depth and Lower basalts N 022/86, N 231/81, and N 078/78 joint sets of 1.2 m spacing (GU3) at 356 m depth, respectively.\u003c/p\u003e \u003cp\u003eThe distribution of failure zones around the tunnels was studied through stress analyses, which involved varying Ko values between 0.5 and 2.0. The modeling results revealed that the presence of particular joint sets had a noticeable impact on the distribution of failed blocks, more obvious when Ko\u0026thinsp;\u0026gt;\u0026thinsp;1.0. The failed blocks in tunnels under the GU1 and GU2 units did distribute along a direction imposed by the joint sets with inclinations of N253/72 and N035/79, respectively. This suggests that these joint sets could induce anisotropic conditions in their corresponding rock mass during tunneling. Owing to better confinement, the presence of large and very large blocks around the opening, and the presence of high-angle dipping joints, the tunnel in the GU3 unit is stable with some local failures around the tunnel periphery. For tunnels in the GU4 unit, a significant concentration of failed blocks occurs in association with the maximum principal stress direction, despite the occurrence of failures throughout the tunnel periphery.\u003c/p\u003e \u003cp\u003eThe possible mode of failure in these tunnels was assessed and observed that all blocky rock mass along the alignment \u0026mdash; the GU1, GU2, and GU3 units \u0026mdash; underwent tensile failure without any change in the mode of failure in all the cases. As a result, it can be expected that tunneling in these rock mass could cause blocks to fail in a tensile mode of failure. Tunneling in the GU4 unit (the fault zone) caused dominant blocks to fail in a shear mode of failure, however both shear and tensile modes of failure could coexist. At Ko\u0026thinsp;=\u0026thinsp;0.5, the sidewalls experienced shear failure, and tension failures were more common on the roof and the floor. Subsequent increase in Ko to 1.0 resulted in a significant number of failed blocks primarily exhibited shear failures, however, the failed blocks near the sidewalls appeared to suffer from tensile failure. In this case, determining the mode of failure at the particular locations should be made based on the specific site conditions encountered.\u003c/p\u003e \u003cp\u003eFurthermore, stress analyses were conducted to investigate the possible vertical and horizontal displacements of the tunnels. The simulation results indicated that tunnels in the GU4 unit, increasing Ko led to a gradual increase in the horizontal displacement and an initial decrease, followed by a gradual increase and a subsequent rapid increase in the vertical displacement. In other blocky rock masses, the vertical displacement gradually decreased, whereas most horizontal displacements increased linearly with higher Ko values, except for the GU3 unit \u0026mdash;which remained unaffected. It can be concluded that tunneling in the fault zone could lead to greater horizontal and vertical convergences, with horizontal displacement exceeding vertical displacement. However, tunnels in the GU1 and GU2 units could primarily be affected by horizontal displacement rather than vertical one.\u003c/p\u003e \u003cp\u003eThe present study has shed a light on the necessity of a support system design for controlling large displacements, specific types of failure modes, and directional failures in the GU1, GU2, and GU4 units. As a result, when designing support measures, it is crucial to consider the anisotropic behavior of the rock mass in the GU1 and GU2 units. This implies that support systems should be oriented intersecting the joint sets with inclinations of N253/72 in the GU1 unit and N035/79 in the GU2 unit. In addition, the simulation results clearly demonstrate that if Ko is less than 1.0 in the tunnels through the GU4 unit, there is a need for longer and dense support systems at sidewalls, targeting the shear mode of failure, whereas shorter and dense support systems at roof and floor, targeting tensile mode of failure. On the other hand, if Ko exceeds 1.0, longer and dense support systems at the roof and floor are required, targeting the shear mode of failure mechanisms, whereas shorter and dense support systems at the sidewalls, targeting the tensile mode of failure. Generally, it is expected that by incorporating these recommendations, a comprehensive and effective rock mass support strategy can be implemented during the construction of these tunnels.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e \u003cstrong\u003eConflict of Interest\u003c/strong\u003e \u003cp\u003eOn behalf of all authors, the corresponding author states that there is no conflict of interest.\u003c/p\u003e \u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eMaterial preparation, data collection and analysis were performed by Mesay and Bayisa. The first draft of the manuscript was written by Mesay and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.\u003c/p\u003e\u003ch2\u003eAcknowledgments\u003c/h2\u003e \u003cp\u003eThis study was funded by the School of Earth Sciences of Addis Ababa University. We also extend our utmost gratitude to the Ethiopian Ministry of Water and Energy for their invaluable support in providing the data for this study.\u003c/p\u003e\u003ch2\u003eData Availability\u003c/h2\u003e \u003cp\u003eData sets and written commands generated during the current study are available from the corresponding author upon reasonable request.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eBarla G, Barla M (2000) Continuum and discontinuum modeling in tunnel engineering. Min Geol Pet Eng Bull. 12:45\u0026ndash;57. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://hrcak.srce.hr/file/8108\u003c/span\u003e\u003cspan address=\"https://hrcak.srce.hr/file/8108\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBarton N (1973) Review of a new shear strength criteria for rock joints. Eng. 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Construction and Building Materials, 259, 119530. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.conbuildmat.2020.119530\u003c/span\u003e\u003cspan address=\"10.1016/j.conbuildmat.2020.119530\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Block failure, Displacement, Distinct element method, Tunneling, Wabe Hydropower","lastPublishedDoi":"10.21203/rs.3.rs-3956277/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3956277/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIn designing suitable support systems and ensuring safe excavation of a tunnel, deformation and block failure assessment around the opening is a crucial aspect of tunneling. In this study, a distinct element modeling approach was employed to evaluate the distribution of failed blocks, failure modes, and displacements of the tunnels to gain insight into support recommendations for the Wabe Hydropower project in central Ethiopia. For this purpose, three representative numerical models were developed considering different rock mass along the tunnel alignment. Subsequently, the influence region classification technique was introduced and the models were systematically classified into three distinct regions. This technique enabled the consideration of blocky rock mass as discontinuum through the direct inclusion of field-measured joints with average spacings of 0.2, 0.56, and 1.2 m into a region surrounding the tunnel opening. The simulation results indicated that tunnels in closely jointed rock mass behave anisotropically, with failed blocks following the joint inclinations of N253/72 and N035/79 and exhibiting a tensile failure mode. Tunneling in the fault zone induced a shear failure mode, with a significant distribution of failed blocks aligned in the maximum principal stress direction. However, under low horizontal in-situ stress, both shear and tensile failure could exist, tensile failure affecting the roof and floor. Furthermore, tunnels in closely jointed rock mass are primarily influenced by horizontal displacement, whereas tunneling in fault zones led to both greater horizontal and vertical convergences, with horizontal displacement being more significant. Finally, the obtained results were used to propose support recommendations.\u003c/p\u003e","manuscriptTitle":"3D Numerical Analysis for Failure and Deformation Assessment of the Waterway Tunnel, Wabe Hydropower Project, Central Ethiopia","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-02-21 05:04:15","doi":"10.21203/rs.3.rs-3956277/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"6826a582-a56c-4d55-a9fc-3de21bce9a1b","owner":[],"postedDate":"February 21st, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2024-04-07T14:29:46+00:00","versionOfRecord":[],"versionCreatedAt":"2024-02-21 05:04:15","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-3956277","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-3956277","identity":"rs-3956277","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}