Magnitude Of Principal Stress Research Articles

Influence of tunnel excavation on the magnitude and rotation angle of principal stress in surrounding rock

The stress disturbances induced by deep tunnel excavation are a key factor leading to the instability and failure of surrounding rock. To investigate the stress evolution in surrounding rock, this study utilizes a physical simulation system for deep caverns to replicate the actual excavation process of tunnels. The study quantitatively analyzes changes in the magnitude and orientation of surrounding rock stresses, and validates the experimental results through numerical analysis. The study revealed that: (1) In elasto-plastic tests, the trajectories of the principal stress axes at the vault and bottom are symmetrical about the XZ plane, whereas in elastic tests, they exhibit symmetry about the origin. (2) The experimental and numerical simulation results of the principal stress axis evolution at four key monitoring points (vault, shoulder, waist, and bottom) are consistent. Using FLAC3D, the regions between these points were further divided, identifying seven distinct regions of surrounding rock, each characterized primarily by one of the four representative patterns, with the shoulder region acting as a transitional zone. (3) Regardless of whether the surrounding rock is in an elastic or elasto-plastic state, the evolution of the principal stress magnitudes and their angles with the coordinate axes remained entirely consistent.

Impact of scan strategy on principal stresses in laser powder bed fusion

Additive manufacturing techniques, such as laser powder bed fusion (PBF-LB), are well known for their exceptional freedom in part design. However, these techniques are also characterized by the development of large thermal gradients during production and thus residual stress (RS) formation in produced parts. In this context, neutron diffraction enables the non-destructive characterization of the bulk RS distribution. By control of the thermal gradients in the powder-bed plane by scan strategy variation we study the impact of in-process scan strategy variations on the microstructure and the three-dimensional distribution of RS. Microstructural analysis by means of electron backscatter diffraction reveals sharp microstructure transitions at the interfaces ranging from 100-200 µm. The components of the RS tensor are determined by means of neutron diffraction and the principal stress directions and magnitudes are determined by eigenvalue decomposition. We find that the distribution of RS in the powder-bed plane corresponds to the underlying scan strategy. When the alternating scan vectors align with the x- and y sample coordinate axes, the principal stress directions co-align. In the present geometry, nearly transverse isotropic stress states develop when the scan vectors are either aligned 45° between x and y or continuously rotated by 67° between each layer.

Mechanism of principal stress rotation and deformation failure behavior induced by excavation in roadways

The failure modes of rock after roadway excavation are diverse and complex. A comprehensive investigation of the internal stress field and the rotation behavior of the stress axis in roadways is essential for elucidating the mechanism of roadway failure. This study aimed to examine the spatial relationship between roadways and stress fields. The law of stress axis rotation under three-dimensional (3D) stress has been extensively studied. A stress model of roadways in the spatial stress field was established, and the far-field stress state at different spatial positions of the roadways was analyzed. A mechanical model of roadways under a 3D stress state was established using far-field stress solutions as boundary conditions. The distribution of principal stresses σ1, σ2 and σ3 around the roadways and the variation of the stress principal axis were solved. It was found that the stability boundary of the stress principal axis exhibits hysteresis when compared with that of the principal stress magnitudes. A numerical analysis model for spatial roadways was established to validate the distribution of principal stress and the mechanism of principal axis rotation. Research has demonstrated that the stress axis undergoes varying degrees of spatial rotation in different orientations and radial depths. Based on the distribution of principal stress and the rotation law of the stress principal axis, the entire evolution mechanism of the two stress adjustments to form the final failure form after roadway excavation has been revealed. The on-site detection results also corroborate the findings presented in this paper. The results provide a basis for the analysis of the failure mechanism under a 3D stress state.

Effect of Mineral Composition and Particle Size on the Failure Characteristics and Mechanisms of Marble in the China Jinping Underground Laboratory.

In deep underground engineering, the deformation, failure characteristics, and mechanism of surrounding rock under the influence of grain sizes and mineral compositions are not clear. Based on CJPL-II variously colored marbles, the differences in grain size and mineral composition of the marble were analyzed by thin-section analysis and XRD tests, and the effect of intermediate principal stress on the mechanical properties of marble was investigated. Both SEM and microfracture analysis were coupled to reveal the failure mechanisms. The results highlight that the crack initiation strength, damage strength, peak strength, and elasticity modulus of Jinping marble exhibit an increasing trend with an increase in intermediate principal stress, while the peak strain initially increases and subsequently decreases. Moreover, this study established negative correlations between marble strength, brittleness characteristics, and fracture angle with grain size, whereas positive correlations were identified with the content of quartz, sodium feldspar, and the magnitude of the intermediate principal stress. The microcrack density in marble was found to increase with larger grain sizes and decrease with elevated quartz and sodium feldspar content, as well as with increasing intermediate principal stress. Notably, as the intermediate principal stress intensifies and grain size diminishes, the transgranular tensile failure of marble becomes more conspicuous. These research findings contribute to the effective implementation of disaster prevention and control strategies.

Recent advances in characterizing the crustal stress field and future applications of stress data: perspectives from North America

Abstract The stress field controls patterns of crustal deformation, including which faults are likeliest to cause earthquakes or transmit fluids. Since the 1950s, maps of maximum horizontal stress ( S Hmax ) orientations have advanced dramatically, and the style of faulting (relative principal stress magnitudes) has recently been mapped in some regions as well. This perspectives paper summarizes developments in characterizing stress orientations and (relative) magnitudes, including new seismic and borehole methods, as well as progress in identifying the causes of stress variations. Despite these advances, adding far more spatiotemporal detail would allow geoscientists to address many of today's key challenges regarding natural hazards, energy development, and geodynamics. In particular, it is critically important to characterize stress heterogeneity at multiple scales while also recognizing the coherent variability of the stress field. The second part of the paper considers how more detailed stress datasets could prove essential to addressing some of the grand questions in geoscience, including deciphering the poorly understood feedbacks between crustal dynamics and surface processes, improving earthquake and eruption forecasts, and determining the origins and shared properties of plate boundaries.

Practical Methodology for Evaluating Mining Front Stability Based on the Diametrical Core Deformation Technique

The state of stress in a mining front constantly changes with mining activities. In a recent study, the authors developed and verified with laboratory measurements an analytical model for the calculation of mining-induced stresses based on measuring the deformations of a diamond drill rock core extracted perpendicular to the mining front or face. The method is called diametrical core deformation technique (DCDT). In this study, the DCDT is used in combination with 3D numerical modelling to develop a practical methodology for the assessment of mining face stability. To demonstrate the methodology, a diamond drill rock core was retrieved from an access drift face 530 m below the surface of an underground mine in northern Quebec. The state of stress in the mining front is estimated from the DCDT and used to adjust the orientation and principal stress magnitudes in the local area around the access drift in a 3D linear-elastic numerical model using an iterative approach. As the rock core is partially fractured due to previous face advance blasting, the numerical model is further adjusted to model the observed damage zone. The 3D model after adjustments is used to examine the mining front stability with the Hoek–Brown failure criterion. It is postulated that the proposed methodology is suitable for the stability assessment of any mining front with or without an observed damage zone.

The Distribution Law of Ground Stress Field in Yingcheng Coal Mine Based on Rhino Surface Modeling

The distribution law of the ground stress field is of great significance in guiding the design of coal mine roadway alignment, determining the parameters of roadway support, and preventing and controlling the impact of ground pressure in coal mines. A geostress inversion method combining Rhino surface modeling and FLAC3D 6.0 numerical simulation software is proposed. Based on the geological data of the coal mine and the results of on-site measurements, a three-dimensional geological model of Yingcheng Coal Mine is established for the geostress inversion, and the distribution law of the geostress field in Yingcheng Coal Mine is obtained. Research shows the following: (1) The horizontal maximum principal stress values of the Yingcheng Mine are between 33.9 and 35.3 MPa, the horizontal minimum principal stress values are between 23.6 and 25.4 MPa, and the direction of the horizontal maximum principal stress is roughly in the southwest to west direction; (2) the three-way principal stress magnitude relationship is σH > σv > σh, indicating that the horizontal stress dominates in the study area, which belongs to the slip-type stress state; (3) The maximum principal stress of No. 3 coal seam is 33.1–34.8 MPa, the middle principal stress is 27.5–29.2 MPa, and the minimum principal stress is 17.3–22.9 MPa. Due to the influence of topography and burial depth, there is a phenomenon of stress concentration in some areas. By comparing the inversion values with the measured values, the accuracy of the geostress inversion is high, and the initial geostress inversion method based on Rhino surface modeling accurately inverts the geostress distribution pattern of the Yingcheng coal mine.

Impact of faults on the remote stress state

Abstract. The impact of faults on the contemporary stress field in the upper crust has been discussed in various studies. Data and models clearly show that there is an effect, but so far, a systematic study quantifying the impact as a function of distance from the fault is lacking. In the absence of data, here we use a series of generic 3-D models to investigate which component of the stress tensor is affected at which distance from the fault. Our study concentrates on the far field, located hundreds of metres from the fault zone. The models assess various techniques to represent faults, different material properties, different boundary conditions, variable orientation, and the fault's size. The study findings indicate that most of the factors tested do not have an influence on either the stress tensor orientation or principal stress magnitudes in the far field beyond 1000 m from the fault. Only in the case of oblique faults with a low static friction coefficient of μ=0.1 can noteworthy stress perturbations be seen up to 2000 m from the fault. However, the changes that we detected are generally small and of the order of lateral stress variability due to rock property variability. Furthermore, only in the first hundreds of metres to the fault are variations large enough to be theoretically detected by borehole-based stress data when considering their inherent uncertainties. This finding agrees with robust stress magnitude measurements and stress orientation data. Thus, in areas where high-quality and high-resolution data show gradual and continuous stress tensor rotations of >20∘ observed over lateral spatial scales of 10 km or more, we infer that these rotations cannot be attributed to faults. We hypothesize that most stress orientation changes attributed to faults may originate from different sources such as density and strength contrasts.

Variations in the present-day stress field and its implications for hydrocarbon development in the Hassi Terfa field, Hassi Messaoud, Algeria

Understanding the contemporary stress field and its variations is important in hydrocarbon production. These fluctuations are significant for borehole stability and trajectory, hydraulic stimulation, fault reactivation, and optimal well completion. In this study, we provide the first geomechanical model to determine the orientation and magnitude of the present-day stress of the Hassi Terfa field using geophysical logs to understand the origin of the spatial variation of the stress state. The breakouts from acoustic image logs provide an average maximum horizontal stress (SHmax) orientation of N115°, consistent with the Africa–Eurasia plate motion, which imposes the largest first-order stress source. However, our analysis demonstrates local stress perturbations near faults. This may mean that the stress field in the Hassi Terfa is superimposed by a third-order source of stress (<100 km). Our model demonstrates variations in stress magnitude with depth interpreted to be lithology-dependent, which act as a natural barrier against fracture propagation. We propose a new approach to quantify these perturbations via the stress regime index R′, using the magnitude of the principal stress components. The results demonstrate different layer-to-layer faulting regimes. These perturbations will limit the vertical propagation of hydraulic fracturing to the overlying formation, which enables it to access a larger reservoir volume and improve production. In general, a strike–slip regime with a slight normal slip component is interpreted for the study area. We develop the first-ever quantitative stress map using the relative principal stress magnitude parameter (Aϕ) to present the lateral variation of the stress regime throughout the Saharan platform. Results demonstrate a consistent strike–slip to normal/strike–slip regime with a uniform SHmax orientation. This map will help operators achieve optimal well direction and optimize hydraulic stimulation. Our results have considerable implications for hydrocarbon production in the central and southeastern Saharan platform.

3D active fault kinematic behaviour reveals rapidly alternating near-surface stress states in the Eastern Alps

Abstract Stress variations in the Earth's crust need to be understood in both the spatial and temporal domains to address a number of pressing societal issues. In this paper, precise three-dimensional records of fault kinematic behaviour obtained by mechanical extensometers are used to investigate changes in stress states along major faults in the Eastern Alps. The monitored faults are fractures with evident Upper Quaternary displacement and are directly attributed to their master tectonic structures. The results demonstrate that activity at the submillimetric scale is highly episodic; periods of repose are punctuated by conspicuous reactivation events affecting one or more of the displacement components. An original approach named the SMB2018 method is used to define the stress state associated with each fault reactivation event. The outputs evidence significant short-term changes in the local stress regime. The directions of the principal normal stresses calculated from these reactivation events present generally similar patterns for both compressional and extensional stress states. Consequently, submillimetric fault activity cannot be controlled by a rotating stress field; such shifts can only be caused by a change in the magnitude of the individual principal normal stresses so that the maximum compression changes to the minimum and vice versa.

The importance of nodal plane orientation diversity for earthquake focal mechanism stress inversions

Abstract Inversions of earthquake focal mechanisms are among the most accessible and reliable methods for determining crustal stress. However, the use of this method varies widely, and the assumptions that underpin it are often violated, potentially compromising stress estimates. We investigate the consequences of violating the little-studied assumption that the focal mechanisms have diverse orientations. Our approach is to employ data-informed synthetic mechanisms, with nodal plane orientations defined by recent earthquake lineaments in the Midland Basin, western Texas, and rakes consistent with slip in the mapped stress field. Using both the traditional stress inversion method that assumes constant shear stress magnitudes on the causative faults as well as a recently published variable shear stress method, we show that low fault plane diversity can cause maximum horizontal stress ( S Hmax ) orientation and relative principal stress magnitude (faulting regime) estimates to differ markedly from the true values. This problem is compounded for catalogues with even modest amounts of noise (≤15°) or few (e.g. 20) mechanisms. Significantly, traditional approaches for quantifying uncertainty such as the bootstrap can severely underestimate the true uncertainty under these circumstances. To remedy this, we provide simple tools to quantify nodal plane orientation diversity and stress inversion reliability.

Computational Modeling of Directed Energy Deposition of Titanium Aluminide Plate Geometries

In this work, transient thermomechanical analysis of the laser-based Directed Energy Deposition (DED) process was carried out to predict melt pool dimensions, thermal cycles and residual stress during Titanium Aluminide (TiAl) plate deposition. The predicted melt pool length, width, and depth increased as the laser power was increased from 250 W to 350 W at a constant travel speed of 15 mm/s. The melt pool length increased from 0.425 mm to 0.55 mm, while the depth increased from 0.1 to 0.29 mm, and the width increased from 0.412 to 0.5 mm. The plate's edges (tracks 1 and 6) were found to experience a slightly higher temperature than the middle tracks, which may contribute to higher thermal gradients at the edges. The highest Principal stress of 140 MPa was found in track 1. The magnitude of Principal stresses diminished as track deposition progressed from track 2 to 6 due to the variation of the thermal gradient along the tracks.

Evaluating the effect of organic matter contained in shale on hydraulic fracturing of infill-well

Organic matter which is scattered uniformly in shale can respond to the applied stress and result in the variation of stress field. However, the effects of organic matter content in organic-rich shale on stress interference have not been well considered during developing infill-wells. A fully coupled numerical model is proposed in this paper to consider the whole flow spectrum of shale gas and investigate the effect of organic matter content on stress variation and fracture propagation in infill-well. Through simulating the production and fracturing process with only one set of code, some conclusions can be drawn that the alteration angle of the maximum horizontal principal stress increases and then decreases with the production time. Furthermore, the shrinkage of organic matter enlarges the alteration angle and the magnitude of the maximum horizontal principal stress. Certainly, the optimal fracturing effect in the infill-wells vary due to the different mass fraction of organic matter. This study not only helps to understand the effect of mass fraction of organic matter on stress variation and fracture propagation, but also provides theoretical support for increasing production from shale gas reservoirs.

Fault stability analysis and its application in stress inversion quality assessment

Fault stability analysis plays an important role in assessing the potential hazard of faults and in studying the mechanism of earthquake occurrence. Fault stability depends on the magnitude of the normal and shear stresses imposed on the fault by the tectonic stress and rock friction, while the magnitude of the normal and shear stresses is related to the spatial orientation of the fault normal with respect to the three principal stress axes, so it is easier to understand the variation of fault stability with its orientation by expressing the stability of different faults in the principal axis coordinate system. In this paper, we first developed a method to plot the stability of faults with different orientations in the principal stress axis coordinate system, then investigated the influence of the magnitude of principal stresses and friction on fault instability, and reached the conclusion that the instability is mainly affected by the relative magnitude of principal stresses (shape ratio). Finally, we proposed to use fault stability as an indicator to evaluate the quality of inverted stress obtained from fault slip data or earthquake focal mechanisms, that is, to evaluate the reliability of the inverted stress according to the compatibility of stress and fault stability. It is described in detail in terms of measured fault slip data from two regions.

Earthquake impact on the stress magnitude at the area of shear zones

Both tectonic activity and geological environment such as faulting and shearing in the rock mass influences the in-situ stress condition in the rock mass. The large-scale earthquakes cause both accumulation and sudden release of strain energy resulting the changes on the magnitude and direction of the in-situ stresses. This is the case in the Himalayan region, where the tectonic movement is active and periodic dynamic earthquakes are common. This manuscript assesses the influence of local shear faults on the in-situ stress condition along the pressure tunnel of Upper Tamakoshi Hydroelectric Project in Nepal. For this a 3D numerical modeling is carried out to assess potential changes in the magnitude of in-situ stresses, in particular the magnitude of minimum principal stress, due to dynamic loading (earthquake).

Effect of gingival height of a titanium base on the biomechanical behavior of 2-piece custom implant abutments: A 3-dimensional nonlinear finite element study

Statement of problemTitanium base (TiBase) abutments to restore an implant-supported single crown are available in different gingival heights, but information on the biomechanical effects of the gingival heights is lacking. PurposeThe purpose of this nonlinear finite element analysis study was to evaluate the effects of TiBase gingival heights on the biomechanical behavior of custom zirconia (CustomZir) abutments and TiBase, including von Mises stress and maximum and minimum principal stress. Material and methodsTiBases with different gingival heights (0.5 mm, 1 mm, 1.5 mm, and 2 mm) with internal hexagon Morse taper connections were simulated in 3-dimensional models. The simulations (ANSYS Workbench 2020; ANSYS Inc) included the OsseoSpeed EV implant (Ø5.4 mm) (AstraTech; Dentsply Sirona), restoration, and surrounding bone in the mandibular first molar region. An occlusal force of 200 N was applied with a 2-mm horizontal offset toward the buccal side and a 30-degree inclination from the vertical axis. ResultsHigh-stress concentration was observed in the uppermost internal connection area on the buccal side and the antirotational part of the titanium abutment on the lingual side in all models. CustomZir abutments with a shorter gingival height exhibited larger concentrated areas of volume average stress von Mises stress and higher magnitude of maximum and minimum principal stress compared with a taller gingival height. ConclusionsA TiBase abutment with a taller gingival height reduced the fracture risk of a CustomZir abutment without increasing any mechanical risk.

Triaxial Deformation of the Goldwyer Gas Shale at In Situ Stress Conditions—Part II: Viscoelastic Creep/Relaxation and Frictional Failure

To understand the geomechanical implications of long-term creep (time-dependent deformation) response of gas shale, short-duration creep was recorded from laboratory triaxial tests on ten Goldwyer gas shale samples in the onshore Canning Basin at in situ stress conditions under constant differential axial stress. A simple power-law function captures primary creep behaviour involving elastic compliance constant B and time-dependent factor n. Experimental creep data revealed larger axial creep strain in clay and organic-rich rocks, than those dominated by carbonates. Anisotropic nature of creep was observed depending upon the direction of constant axial stress application (perpendicular or parallel to the bedding plane). Upon the application of linear viscoelastic theory on laboratory creep fitting coefficients, differential horizontal stress accumulation over a geological time scale was estimated from the viscoelastic stress relaxation concept. Further, this model was used to derive lithology-dependent least principal stress (Shmin) magnitude at depth for two vertical wells intersecting the Goldwyer gas shale formations. This newly proposed Shmin model was found to have a profound influence on designing hydraulic fracture simulation. Further, pore size distribution and specific surface area value SN2 were derived from low-pressure gas adsorption experiments. These physical properties along with weak mineral components were linked with creep constitutive parameters to understand the physical mechanisms of creep. A strong correlation was noted between SN2 and creep parameters n and B. Finally, an attempt was made to investigate how gas shale composition and failure frictional properties can influence shear fracturing.

Induced hydraulic fractures in underground block caving mines using an extended finite element method

Block caving has become an attractive underground rock mining method that requires effective preconditioning of the orebody to initiate the progressive rock collapse by its weight. Hydraulic fracturing is commonly used in cave mining as a preconditioning method to induce artificial fractures in the orebody rock mass. This paper presents the numerical model of hydraulic fracture propagation in underground caving mines. An extended finite element method based on phantom nodes is adopted to simulate the propagation of multiple fractures along arbitrary paths. A poroelastic constitutive model governs the behavior of orebody rock mass, while a cohesive zone model controls the hydraulic fracture propagation. The adopted method is validated against analytical solutions for penny-shaped hydraulic fracture. The stress shadowing effect on hydraulic fracturing is investigated using representative rock properties from the “El Teniente mine”, obtained by calibrating a hydraulic fracturing field test. Several analyses of multiple hydraulic fractures considering a sequential fracturing scheme are simulated to investigate the influence of in-situ stresses, fracture spacing, injection flow rate, and Young's modulus and permeability of the matrix. The numerical results show that small fracture spacing, in-situ stress, and rock permeability locally change the principal stress magnitude, resulting in a more extensive fracture propagation. Also, the injection of new fractures induces stress shadows that reinitiate the propagation of the previous ones. This behavior is reduced by increasing the fracture spacing and rock permeability. Finally, this paper provides insights into the main parameters that affect fracture extension, which can be used to optimize the preconditioning process of underground block caving mines.

Determination of geo-stress in deep strata incorporating borehole diametral deformation measurement and overcoring

In deep energy engineering such as coal mining, oil & gas extraction, underground hydropower projects and deep buried water tunnels, rock failure and large deformation hazards often occur due to the complicated geological conditions and high geo-stress. Knowledge of the geo-stress state is an essential content in deep rock engineering. The complex environment of high temperature and high hydraulic pressure in deep rock mass makes geo-stress measurement more difficult than shallow strata. In this study, a novel method for geo-stress measurement based on the cross-sectional borehole diametral deformation is proposed. A borehole diametral deformation gage (BDD gage) is developed based on the measurement method. The scheme design of multi-contacts and micro-optical imaging avoid the influence of the high temperature and high hydraulic pressure environment. The results of the calibration experiment show that the measurement accuracy of BDD gage reaches 3 μm. Incorporating with the wireline coring tool for rapid overcoring, geo-stress measurement in deep vertical borehole via stress relief is realized. Field test procedure is summarized and application is carried out in a deep borehole of limestone stratum in Guizhou Province, China. Measurement process is verified to be rapid and simple. Measurement results including magnitude and direction of principal stresses are consistent with the results from hydraulic fracturing method. Special discussions were conducted on the measurement error of BDD gage and the improvement design of wireline coring tools. This article provides new ideas for geo-stress measurement in deep borehole.

Triaxial stress and failure modes in hydrothermal mineral systems

Rock mechanics experiments show that the magnitude of the intermediate principal stress significantly affects rock failure. Since triaxial stress states (no principal stress is zero) are ubiquitous in the crust, and polyaxial axial states (all three principal stresses are different) are general, the magnitude of the intermediate principal stress should have an important effect on hydrothermal mineralisation. For example, extensional veins or dykes in vein-hosted gold or porphyry deposits may have multiple orientations when the intermediate and least principal stresses have similar magnitudes, or single orientations when the intermediate and maximum principal stresses are similar. The Griffith-Murrell triaxial fracture criterion with a tensile cutoff can be used to illustrate the effects of the intermediate principal stress on failure. At the lowest values of mean stress, the criterion suggests that only extensional failure can occur. At low–intermediate values of mean stress, either extensional or shear failure may occur: extensional failure is favoured when the intermediate and maximum principal stresses have similar magnitudes. At higher mean stresses, shear failure will occur at lower values of pore fluid pressure and differential stress when the magnitudes of the intermediate and minimum principal stresses are similar.