Hanoi University of Mining & Geology Entrance Exam Set

The question probes the understanding of geological stress regimes and their relationship to faulting mechanisms, a core concept in structural geology relevant to mining and resource exploration. The scenario describes a rock mass subjected to a stress state where the maximum principal stress (\(\sigma_1\)) is vertical, and the minimum principal stress (\(\sigma_3\)) is horizontal. The intermediate principal stress (\(\sigma_2\)) is also horizontal and lies perpendicular to \(\sigma_3\). In this configuration, the shear stress (\(\tau\)) on a plane is maximized when the plane is oriented at an angle of \(45^\circ\) to the principal stress directions. Specifically, for a vertical \(\sigma_1\) and horizontal \(\sigma_3\), the maximum shear stress occurs on planes oriented at \(45^\circ\) to the vertical and horizontal axes. According to the Andersonian theory of faulting, normal faults form when the least principal stress (\(\sigma_3\)) is horizontal and the greatest principal stress (\(\sigma_1\)) is vertical. In this case, the shear planes are oriented at approximately \(30^\circ\) to \(\sigma_1\) (or \(60^\circ\) to \(\sigma_3\)). Reverse faults form when \(\sigma_1\) is horizontal and \(\sigma_3\) is vertical, with shear planes at \(30^\circ\) to \(\sigma_1\). Strike-slip faults occur when \(\sigma_1\) and \(\sigma_3\) are both horizontal and perpendicular to each other, with the intermediate principal stress (\(\sigma_2\)) being vertical. The shear planes for strike-slip faults are oriented at approximately \(30^\circ\) to the maximum horizontal stress (\(\sigma_1\)). The scenario presented, with \(\sigma_1\) vertical and \(\sigma_3\) horizontal, directly corresponds to a normal faulting regime. The question asks about the orientation of the fault plane that would experience the *maximum shear stress* under this specific stress state. The maximum shear stress occurs on planes oriented at \(45^\circ\) to the principal stress directions. Therefore, the fault plane experiencing maximum shear stress would be oriented at \(45^\circ\) to the vertical (the direction of \(\sigma_1\)) and \(45^\circ\) to the horizontal (the direction of \(\sigma_3\)). This orientation is characteristic of the planes where shear failure is most likely to initiate, even though the resulting fault type (normal fault) is typically associated with planes at \(30^\circ\) to the maximum principal stress. The question specifically asks for the orientation of maximum shear stress, not the orientation of the resulting fault plane according to Anderson’s theory. The correct answer is therefore a plane oriented at \(45^\circ\) to the vertical and \(45^\circ\) to the horizontal.

The question probes the understanding of geological stress regimes and their influence on rock deformation, a core concept in mining and geological engineering relevant to Hanoi University of Mining & Geology. The scenario describes a rock mass subjected to differential stress, where the maximum principal stress (\(\sigma_1\)) is significantly greater than the minimum principal stress (\(\sigma_3\)), and the intermediate principal stress (\(\sigma_2\)) lies between them. This condition, \(\sigma_1 > \sigma_2 > \sigma_3\), is characteristic of a **strike-slip faulting** regime. In such a regime, the intermediate principal stress is oriented horizontally, and the maximum principal stress is also horizontal but perpendicular to the intermediate stress. The minimum principal stress is vertical, typically due to gravity. This stress orientation leads to shear failure along planes that are inclined to the maximum principal stress, resulting in strike-slip fault movement. The other options represent different stress regimes: * **Normal faulting** occurs when \(\sigma_1\) is vertical and \(\sigma_3\) is horizontal (\(\sigma_1 > \sigma_2 = \sigma_3\)). * **Thrust faulting** (or reverse faulting) occurs when \(\sigma_1\) is horizontal and \(\sigma_3\) is vertical (\(\sigma_1 = \sigma_2 > \sigma_3\)). * A **hydrostatic** stress condition implies equal stress in all directions (\(\sigma_1 = \sigma_2 = \sigma_3\)), which would not induce directional shear failure. Therefore, the described stress state, with a significant difference between the maximum and minimum principal stresses and the intermediate stress being horizontal and perpendicular to the maximum, directly corresponds to the conditions necessary for strike-slip faulting. This understanding is crucial for predicting rock mass behavior in underground excavations and for analyzing tectonic activity in mining regions studied by Hanoi University of Mining & Geology.

The question probes the understanding of geological stress regimes and their influence on rock deformation, a core concept in mining and geological engineering programs at Hanoi University of Mining & Geology. The scenario describes a deep underground excavation where the ambient stress state is predominantly horizontal and anisotropic. In such a condition, the maximum principal stress (\(\sigma_1\)) is horizontal, and the minimum principal stress (\(\sigma_3\)) is also horizontal but perpendicular to \(\sigma_1\). The vertical stress (\(\sigma_v\)) is typically less than the horizontal stresses at significant depths. The key to answering this question lies in understanding how these stress orientations affect the failure mechanisms of the surrounding rock mass. When an excavation is made, stress concentrations occur around the opening. The rock will fail when the stresses exceed its strength. In a regime with dominant horizontal stresses, shear failure is often the primary mode of deformation. The orientation of these shear planes is typically at an angle to the maximum principal stress. Considering the anisotropic horizontal stress field, the stress concentration around the excavation will be uneven. The rock mass will tend to fail along planes that are oriented relative to the maximum horizontal stress. Specifically, shear failure planes are expected to form at an angle of approximately 30 degrees to the direction of the maximum principal stress (\(\sigma_1\)). Given that \(\sigma_1\) is horizontal and the excavation is also horizontal, the shear planes will be oriented at an angle to the horizontal axis of the excavation. The presence of a significant intermediate principal stress (\(\sigma_2\)) also influences the failure mode, but the dominant factor in this anisotropic horizontal stress scenario is the orientation of \(\sigma_1\). Therefore, the most likely failure orientation will be at an angle to the excavation’s axis, dictated by the direction of the maximum horizontal stress. The question asks about the orientation of the failure *zone*, which implies the planes of shear. The most common failure mode under these conditions is conjugate shear failure, where two sets of shear planes form, bisecting the angle between the maximum and minimum principal stresses. However, the question asks for the orientation relative to the excavation axis, which is aligned with the horizontal plane. The critical factor is the angle to the maximum principal stress. The correct answer is the orientation that reflects shear failure planes oriented at an angle to the maximum horizontal stress. This angle is typically around 30 degrees. Therefore, failure zones oriented at approximately 30 degrees to the horizontal axis of the excavation, which aligns with the direction of the maximum horizontal stress, are the most probable.

The core concept here relates to the principles of geotechnical engineering and rock mechanics, specifically concerning the influence of discontinuities on rock mass behavior, a fundamental area of study at Hanoi University of Mining & Geology. The question probes the understanding of how the orientation and characteristics of joints affect the shear strength and stability of a rock slope. Consider a rock mass with a dominant joint set dipping at an angle \( \beta \) into the slope. The friction angle of the joint surface is \( \phi \). For a planar failure to occur along this joint, the dip angle of the joint must be less than the dip of the slope face, and the dip of the slope face must be greater than the friction angle of the joint. More critically, for sliding to be initiated, the driving forces (component of gravity acting parallel to the joint) must overcome the resisting forces (friction along the joint). The critical condition for instability, assuming a simple planar failure mechanism, occurs when the dip of the discontinuity is equal to the dip of the slope face, and this dip angle is greater than the friction angle of the discontinuity. However, the question asks about the *most influential factor* in determining the *potential* for failure, which is the relative orientation of the discontinuity to the slope face and the shear strength along that discontinuity. The shear strength of a rock mass is significantly governed by the shear strength of its discontinuities. The Mohr-Coulomb failure criterion, often applied to discontinuities, states that shear strength (\( \tau \)) is a function of cohesion (\( c \)) and the normal stress (\( \sigma_n \)) acting on the surface: \( \tau = c + \sigma_n \tan \phi \). In the context of a rock slope, the normal stress is influenced by the weight of the rock mass and its geometry, and the friction angle (\( \phi \)) is a critical parameter representing the inherent resistance to sliding along the joint. When analyzing rock slope stability, the orientation of discontinuities relative to the slope face is paramount. If a joint set is favorably oriented (dipping out of the slope at an angle similar to or less than the slope face angle, and with a dip direction parallel to the slope strike), it can create a kinematic mechanism for failure. However, even with a favorable orientation, if the shear strength along the discontinuity is high (e.g., due to roughness or infill), failure may not occur. Conversely, a discontinuity with a low shear strength, even if not perfectly oriented for planar failure, can still contribute to overall slope instability through complex failure modes or by reducing the effective shear strength of the rock mass. Therefore, while the orientation of the discontinuity is crucial for kinematic feasibility of failure, the *shear strength along the discontinuity* is the fundamental parameter that dictates whether failure will actually occur under a given stress state. A discontinuity with a very low friction angle and minimal cohesion will be prone to failure even under moderate normal stresses and less critical orientations, whereas a very strong discontinuity might resist failure even with a more favorable orientation. At Hanoi University of Mining & Geology, understanding these fundamental rock mass properties is essential for designing safe and stable excavations and slopes in mining and civil engineering projects. The ability to accurately assess and model the shear strength of discontinuities is a cornerstone of geotechnical analysis.

The question probes the understanding of geological surveying principles, specifically focusing on the selection of appropriate geophysical methods for subsurface investigation in a mining context. The scenario describes a need to identify potential ore bodies and assess their depth and lateral extent within a sedimentary basin, characterized by varying lithologies and potential groundwater influence. For this scenario, the most suitable geophysical method would be Electrical Resistivity Tomography (ERT). ERT is highly effective in mapping subsurface resistivity variations, which are directly related to lithological changes, the presence of conductive minerals (like metallic ores), and pore fluid content (including groundwater). The technique involves deploying an array of electrodes on the surface and measuring apparent resistivity values for various current injection and potential measurement electrode pairs. These data are then inverted to produce a 2D or 3D model of the subsurface resistivity distribution. This allows for the visualization of geological structures, identification of anomalous zones indicative of mineralization, and estimation of their depths and geometries. Seismic refraction, while useful for determining bedrock depth and seismic velocity contrasts, is less sensitive to subtle resistivity variations associated with disseminated mineralization or variations in pore fluid salinity. Ground Penetrating Radar (GPR) is excellent for shallow subsurface investigations and detecting interfaces, but its penetration depth is significantly limited in conductive environments, which are common in mining areas with groundwater or clay-rich sediments. Magnetometry is primarily used to detect magnetic anomalies, typically associated with iron-bearing minerals or igneous intrusions, and would be less effective for non-magnetic ore bodies or in areas with significant magnetic noise from geological or anthropogenic sources. Therefore, ERT offers the best balance of penetration depth, resolution, and sensitivity to the geological and hydrogeological conditions described, making it the most appropriate choice for the stated objectives at the Hanoi University of Mining & Geology.

The question probes the understanding of geological stress regimes and their implications for rock mechanics, a core area for students at Hanoi University of Mining & Geology. The scenario describes a deep underground excavation where the primary stress is vertical due to overburden, and the horizontal stresses are equal. This defines a hydrostatic stress state, where \(\sigma_1 = \sigma_2 > \sigma_3\). In this context, \(\sigma_v\) represents the vertical stress, and \(\sigma_h\) represents the horizontal stress. Given that the horizontal stresses are equal, \(\sigma_h = \sigma_h\). The problem states the primary stress is vertical, implying \(\sigma_v\) is the maximum or at least a significant component. The condition of equal horizontal stresses means \(\sigma_1 = \sigma_2\) and \(\sigma_3\) is the minimum. In a hydrostatic stress state, the vertical stress is equal to the horizontal stress, i.e., \(\sigma_v = \sigma_h\). Therefore, the stress regime is characterized by equal principal stresses, \(\sigma_1 = \sigma_2 = \sigma_3\). This condition is crucial for predicting rock behavior, such as the likelihood of brittle fracture or ductile deformation, and influences the design of underground openings to prevent collapse. Understanding these stress states is fundamental for mining engineering, geotechnical engineering, and petroleum engineering, all of which are prominent disciplines at Hanoi University of Mining & Geology. The ability to identify a hydrostatic stress state from a description of stress components is a key analytical skill for assessing geological conditions and engineering challenges.

The question probes the understanding of geological stress regimes and their impact on rock deformation, a core concept in mining and geological engineering relevant to Hanoi University of Mining & Geology. The scenario describes a rock mass subjected to differential stresses. In a compressional stress regime, the maximum principal stress (\(\sigma_1\)) is vertical, and the minimum principal stress (\(\sigma_3\)) is horizontal. However, the question specifies that the horizontal stresses are unequal, meaning \(\sigma_2\) and \(\sigma_3\) are both horizontal, with \(\sigma_2 > \sigma_3\). This configuration, where the intermediate principal stress (\(\sigma_2\)) is horizontal and greater than the minimum principal stress (\(\sigma_3\)), is characteristic of a strike-slip faulting environment. In such a regime, the vertical stress (\(\sigma_v\)) is typically the intermediate principal stress (\(\sigma_2\)) or the maximum principal stress (\(\sigma_1\)), depending on the relative magnitudes of horizontal stresses and overburden pressure. Given the description of significant horizontal stress anisotropy, the most likely scenario for the principal stress orientation is that the maximum principal stress (\(\sigma_1\)) is horizontal, the minimum principal stress (\(\sigma_3\)) is horizontal and perpendicular to \(\sigma_1\), and the intermediate principal stress (\(\sigma_2\)) is vertical (\(\sigma_v\)). This orientation is consistent with strike-slip faulting, where horizontal stresses dominate. Therefore, the vertical stress is the intermediate principal stress.

The question probes the understanding of the fundamental principles governing the stability of slopes in geotechnical engineering, a core area for Hanoi University of Mining & Geology. The scenario describes a potential failure mechanism where a block of soil detaches along a curved surface. The most critical factor influencing the likelihood of such a failure, particularly in the context of a curved slip surface, is the shear strength of the soil along that surface. Shear strength, which is a combination of cohesion and friction, directly opposes the driving forces (gravity acting on the soil mass). While factors like groundwater pressure and the geometry of the slope are crucial, they influence the *magnitude* of the driving forces and the *effective stress* at the slip surface, thereby impacting the shear resistance. However, the *inherent capacity* of the soil to resist sliding is its shear strength. Therefore, an increase in the shear strength of the soil along the potential slip surface would most directly and significantly enhance the overall stability of the slope against this type of failure. This aligns with the principles of limit equilibrium methods used in slope stability analysis, where the factor of safety is calculated as the ratio of resisting forces (derived from shear strength) to driving forces.

The question probes the understanding of geological surveying principles, specifically focusing on the challenges of mapping in areas with complex geological structures and limited accessibility, a core competency for students at Hanoi University of Mining & Geology. The scenario describes a survey team in a mountainous region of Vietnam, characterized by steep slopes, dense vegetation, and potential fault lines. The objective is to determine the most efficient and accurate method for establishing control points for a detailed geological map. Option A, “Establishing a dense network of ground-based control points using total stations and GPS, supplemented by drone-based photogrammetry for inaccessible areas,” represents the most comprehensive and robust approach. Total stations and GPS are standard for establishing precise horizontal and vertical control, crucial for accurate mapping. The addition of drone photogrammetry addresses the accessibility issue, allowing for data acquisition in steep or vegetated terrain where traditional methods are difficult or impossible. This integrated approach aligns with modern surveying practices and the need for high-resolution data in complex environments, reflecting the advanced training expected at Hanoi University of Mining & Geology. Option B, “Relying solely on satellite imagery for topographic and geological feature identification,” would be insufficient due to the resolution limitations of satellite imagery for detailed geological mapping and the potential obscuration by canopy cover. Option C, “Utilizing only traditional compass and clinometer measurements for orientation and elevation,” would be highly inaccurate and time-consuming in such a challenging terrain, lacking the precision required for a geological map. Option D, “Implementing a purely airborne LiDAR survey without ground-truthing,” while providing good topographic data, might miss subtle geological features and requires ground verification for accurate geological interpretation, especially in areas with dense vegetation that can interfere with LiDAR signals. Therefore, the integrated approach in Option A is the most appropriate for the described scenario and the academic rigor of Hanoi University of Mining & Geology.

The question probes the understanding of geological stress regimes and their impact on rock deformation, a core concept in mining and geological engineering relevant to Hanoi University of Mining & Geology. The scenario describes a deep underground excavation where the ambient stress state is predominantly vertical due to overburden, with horizontal stresses being significantly less pronounced. This condition, where the maximum principal stress (\(\sigma_1\)) is vertical and the minimum principal stress (\(\sigma_3\)) is horizontal, defines a **normal faulting stress regime**. In such a regime, shear failure along planes oriented at an angle to the maximum principal stress is facilitated, leading to the formation of normal faults. This is crucial for understanding rock mass behavior, potential instability, and the design of underground openings in mining operations. The other options represent different stress regimes: strike-slip faulting occurs in a transcurrent stress regime where the maximum and minimum principal stresses are horizontal and intermediate stress is vertical; reverse faulting (or thrust faulting) occurs in a compressional stress regime where the maximum principal stress is horizontal and the minimum principal stress is vertical; and finally, a hydrostatic stress state implies equal stress in all directions, which is not typical for deep geological environments with overburden. Therefore, the described conditions directly correspond to a normal faulting stress regime.

The question probes the understanding of geological stress regimes and their impact on rock deformation, a core concept in mining and geological engineering programs at Hanoi University of Mining & Geology. The scenario describes a deep underground excavation where the ambient stress state is characterized by a dominant vertical stress (\(\sigma_v\)) due to overburden, and significantly lower horizontal stresses (\(\sigma_h\)). This typically corresponds to a normal faulting stress regime, where \(\sigma_v > \sigma_h\). In such a regime, shear failure is most likely to occur on planes oriented at an angle to the maximum principal stress. According to the Mohr-Coulomb failure criterion, the angle of the failure plane relative to the maximum principal stress (\(\sigma_1\)) is given by \(45^\circ – \frac{\phi}{2}\), where \(\phi\) is the angle of internal friction. In a normal faulting regime, the vertical stress is the maximum principal stress (\(\sigma_1 = \sigma_v\)), and the minimum principal stress (\(\sigma_3\)) is the least horizontal stress (\(\sigma_h\)). Therefore, shear failure will occur on planes oriented at \(45^\circ – \frac{\phi}{2}\) to the vertical. The question asks about the orientation of potential failure planes relative to the *least* principal stress (\(\sigma_3\)). The angle between the maximum and minimum principal stress is \(90^\circ\). If the failure plane is at \(45^\circ – \frac{\phi}{2}\) to \(\sigma_1\), then its angle to \(\sigma_3\) will be \(90^\circ – (45^\circ – \frac{\phi}{2}) = 45^\circ + \frac{\phi}{2}\). This orientation is critical for understanding rock mass stability around mine openings, tunnel design, and the potential for seismic events in mining environments, aligning with the research strengths of Hanoi University of Mining & Geology in geomechanics and underground engineering.

The question probes the understanding of geological surveying principles, specifically focusing on the selection of appropriate geophysical methods for subsurface anomaly detection in a mining context relevant to Hanoi University of Mining & Geology’s curriculum. The scenario describes a need to identify potential mineral deposits characterized by variations in electrical resistivity. Electrical resistivity methods, such as Electrical Resistivity Tomography (ERT) and Induced Polarization (IP), are highly sensitive to changes in the subsurface electrical properties, which are directly influenced by mineral content, porosity, and fluid saturation. ERT provides detailed 2D or 3D images of resistivity distribution, making it ideal for delineating geological structures and potential ore bodies. IP, often used in conjunction with resistivity, measures chargeability, which can indicate the presence of disseminated sulfides or other chargeable minerals. Seismic methods (reflection and refraction) primarily detect variations in seismic velocity, which are related to rock density and elastic properties. While useful for structural mapping and identifying different rock layers, they are less directly sensitive to the subtle electrical property changes associated with many ore types compared to electrical methods. Gravity surveys detect density variations, and magnetic surveys detect magnetic susceptibility variations. These methods are excellent for identifying massive sulfide deposits or iron ore bodies, but their effectiveness for detecting disseminated or non-magnetic mineralizations with significant resistivity contrasts is generally lower than electrical methods. Therefore, given the emphasis on resistivity variations for mineral deposit identification, electrical resistivity and induced polarization techniques are the most suitable primary geophysical tools.

The question probes the understanding of geological stress regimes and their influence on rock deformation, a core concept in mining and geological engineering relevant to Hanoi University of Mining & Geology. The scenario describes a deep underground excavation where the in-situ stress state is predominantly horizontal, with the maximum principal stress (\(\sigma_1\)) oriented horizontally and the minimum principal stress (\(\sigma_3\)) also horizontal, perpendicular to \(\sigma_1\). The vertical stress (\(\sigma_v\)) is the overburden pressure. In such a regime, the horizontal stresses are greater than the vertical stress. When an excavation is made, stress concentrations occur around the opening. The critical factor for stability, particularly in terms of rockbursts or spalling, is the magnitude of the tangential stress developed around the excavation. In a situation with high horizontal stresses, the tangential stress will be maximized in the direction of the minimum horizontal stress. If this tangential stress exceeds the rock’s tensile strength or compressive strength (depending on the failure mechanism), failure will occur. The question asks about the orientation of the maximum tangential stress concentration relative to the excavation. Given that \(\sigma_1\) is horizontal and \(\sigma_3\) is horizontal and perpendicular to \(\sigma_1\), and \(\sigma_v\) is vertical, the stress field is characterized by significant horizontal compression. For a circular opening, the tangential stress is highest in the direction of the minimum principal stress. Therefore, the maximum tangential stress concentration will develop parallel to the direction of the minimum horizontal stress, which is also horizontal. This means the failure would likely initiate along the sides of the excavation that are aligned with the direction of the maximum horizontal stress, and the tangential stress would be highest in the direction of the minimum horizontal stress. The question asks for the orientation of the *maximum tangential stress concentration*. In a stress field where horizontal stresses dominate, and assuming a circular opening, the tangential stress is highest in the direction of the minimum principal stress. If the maximum horizontal stress is \(\sigma_H\) and the minimum horizontal stress is \(\sigma_h\), and \(\sigma_v\) is the vertical stress, with \(\sigma_H > \sigma_h\) and potentially \(\sigma_H > \sigma_v\), the tangential stress around a circular opening will be \(2\sigma_H – \sigma_h\) in the direction of \(\sigma_h\) and \(2\sigma_h – \sigma_H\) in the direction of \(\sigma_H\). The maximum tangential stress is therefore in the direction of the minimum horizontal stress. Thus, the maximum tangential stress concentration will be oriented parallel to the minimum horizontal stress.

The question probes the understanding of rock mechanics principles relevant to underground excavation stability, a core area for Hanoi University of Mining & Geology. The scenario describes a tunnel excavation in a rock mass characterized by a specific stress state and rock mass properties. The critical factor for assessing stability in such a context, especially concerning the potential for brittle failure or spalling around the excavation periphery, is the relationship between the in-situ stress and the rock’s tensile strength. The primary failure mechanism in many rock excavations, particularly in competent but brittle rock masses under significant confinement, is tensile failure or splitting, often initiated by stress concentrations around the opening. This occurs when the tangential stress at the excavation boundary exceeds the rock’s tensile strength. While compressive strength is important for overall rock mass behavior, tensile strength is the limiting factor for the immediate zone of failure around an opening where tensile stresses can develop due to stress redistribution. The calculation, though conceptual and not requiring numerical input, would involve comparing the tangential stress around the tunnel to the rock’s tensile strength. In a simplified elastic analysis, the tangential stress (\(\sigma_\theta\)) at the excavation boundary can be significantly higher than the in-situ stresses. For a circular opening under uniform external pressure (\(P_0\)), the tangential stress at the crown and invert (where tensile stresses are most likely to occur in a vertical stress regime) can be approximately \(3P_0\). However, the question focuses on the *initiation* of failure. The rock mass’s ability to withstand these induced tensile stresses is dictated by its tensile strength. Therefore, the most direct indicator of the potential for immediate failure, such as spalling or tensile fracturing, is the comparison of the tangential stress to the rock’s tensile strength. The explanation emphasizes that the tensile strength of the rock mass is the critical parameter because it directly governs the onset of tensile failure, which is a common mode of instability in tunnel excavations where stress concentrations can induce tensile stresses at the excavation boundary. Understanding this relationship is fundamental to selecting appropriate support systems and excavation methods to ensure the safety and stability of underground structures, a key competency for graduates of Hanoi University of Mining & Geology. The other options, while related to rock mechanics, are not the *primary* determinant for the initial tensile failure around an excavation. Uniaxial compressive strength is a measure of resistance to crushing, not tensile splitting. The Hoek-Brown failure criterion is a more complex model for predicting failure in rock masses, but the question is focused on the initial tensile failure mechanism. The friction angle is crucial for shear failure, not tensile failure.

The core principle at play here is the concept of **geological stress regimes** and their influence on rock deformation and faulting. A compressional stress regime, characterized by dominant horizontal compression and weaker vertical stress, leads to the formation of **reverse faults** or **thrust faults**. In such a scenario, the hanging wall moves up relative to the footwall due to the compressive forces. Conversely, a tensional stress regime, with dominant horizontal extension and weaker vertical stress, results in **normal faults**, where the hanging wall moves down. A shear stress regime, where stresses are oriented obliquely to the potential fault plane, produces **strike-slip faults**. The question describes a situation where a geologist at Hanoi University of Mining & Geology observes evidence of significant horizontal shortening within a sedimentary basin. This shortening implies that the rock layers have been squeezed together from the sides. Such squeezing is a direct manifestation of **compressional forces** acting predominantly in the horizontal plane. When compressional forces are the dominant stress component, they tend to shorten the crust in one direction and thicken it in another. This compression, when it exceeds the rock’s strength, causes brittle failure along planes of weakness, resulting in faulting. Specifically, the upward movement of the hanging wall relative to the footwall, which is characteristic of reverse and thrust faults, is the direct consequence of these horizontal compressional stresses. Therefore, the most likely geological structure to be observed in a region experiencing pronounced horizontal shortening, indicative of a compressional stress regime, would be reverse faults.

The question assesses understanding of geological surveying principles, specifically the impact of sampling density on the accuracy of resource estimation in a mining context, relevant to Hanoi University of Mining & Geology’s curriculum. The core concept is the relationship between spatial data resolution and the reliability of interpolating values between sample points. A higher sampling density leads to a more detailed and accurate representation of the subsurface geological features and mineral distribution. This, in turn, reduces the uncertainty in estimating the total volume and grade of the mineral deposit. Conversely, sparse sampling can result in significant overestimation or underestimation of resources due to the inability to capture localized variations in ore body geometry and grade. Therefore, to achieve a high degree of confidence in resource classification, particularly for categories requiring greater certainty like “Indicated” or “Measured” resources, a denser sampling grid is paramount. This is because the geological variability within the deposit necessitates more data points to establish reliable spatial correlations and reduce the extrapolation error inherent in interpolation methods. The Hanoi University of Mining & Geology emphasizes rigorous data acquisition and analysis for responsible resource management, making this understanding crucial for its students.

The question probes the understanding of geological stress regimes and their impact on rock deformation, a core concept in mining and geological engineering relevant to Hanoi University of Mining & Geology. The scenario describes a rock mass subjected to differential stresses, leading to a specific type of failure. In a triaxial compression test, the confining pressure (\(\sigma_3\)) is applied uniformly around the sample, while the axial stress (\(\sigma_1\)) is increased. The relationship between these stresses and the rock’s strength is governed by failure criteria, such as the Mohr-Coulomb criterion. The question implies a situation where the horizontal stresses are significantly different, and the vertical stress is also a factor. Let’s consider the principal stresses: \(\sigma_1\) (maximum principal stress), \(\sigma_2\) (intermediate principal stress), and \(\sigma_3\) (minimum principal stress). The scenario implies that the rock is failing due to shear. In a typical underground mining environment, the vertical stress (\(\sigma_v\)) is often related to the overburden depth. Horizontal stresses (\(\sigma_h\)) can be influenced by tectonic forces and the rock’s elastic properties. If \(\sigma_1 > \sigma_2 > \sigma_3\), and failure occurs along a plane inclined at an angle to \(\sigma_1\), this is characteristic of shear failure. The question describes a situation where the rock is being compressed axially and laterally, but the lateral confinement is not uniform. The key is to identify the stress state that leads to shear failure in this context. Consider a scenario where the vertical stress (\(\sigma_v\)) is the maximum principal stress (\(\sigma_1\)), and the two horizontal stresses (\(\sigma_{h1}\) and \(\sigma_{h2}\)) are less than \(\sigma_v\). If \(\sigma_{h1} \neq \sigma_{h2}\), this creates an anisotropic stress field. However, the question describes a situation where the rock is failing under compression, implying that the applied stresses are causing it to yield. The most appropriate answer relates to the conditions that promote shear failure. Shear failure typically occurs when the shear stress on a plane exceeds the shear strength of the rock. In a compressional regime, this often manifests as failure along planes inclined at an angle to the maximum principal stress. The presence of differential horizontal stresses, combined with vertical stress, creates a complex stress state. The correct answer describes a situation where the maximum principal stress is significantly greater than the intermediate and minimum principal stresses, leading to shear failure. This is a common failure mode in many geological and mining contexts. The other options describe stress states that would lead to different deformation mechanisms or would not necessarily result in the described shear failure. For instance, a hydrostatic stress state would cause volumetric strain but not typically shear failure. A purely tensile stress state would lead to tensile fracture. A state where the intermediate and minimum principal stresses are equal but significantly lower than the maximum principal stress would still promote shear failure, but the specific wording of the correct answer best captures the essence of the described failure under differential compression. The scenario implicitly describes a compressional stress regime where the maximum principal stress is significantly larger than the other two principal stresses, leading to shear failure along planes oriented at an angle to the maximum principal stress. This is a fundamental concept in rock mechanics taught at the Hanoi University of Mining & Geology, crucial for understanding underground excavation stability and rock mass behavior.

The question probes the understanding of the fundamental principles governing the stability and performance of slopes in geotechnical engineering, a core area for Hanoi University of Mining & Geology. The scenario describes a cut slope in a saturated clay deposit. The critical factor for slope stability in saturated clays, particularly under undrained conditions often assumed for short-term stability analysis of excavations, is the undrained shear strength (\(c_u\)). The factor of safety (FS) for a slope is generally calculated as the ratio of resisting forces to driving forces. In the context of shear strength, this translates to the ratio of the available shear strength along a potential slip surface to the shear stress acting on that surface. For a saturated clay, the undrained shear strength is the primary parameter contributing to the resisting forces. The question asks which factor, if increased, would most significantly improve the stability of the slope. Let’s analyze the options: * **Increased pore water pressure:** Higher pore water pressure reduces the effective stress in the soil. Effective stress is the stress that controls the soil’s strength. Therefore, increased pore water pressure *decreases* the shear strength and thus *reduces* the factor of safety, making the slope less stable. This is a critical concept in geotechnical engineering, especially relevant to the university’s focus on mining and geology where water management is paramount. * **Increased unit weight of the soil:** An increase in the unit weight of the soil increases the driving forces (due to increased overburden pressure) and potentially the resisting forces (if strength is dependent on effective stress). However, for a saturated clay where undrained shear strength is dominant, an increase in unit weight generally leads to a higher driving force for a given geometry, thus *decreasing* the factor of safety. * **Increased undrained shear strength (\(c_u\)):** The undrained shear strength (\(c_u\)) directly represents the soil’s resistance to shearing failure under undrained conditions. A higher \(c_u\) means greater resisting forces along any potential slip surface. Since the factor of safety is directly proportional to the shear strength, increasing \(c_u\) will directly increase the factor of safety, thereby improving slope stability. This is a foundational principle in slope stability analysis taught at the university. * **Increased slope angle:** Increasing the slope angle increases the driving forces (due to a steeper inclination of the weight vector of the soil mass) while the resisting forces (related to the shear strength along the slip surface) might not increase proportionally or could even decrease if the slip surface length changes unfavorably. Therefore, increasing the slope angle generally *reduces* the factor of safety, making the slope less stable. Based on this analysis, increasing the undrained shear strength (\(c_u\)) is the most direct and significant method to improve the stability of a slope in saturated clay. This aligns with the university’s emphasis on understanding soil mechanics and its application in excavation and infrastructure projects. The ability to assess and enhance the shear strength of soil is vital for safe and efficient operations in mining and civil engineering.

The question probes the understanding of geological principles related to the formation and stability of underground excavations, a core area for students at Hanoi University of Mining & Geology. The scenario describes a deep underground mine shaft in a region characterized by high in-situ stresses and the presence of a significant fault zone. The primary concern for stability in such an environment is the potential for rock mass failure due to these stresses, particularly around discontinuities like faults. The concept of “stress concentration” is paramount. When an excavation is made, the stress field around it redistributes. In areas of high in-situ stress, especially near geological structures like faults, these stresses can become significantly amplified. This concentration can exceed the rock mass’s strength, leading to failure mechanisms such as shear slip along the fault, brittle fracture, or even large-scale block failure. Considering the options: 1. **”The presence of a major fault zone, acting as a pre-existing plane of weakness, significantly amplifies stress concentrations around the excavation, increasing the likelihood of shear failure along the fault.”** This option directly addresses the combined effects of high in-situ stress and a geological discontinuity. Faults are inherently weaker zones and act as conduits for stress redistribution. The excavation’s presence will further concentrate stress at the intersection with the fault, making shear failure the most probable outcome. This aligns with fundamental rock mechanics principles taught at Hanoi University of Mining & Geology. 2. **”The primary concern is the potential for seismic activity induced by the excavation, which is independent of the fault’s presence.”** While induced seismicity can occur, it’s often linked to stress changes and slip on existing faults. Attributing it as *independent* of the fault and the primary concern over direct shear failure is less accurate in this high-stress, fault-proximate scenario. 3. **”The excavation will primarily lead to a reduction in pore water pressure, causing consolidation and potential subsidence, irrespective of the fault.”** While pore water pressure is a factor in rock mechanics, a reduction in pressure leading to consolidation and subsidence is more typical in unconsolidated or saturated granular materials, not necessarily the primary failure mode in a deep, high-stress rock mass with a fault. The stress concentration and fault weakness are more immediate threats. 4. **”The main challenge will be managing heat generated from geothermal gradients, which is exacerbated by the depth but not directly influenced by the fault.”** Geothermal gradients are relevant at depth, but the question emphasizes stress and faulting as the primary drivers of *stability* concerns. Heat management is a secondary operational concern compared to immediate structural integrity. Therefore, the most accurate and critical concern, reflecting the principles of rock mechanics and engineering geology relevant to Hanoi University of Mining & Geology’s curriculum, is the amplified stress concentration and shear failure along the fault.

The question tests the understanding of the principles of geological surveying and the selection of appropriate geophysical methods for subsurface exploration, particularly in the context of mineral resource assessment relevant to Hanoi University of Mining & Geology’s curriculum. The scenario describes a need to identify a potential disseminated sulfide deposit, which is characterized by variations in electrical conductivity and magnetic susceptibility due to the presence of metallic minerals. Electrical Resistivity Tomography (ERT) is highly effective for mapping subsurface structures based on their electrical properties. Disseminated sulfide deposits, containing metallic minerals, typically exhibit lower resistivity compared to surrounding host rocks due to the conductive nature of sulfides. Therefore, ERT can delineate zones of anomalously low resistivity that may indicate the presence of such deposits. Induced Polarization (IP) is another crucial geophysical method for detecting disseminated sulfide mineralization. IP measures the chargeability of the subsurface, which is the ability of the ground to store electrical charge after the applied electric field is removed. Sulfide minerals, particularly those with a surface film of oxidation products, exhibit significant IP effects. Thus, IP surveys can directly identify zones with a high chargeability, correlating with the presence of disseminated sulfides. Magnetic surveys are useful for detecting magnetic minerals, such as pyrrhotite or magnetite, which are often associated with sulfide deposits. However, disseminated sulfides might not always be strongly magnetic, making magnetic methods less universally applicable for this specific type of deposit compared to electrical methods. Ground Penetrating Radar (GPR) is primarily used for shallow subsurface investigations and is sensitive to changes in dielectric properties. While it can detect interfaces and anomalies, it is generally less effective for identifying disseminated sulfide deposits at typical exploration depths compared to electrical methods, especially in environments with high conductivity. Considering the nature of disseminated sulfide deposits (conductivity and chargeability anomalies), a combination of ERT and IP would provide the most comprehensive and reliable data for initial exploration and targeting. ERT maps the resistivity structure, highlighting potential conductive zones, while IP directly probes the chargeability, confirming the presence of mineralized material. Therefore, the most appropriate approach for the initial phase of exploration at Hanoi University of Mining & Geology would be the integrated application of ERT and IP.

The question probes the understanding of geological surveying principles and their application in resource exploration, specifically concerning the identification of mineral deposits. The scenario describes a team using geophysical methods to investigate a subsurface anomaly. The core concept being tested is the interpretation of geophysical data in the context of geological formations and potential ore bodies. Geophysical surveys employ various techniques to infer subsurface properties. Magnetic surveys detect variations in the Earth’s magnetic field caused by differences in magnetic susceptibility of rocks. Gravity surveys measure subtle changes in gravitational acceleration, indicating density variations. Electrical resistivity surveys assess how well the ground conducts electricity, revealing differences in mineral content and pore fluids. Seismic surveys use sound waves to map subsurface structures and rock layers. In the context of identifying a potential polymetallic sulfide deposit, which often exhibits high density, magnetic susceptibility, and electrical conductivity due to the presence of metallic minerals like chalcopyrite, pyrite, and sphalerite, a combination of geophysical methods would be employed. However, the question asks which single method would be *most* indicative of such a deposit based on the provided scenario. Polymetallic sulfide ores are typically denser than the surrounding host rock. Therefore, a gravity survey would directly detect this density anomaly. While magnetic and electrical methods can also be sensitive to these deposits, their effectiveness depends on the specific mineralogy and geological setting. For instance, not all sulfide deposits are strongly magnetic, and electrical conductivity can be influenced by factors other than metallic sulfides, such as groundwater salinity. Seismic methods are primarily used for structural mapping and less directly for identifying specific mineral types unless they cause significant velocity contrasts. Considering the typical characteristics of polymetallic sulfide deposits and the direct relationship between density and gravity anomalies, a gravity survey is the most universally applicable and indicative geophysical method for initial detection of such subsurface concentrations. The calculation, therefore, involves understanding the direct correlation between the physical properties of the target deposit (density) and the property measured by the geophysical method (gravitational acceleration). A higher density (\(\rho_{ore} > \rho_{host}\)) will result in a positive gravity anomaly, making it a primary indicator.

The question probes the understanding of geological surveying principles, specifically focusing on the impact of varying rock mass discontinuities on the accuracy of volumetric estimations in underground excavation planning for a project at the Hanoi University of Mining & Geology. The core concept is how the presence and characteristics of joints, faults, and bedding planes (discontinuities) affect the bulk density and, consequently, the estimated mass of excavated material. A highly fractured rock mass with numerous, open, and persistent discontinuities will exhibit a lower bulk density than a massive, intact rock mass. This is because the discontinuities introduce voids and reduce the effective cross-sectional area of solid rock per unit volume. When calculating the total mass of excavated material for a given volume, a lower bulk density will result in a lower mass estimate. Conversely, a rock mass with fewer, tighter, and less persistent discontinuities will have a higher bulk density, leading to a higher mass estimate for the same excavation volume. Therefore, if a geological survey initially assumes a relatively intact rock mass (higher bulk density) but later discovers a significantly more fractured zone with extensive jointing, the actual excavated mass for a planned volume will be lower than initially predicted. This is because the bulk density used in the initial calculation would have been an overestimation. The question requires understanding that the physical properties of the rock mass, particularly its degree of fracturing, directly influence the relationship between excavated volume and mass, a critical consideration in material handling, transportation, and cost estimation for mining and civil engineering projects undertaken by students of Hanoi University of Mining & Geology.

The question probes the understanding of geological deformation mechanisms under varying stress and temperature conditions, a core concept in the study of structural geology and geomechanics at Hanoi University of Mining & Geology. The scenario describes a rock mass subjected to increasing confining pressure and temperature, simulating conditions found at greater depths within the Earth’s crust. At shallow depths, where confining pressures are low and temperatures are moderate, brittle deformation mechanisms like fracturing and faulting dominate. As pressure and temperature increase, the rock’s ductility rises. Ductile deformation, characterized by plastic flow and folding, becomes more prevalent. The transition from brittle to ductile behavior is not instantaneous but occurs over a range of conditions. At very high pressures and temperatures, typically found in the lower crust and upper mantle, diffusion creep and dislocation creep become the primary deformation mechanisms. Diffusion creep involves the movement of atoms along grain boundaries or through the crystal lattice, driven by stress gradients. Dislocation creep involves the movement of dislocations within the crystal structure, which is highly temperature-dependent. The question asks about the dominant mechanism at *significantly increased* confining pressure and temperature, implying conditions well beyond the shallow crust. While fracturing might still occur under specific localized stress concentrations, it is not the *dominant* mechanism in a uniformly stressed, high-pressure, high-temperature environment. Elastic deformation is always present but is recoverable and not the primary mode of permanent change. Plastic deformation encompasses a range of ductile mechanisms, but diffusion creep and dislocation creep are more specific and dominant at the extreme conditions implied. Between diffusion creep and dislocation creep, dislocation creep is generally considered the more significant contributor to bulk rock deformation at the elevated temperatures and pressures characteristic of deeper crustal and upper mantle environments, especially when considering the strain rates relevant to geological processes. Therefore, dislocation creep is the most appropriate answer for the dominant mechanism under significantly increased confining pressure and temperature.

The question probes the understanding of geological surveying principles, specifically concerning the accurate representation of subsurface geological structures on a topographic map. The core concept is how the dip and strike of a geological stratum interact with the contour lines of a topographic map to reveal its orientation. When a geological layer is horizontal, its strike line is parallel to the strike of the land surface. On a topographic map, this means the geological boundary representing the outcrop of this horizontal layer will follow the contour lines precisely. Therefore, if a geological stratum is perfectly horizontal, its outcrop trace on a topographic map will coincide with the contour lines of the same elevation. This is because the stratum’s intersection with the Earth’s surface occurs at a constant elevation, which is the definition of a contour line. Conversely, if the stratum were dipping, its outcrop trace would intersect contour lines at an angle, with the angle of intersection being related to the dip angle. The question requires recognizing this fundamental geometric relationship between a horizontal plane (the geological stratum) and the representation of elevation on a map.

The question probes the understanding of the fundamental principles governing the stability and behavior of slopes in geological formations, a core concern in mining and civil engineering at Hanoi University of Mining & Geology. The scenario describes a potential failure mechanism in a rock mass characterized by discontinuities. The critical factor in assessing the stability of such a block, particularly in the context of a potential toppling failure, is the orientation of the discontinuities relative to the slope face and the gravitational forces. Toppling failure occurs when blocks of rock pivot outwards from the slope face. This is most likely when the bedding planes or joints dip out of the slope at an angle that allows for rotation. Specifically, for a planar toppling failure, the critical condition is when the dip angle of the discontinuity (\(\alpha\)) is less than the dip angle of the slope face (\(\beta\)), and the dip direction of the discontinuity is roughly parallel to the dip direction of the slope face. Furthermore, the friction angle along the discontinuity (\(\phi\)) plays a crucial role. A key criterion for toppling is that the resultant force acting on the block must fall outside the base of support, which is influenced by the friction angle. The condition for toppling is often simplified by considering the relationship between the dip of the discontinuity and the dip of the slope. When the dip of the discontinuity is less than the dip of the slope, and the dip direction is favorable, the block can rotate. The presence of tension cracks behind the block can also facilitate toppling by reducing the effective weight and providing a pivot point. Considering the options, the most critical factor for initiating toppling failure in this context is the relationship between the discontinuity’s dip and the slope’s dip, coupled with the influence of friction. A discontinuity dipping out of the slope at an angle less than the slope face, with a favorable dip direction, and a friction angle that does not provide sufficient resistance to sliding or rotation, will lead to toppling. The question implicitly asks for the most significant geometric and frictional condition that predisposes a block to toppling. The critical angle for toppling is related to the angle of the slope face and the friction angle. A common criterion for the initiation of toppling is when the dip of the discontinuity (\(\alpha\)) is less than the dip of the slope (\(\beta\)), and the friction angle (\(\phi\)) is also less than the dip of the discontinuity. However, a more precise condition for the onset of toppling, considering the block’s stability, involves the angle of the discontinuity relative to the slope face and the friction angle. The critical condition for toppling is often expressed in terms of the angle of the discontinuity relative to the slope face and the friction angle. Specifically, if the dip of the discontinuity (\(\alpha\)) is less than the dip of the slope (\(\beta\)) and the friction angle (\(\phi\)) is less than the dip of the discontinuity, toppling can occur. A more refined analysis considers the resultant force. However, in a simplified assessment, the relationship between the discontinuity’s dip and the slope’s dip is paramount. The most critical factor that predisposes a rock block to toppling failure, given the described scenario of discontinuities dipping out of the slope, is when the dip angle of these discontinuities is less than the dip angle of the slope face, and the friction angle along these discontinuities is insufficient to resist the outward rotation. This geometric arrangement allows gravity to create a moment that can overcome the resisting forces.

The question probes the understanding of geological stress regimes and their influence on rock deformation, a core concept in mining and geological engineering programs at Hanoi University of Mining & Geology. The scenario describes a deep underground excavation in a region characterized by a specific stress state. The key is to identify which stress component is likely to be the dominant factor in inducing failure or instability around the excavation. In a typical geologically stable region at depth, the vertical stress (\(\sigma_v\)) is primarily due to the weight of the overlying rock column. The horizontal stresses (\(\sigma_h\) and \(\sigma_H\)) are influenced by tectonic forces, geological history, and the elastic properties of the rock mass. The question implies a situation where the horizontal stresses are significantly greater than the vertical stress, a condition known as a high horizontal stress regime. This is often encountered in tectonically active areas or regions with specific geological formations. When an excavation is made, it disrupts the pre-existing stress field. The stress concentration around the opening will redistribute the existing stresses. In a high horizontal stress regime, the maximum principal stress (\(\sigma_1\)) is horizontal, and the minimum principal stress (\(\sigma_3\)) is vertical. The excavation will tend to cause failure when the tangential stress around the opening exceeds the rock’s strength. In this context, the tangential stress will be most significantly influenced by the magnitude of the dominant horizontal stress. Therefore, the maximum horizontal stress (\(\sigma_H\)) is the most critical factor in determining the stability of the excavation, as it will contribute most significantly to the tangential stresses that can cause rock failure (e.g., spalling, buckling, or shear failure) in the excavation walls. The vertical stress, while present, is less likely to be the primary driver of failure in such a scenario compared to the amplified horizontal stresses. The intermediate principal stress (\(\sigma_2\)) also plays a role, but in many practical scenarios, the difference between the two horizontal stresses is more pronounced and thus more influential on failure mechanisms.

The question assesses understanding of the principles of geological surveying and the impact of different surveying techniques on data accuracy and interpretation in the context of mining exploration, a core area for Hanoi University of Mining & Geology. The scenario involves a geophysicist evaluating two distinct survey methods for identifying potential ore bodies. Method A, using a grid-based approach with closely spaced measurements, is more likely to capture subtle variations in subsurface anomalies, leading to a higher resolution and more detailed understanding of geological structures. This increased detail is crucial for pinpointing promising exploration targets and minimizing the risk of overlooking significant deposits due to sparse data. Method B, employing a more generalized sampling pattern, might miss localized but economically viable mineralizations. Therefore, Method A, with its emphasis on detailed spatial data acquisition, is superior for the objective of precise ore body delineation. The explanation focuses on the concept of spatial resolution in geophysical surveys and its direct correlation with the ability to identify and characterize geological features relevant to resource extraction. It highlights how denser sampling, as in Method A, improves the fidelity of the subsurface model, which is paramount in the early stages of mining exploration where accurate targeting is key to efficient resource development and economic viability. This aligns with the university’s focus on practical application of geological sciences in resource management.

The question probes the understanding of geological stress regimes and their influence on rock deformation, a core concept in mining and geological engineering at Hanoi University of Mining & Geology. The scenario describes a deep underground excavation where the ambient stress state is predominantly horizontal and deviatoric. This implies that the maximum principal stress (\(\sigma_1\)) is horizontal, and the minimum principal stress (\(\sigma_3\)) is also horizontal but perpendicular to \(\sigma_1\), with the vertical stress (\(\sigma_v\)) being intermediate. This configuration is characteristic of a strike-slip faulting regime or a compressional regime where horizontal stresses dominate over vertical overburden pressure. In such a stress environment, the orientation of failure planes (fractures or faults) is governed by the Mohr-Coulomb failure criterion, which relates shear strength to normal stress and cohesion. For a purely frictional material (\(c=0\)), failure occurs when the shear stress on a plane reaches a critical value proportional to the normal stress on that plane. The angle of the failure planes relative to the maximum principal stress (\(\sigma_1\)) is typically \(45^\circ – \frac{\phi}{2}\), where \(\phi\) is the angle of internal friction. Given that the maximum principal stress is horizontal, the failure planes will be oriented such that they are inclined to this horizontal maximum stress. Specifically, two sets of conjugate shear planes will form. One set will be inclined at an angle of \(45^\circ – \frac{\phi}{2}\) to the \(\sigma_1\) direction, and the other set will be inclined at \(45^\circ + \frac{\phi}{2}\) to the \(\sigma_1\) direction. Since \(\sigma_1\) is horizontal, these planes will have a significant vertical component of their orientation. The critical aspect for underground excavations is how these failure planes interact with the excavation boundary. If the excavation is oriented such that it intersects these planes at a low angle, it can lead to instability. The question asks about the most likely orientation of induced fractures or failure planes relative to the excavation’s axis. In a regime with dominant horizontal stresses, the failure planes will not be purely vertical or purely horizontal. They will be inclined. The most stable orientation for an excavation in this stress regime would be one that minimizes the intersection angle with these predicted failure planes. However, the question asks about the orientation of the failure planes themselves. The key is that the maximum principal stress is horizontal. Therefore, the failure planes will be oriented at an angle to this horizontal stress. The angle of inclination of these planes with respect to the horizontal plane will depend on the angle of internal friction, but they will not be parallel to the horizontal plane or perpendicular to it. They will be inclined, with one set dipping at an angle relative to the horizontal and the other set dipping at a complementary angle. Considering the typical orientation of failure planes in a strike-slip or compressional regime where \(\sigma_1\) is horizontal, the failure planes will be inclined at approximately \(30^\circ\) to \(45^\circ\) to the horizontal, depending on the friction angle. This means they will have a significant dip. Therefore, the most likely orientation of induced fractures or failure planes relative to the excavation’s axis, which is typically oriented to minimize stress concentration, would be inclined planes.

The question assesses the understanding of rock mass classification systems and their application in geotechnical engineering, a core area for Hanoi University of Mining & Geology. The scenario describes a tunnel excavation in a rock mass characterized by specific geological conditions. To determine the most appropriate support system, a rock mass classification is needed. The Rock Mass Rating (RMR) system, developed by Zienkiewicz and later refined by Bieniawski, is a widely used empirical method for classifying rock masses based on several parameters: compressive strength of the rock, RQD (Rock Quality Designation), spacing of discontinuities, condition of discontinuities, groundwater conditions, and orientation of discontinuities. Each parameter is assigned a rating, and these ratings are summed to obtain the RMR. The total RMR value then falls into one of five classes, each corresponding to a general recommendation for support. In this scenario, the rock mass exhibits: 1. **Uniaxial Compressive Strength (UCS):** \(20\) MPa. This falls into the \(5\) to \(10\) MPa range, which typically gets a rating of \(7\) in the Bieniawski RMR system. 2. **Rock Quality Designation (RQD):** \(75\%\). This falls into the \(75\% – 90\%\) range, typically rated \(12\). 3. **Discontinuity Spacing:** Medium spacing (e.g., \(0.2 – 0.6\) m). This usually corresponds to a rating of \(10\). 4. **Discontinuity Conditions:** Fairly rough surfaces with slight separation (e.g., \(1-5\) mm opening, rough surfaces). This would typically receive a rating of \(15\). 5. **Groundwater Conditions:** Moderate inflow, some joint water pressure. This often corresponds to a rating of \(10\). 6. **Discontinuity Orientation:** Discontinuities are generally unfavorable for the tunnel excavation. This would typically result in a reduction of \(25\) points from the sum of the other parameters. Summing the typical ratings for the first five parameters: \(7 + 12 + 10 + 15 + 10 = 54\). Applying the unfavorable orientation adjustment: \(54 – 25 = 29\). An RMR of \(29\) falls into Class III (Fair Rock). Class III rock masses typically require a moderate level of support, such as shotcrete with wire mesh and possibly rock bolts. The question asks for the *most appropriate* initial support strategy. Considering the RMR classification, a combination of shotcrete and rock bolts is a standard and effective approach for fair rock conditions in tunnel excavations, providing both surface stabilization and reinforcement. Other options might be too light (e.g., only mesh) or too heavy (e.g., heavy steel sets) for this classification, making the shotcrete and rock bolt combination the most balanced and appropriate initial response. The explanation emphasizes the empirical nature of RMR and its direct link to practical support design, a crucial aspect for students at Hanoi University of Mining & Geology.

The question probes the understanding of geological surveying principles, specifically the impact of varying geological formations on the accuracy of geophysical prospecting methods. The scenario describes a survey aimed at identifying subsurface mineral deposits using electrical resistivity. Different rock types exhibit distinct electrical properties. Igneous rocks, particularly those with crystalline structures and low porosity like granite, generally possess high resistivity. Sedimentary rocks, such as sandstone or limestone, can have variable resistivity depending on their pore fluid content and cementation. Metamorphic rocks, like schist or marble, also show a range of resistivities influenced by their mineral composition and foliation. Highly fractured or porous formations, regardless of their primary lithology, tend to have lower resistivity due to the presence of conductive pore fluids (e.g., groundwater). Therefore, a survey conducted over a region with significant lithological variation, especially including highly resistive igneous intrusions juxtaposed with more conductive sedimentary layers or fractured zones, would present the greatest challenge to achieving a uniform and interpretable resistivity profile. The presence of a highly resistive igneous intrusion within a generally more conductive sedimentary basin would create a sharp contrast in resistivity, potentially masking or distorting the signals from deeper, less resistive mineralized zones. This contrast necessitates more sophisticated data processing and interpretation techniques to differentiate between the geological background and the target anomaly.