Minimum Stress Research Articles

Static and dynamic stress analysis of different crown materials on a titanium base abutment in an implant-supported single crown: a 3D finite element analysis

BackgroundThis Finite Element Analysis was conducted to analyze the biomechanical behaviors of titanium base abutments and several crown materials with respect to fatigue lifetime and stress distribution in implants and prosthetic components.MethodsFive distinct designs of implant-supported single crowns were modeled, including a polyetheretherketone (PEEK), polymer-infiltrated ceramic network, monolithic lithium disilicate, and precrystallized and crystallized zirconia-reinforced lithium silicates supported by a titanium base abutment. For the static load, a 100 N oblique load was applied to the buccal incline of the palatal cusp of the maxillary right first premolar. The dynamic load was applied in the same way as in static loading with a frequency of 1 Hz. The principal stresses in the peripheral bone as well as the von Mises stresses and fatigue strength of the implants, abutments, prosthetic screws, and crowns were assessed.ResultsAll of the models had comparable von Mises stress values from the implants and abutments, as well as comparable maximum and minimum principal stress values from the cortical and trabecular bones. The PEEK crown showed the lowest stress (46.89 MPa) in the cervical region. The prosthetic screws and implants exhibited the highest von Mises stress among the models. The lithium disilicate crown model had approximately 9.5 times more cycles to fatique values for implants and 1.7 times more cycles to fatique values for abutments than for the lowest ones.ConclusionsWith the promise of at least ten years of clinical success and favorable stress distributions in implants and prosthetic components, clinicians can suggest using an implant-supported lithium disilicate crown with a titanium base abutment.

Shear wave anisotropy response characteristics of laminated shale and its correction methods

Laminated shale exhibits strong anisotropic characteristics in horizontal wells, significantly affecting the application of shear wave travel time data. Using equivalent medium theory and the elastic wave equation, we constructed a physical model for laminated shale, simulating the impact of lamination angle and lamination density on shear wave velocity and shear wave anisotropy coefficient. We established the relationship between the shear wave anisotropy coefficient and the cosine of the lamination angle. The simulation results indicate that shear wave velocity decreases with an increase in lamination angle and density, while the shear wave anisotropy coefficient gradually decreases with an increase in lamination angle and initially increases and then decreases with an increase in lamination density. Moreover, it exhibits a power exponential relationship with the cosine of the lamination angle. After correction, the minimum horizontal principal stress and fracture pressure calculated from shear wave data show an average relative error reduction of 6.72% and 7.77%, respectively, compared to measured data. This demonstrates that the correction method effectively eliminates the impact of laminated shale anisotropy on shear waves.

Evaluating the Relation of Cave Passage Formation to Stress-Field: Spatio-Temporal Correlation of Speleogenesis with Active Tectonics in Asprorema Cave (Mt. Pinovo, Greece)

Caves serve as time capsules, preserving significant markers of tectonic activity and offering insights into geological history. Fault geometries and past activations found in caves can be correlated with known deformational events in the broader area, temporally delimiting the speleogenesis. More specifically, cave passage formation is suggested to be affected by the regional stress-field. The Asprorema Cave in Northern Greece is a typical example of a fracture guided cave, with passage geometry influenced by relative sidewall movements, revealing these discontinuities as faults. This study constructs the timeframe and conceptual model of speleogenesis in relation to tectonic events, geomorphological evolution and hydrological zones, and verifies its relation to the stress-field. Active tectonics, mineralogy and cave geomorphology are investigated. Results suggest syntectonic speleogenesis under phreatic and epiphreatic conditions. The absence of corrosion on fault slip surfaces implies recent activations post cave’s shift to the vadose zone. Structural analysis identifies three main neotectonic phases: NNW-SSE striking faults (oldest group of structures), NE-SW striking faults with dextral strike-slip movement (post-middle Miocene), and NE-SW striking normal faults indicating extensional stress-regime (Quartenary). The last two phases affect cave passage shape causing wall displacement, highlighting passage formation along discontinuities perpendicular to the horizontal minimum stress axis.

Numerical study of time-dependent stresses in the floor of the stope with powered support

When sections of the powered support are clamped in the stope, one of the ways to move them is to explode the rock under them. In the case when there is outburst-prone sandstone in the seam floor, blasting operations becomes dangerous and it is necessary to study the stress field in the host rocks. In this work, a numerical study of the time-dependent stress field in the floor of the stope with powered support is performed. Distributions of values of geomechanical parameters characterizing the stress field and zones of inelastic deformations at different time steps are given. Graphs of changes in these parameters in the floor of the stope are plotted. The minimum time for unloading sandstone at the place of drilling the hole for explosive charge is calculated. It is shown that in front of the mine face plane, the sandstone in the seam floor is in a uniform compressed state; all components of the stress field are close to unity. However, they start to decrease already 2.5 m before the mine face plane. At the hole drilling site, the maximum stress is 0.77γH, the minimum stress is 0.35γH at a depth of 1 m for given conditions.

Damage characteristics of rock induced by unloading in hole under true triaxial boundary stresses: Experimental study

In order to study the effect of unloading of underground rock excavation on the stability of surrounding rock, the true triaxial compression (TTC) and coupled true triaxial compression and in-hole loading-unloading tests (TTC-HU) were conducted on hollow cubic rock (100mm × 100mm × 100mm). The experimental results indicate that the compressive strengths of the specimens increase as confining pressure increases in the equal biaxial stressand increase with increasing intermediate principal stresses in the unequal biaxial stress. At low confining pressure (σ < 30 MPa), the internal stress at unloading damage in the hole of hollow cubic specimen increases with the increase of the three-directional boundary stresses. At high confining pressure (σ ⩾ 30 MPa), the specimen will not be damaged during the entire unloading process in the hole. The damage mode of the specimen is dominated by tensile damage. The shape of the holes in the specimens did not significant change, and hole wall of specimen have layered destruction along the circumference in low confining pressure. In high confining pressure, the hole area of the specimen undergoes significant deformation damage, forming a V-groove along the direction of the minimum principal stress, and the wall of the hole is completely peeled off. This study can reasonably predict the actual engineering damage patterns and guide the optimization of surrounding rock support.

Isogeometric topology optimization of structures using the overweight approach

In this paper, a 2D isogeometric formulation of the material distribution for structural topology optimization considering minimum weight and local stress constraints using the overweight approach is proposed. The aim of this isogeometric formulation is to provide solutions with high spatial definition using a lower number of design variables in comparison with the formulations previously developed to define the material layout. Despite of this, an important number of local stress constraints has to be considered in the solution of the problem. For this purpose, an Overweight Constraint is used to consider all of them. The structural analysis is performed by means of the Isogeometric Analysis (IGA) and the distribution of material is modeled by means of quadratic B-splines. Moreover, the optimization is addressed by means of the Sequential Linear Programming algorithm (SLP) that is driven by the information provided by a full first-order sensitivity analysis extension of the IGA formulation. Finally, the proposed formulation is tested by means of some benchmark problems, and the results show that the isogeometric formulation provides solutions with high spatial definition. A comparison with a Finite Element Method (FEM) topology optimization formulation is included.

Mechanical Properties of Super-large and Shallow-buried Loess Tunnel with the Prefabricated Temporary Support

Background: At present, there are few studies on the mechanical properties of tunnels with prefabricated temporary support. Based on the project of the Xichengshan Tunnel on the highway from Zhuanglang to Tianshui, this paper studies the mechanical properties of tunnels with prefabricated temporary support The utility model patent for this article is a temporary steel support device for loess tunnel excavation. The patent number is ZL 2022 2 0141276. 1. Objective: The study aims to show the mechanical properties of a super large section of prefabricated temporary support shallow tunnel. Methods: The mechanical properties of the tunnel surrounding rock, lining, steel arch, anchor, and temporary support during construction were analyzed by combining numerical simulation and theoretical analysis. The maximum and minimum stresses of the tunnel surrounding rock, lining, steel arch, and anchor, and the maximum and minimum displacements of prefabricated temporary support were found through the analysis results. Results: The stress and displacement fields of surrounding rock, lining, steel arch, bolt, and temporary support of loess tunnel were analyzed. Results showed that the maximum principal stress of the surrounding rock is 0.293MPa, and the maximum horizontal displacement is 0.359cm. The maximum horizontal displacement of the lining is 0.413cm, the maximum vertical displacement of the steel arch is 1.538 cm, and the maximum displacement of the temporary support structure is 1.459 cm. The above data verify the safety of the proposed combined temporary support structure. Conclusion: Through the analysis results, the maximum and minimum stresses of the tunnel surrounding rock, lining, steel arch, and anchor, and the maximum and minimum displacements of assembled temporary support are found, which can guide subsequent construction.

Wellbore Instability Analysis to Determine the Safe Mud Weight Window for Deep Well, Halfaya Oilfield

Wellbore instability is one of the most common issues encountered during drilling operations. This problem becomes enormous when drilling deep wells that are passing through many different formations. The purpose of this study is to evaluate wellbore failure criteria by constructing a one-dimensional mechanical earth model (1D-MEM) that will help to predict a safe mud-weight window for deep wells. An integrated log measurement has been used to compute MEM components for nine formations along the studied well. Repeated formation pressure and laboratory core testing are used to validate the calculated results. The prediction of mud weight along the nine studied formations shows that for Ahmadi, Nahr Umr, Shuaiba, and Zubair formations ranges between 12.5 to 15 ppg. The predicted safe mud weight value seems to be narrow with a well deviation higher than 350. Therefore, for Ahmadi, Nahr Umr, Shuaiba, and Zubair formations, the wellbore appears unstable compared to other formations. The results of stability analyses indicate that the breakout mud weight wasn’t affected by wellbore azimuth because of low-stress contrast. Furthermore, shear failure can be prevented by drilling the well with an inclination of less than 350. As well as, to prevent breakdown the well should be drilled with an inclination between 25o to 65o in the direction of minimum horizontal stress. These outcomes could be used to prevent wellbore instability and determine a safe mud-weight window when planning to drill nearby wells in the future.

Investigating interphase bond behavior of waste badminton string fiber in composite matrix

ABSTRACT Recently moving towards the usage of sustainable and renewable construction materials, the badminton strings are identified as alternate material for commercial fibers. These recycled badminton strings once discarded from the racquets become a waste and cannot be reused. Hence investigation of the interphase bond behavior of these fibers with the cement and epoxy polymer matrix plays a major role. Therefore, the pullout mechanism between the fibers with the epoxy matrix is examined using the photoelasticity technique with a 40 mm embedment length. Whereas the pullout mechanism between the fibers with the cementitious matrix is examined for a single string of fiber using a pullout test with varied embedment lengths of 10, 20, 30, 40, 50, 60, 70, and 80 mm. From the study, the minimum and maximum bond stress between the fiber and epoxy interface is 3.23 MPa and 11.59 MPa respectively. Whereas between the fiber and cementitious interface, the minimum and maximum bond stress is 1.02 MPa and 2.15 MPa respectively. The experimental results are validated by the Weibull modulus approach which shows less variability. Thus, the results of the pullout test in composite matrix recommend the usage of waste badminton strings in fiber-reinforced concrete applications.

Numerical Simulation of Stress Disturbance Mechanism Caused by Hydraulic Fracturing of Shale Formation

Characterizing changes in rock properties is essential for the hydraulic fracture and re-fracture parameter optimization of shale formations. This paper proposed a hydraulic fracturing model to investigate the changes in rock properties during hydraulic fracturing using SPH, and the changes in the stress field and rock properties were quantitatively characterized. The simulation results indicated that the minimum horizontal principal stress increased by 10 MPa~15 MPa during fracture propagation, which is the main reason for the uneven propagation in multi-fracture propagation. Affected by the stress disturbance, the stimulated area was divided into four parts based on the changes in Young’s modulus and permeability; the more seriously the stress disturbance was affected, the higher the permeability of the stimulated zone was, and the smaller the stimulated zone was. Meanwhile, a zone with reduced permeability appeared due to the compression effect caused by the high injection pressure, and this increased with the increase in stress disturbance. The main reason for this was that strain formed because of the compression effect from the high injection pressure. The higher the stress disturbance, the higher the accumulated strain. This new model provides a new method for fracture parameter optimization, which also provides a foundation for the re-fracture parameter optimization of shale formations.

Petrographical, petrophysical, and geomechanical characterization of the Pliocene sandstone reservoirs of the Scarab Gas Field, deepwater Nile Delta, Egypt – Inferences on reservoir development

This study presents a comprehensive reservoir characterization of the channel sandstones of the Pliocene El Wastani Formation from the deepwater Scarab field, in Egypt. Routine core analysis, wireline logs, petrographic thin sections, X-ray diffraction, and drilling data were integrated to characterize the petrographical, petrophysical and geomechanical properties of the studied gas reservoirs to infer the implications for reservoir development. The petrographic analysis indicates fine to medium-grained glauconitic subfeldspathic wacke with dominantly primary intergranular porosity and minor secondary porosity contributed by feldspar dissolution. The reservoir facies exhibit pore-filling detrital clay (dominantly illite, smectite mixed-layer clay) along with minor carbonate and silica cementation. These reservoirs are megaporous and consist of an isotropic pore system, with 20–35 % porosity, 2400–3400 mD horizontal permeability, and 1300–2900 mD vertical permeability. Wireline log-based petrophysical assessments indicate excellent reservoir qualities with low shale volume (9–23%) and high hydrocarbon saturation of about 65–85%. Based on the geomechanical analysis, rock-mechanical properties, pore pressure, vertical stress, and minimum horizontal stress magnitudes were interpreted. The production and depletion-related risks were analyzed by utilizing geomechanical modeling which provided a quantitative assessment of drawdown and depletion limit to ensure sand-free hydrocarbon production without the risk of shear slippage on pre-existing weak planes. Considering the average unconfined compressive strength of 14 MPa, the Pliocene reservoir will require a 9.2 MPa depletion or 16.9 MPa drawdown to reach the onset of sanding, while the reservoir can be depleted to a pore pressure level of 4 MPa before it induces shear slippage on the optimally oriented fractures or fault planes. Inferences are drawn on reservoir quality, and reservoir development strategies are discussed accordingly.

Correlation of BMI With Educational Stress By Psychometric Analysis Via Perceived Stressed Scale In Non-State University Students

Overweight and Educational Stress had become two dominant problems in young population. We evaluated the effects of Educational Stress on BMI among non-state university students. Gender deference on stress and BMI, correlation between BMI and stress were determined. A google form was used for collection of data from 384 participants and stress was analyzed by Perceived Stress Scale (PSS). Majority of our study group 55.2% were female, and 44.8% were male. Mean BMI was 23.54kgm-2 (Overweight) and it was 24.70kgm-2 (overweight) in male and 22.60kgm-2 (normal) in female. As per the PSS, 52% of male participant showed moderate stress and 48% male showed high perceived stress. In female population, 50% showed moderate stress, 47% showed high perceived stress and 3% showed minimum stress. Results show that &gt;90% of students suffer from moderate to high perceived stress and it was positively correlated with BMI (p=0.01, r=0.239) seen in both genders. Educational stress can increase the students BMI and this finding is important for an institutional intervention for better outcome of the student performances. We recommend considering the program interventions to minimize the educational stress and to reduce the high BMI related non communicable diseases in future.

Experimental Study on Energy Release Mechanism and Crack Propagation Evolution of Sandstone under True Triaxial Loading

The instability of hard and brittle rock often leads to disastrous consequences in underground engineering. Under various surrounding rock pressure conditions, in situ stress induces corresponding deformation and damage to the floor post-mining. Therefore, it is crucial to examine the effects of mining under different confining pressures on rock disturbance, damage characteristics, and their distribution. Consequently, triaxial loading experiments under varying intermediate principal stress conditions were conducted on red sandstone specimens, using an acoustic emission monitoring system to track energy changes during rock damage and failure. This approach aids in studying crack generation, propagation, and fracture damage evolution. The results indicate that rock deformation results in axial compression and dilatancy, aligned with the direction of minimum and intermediate principal stresses. Ductility in rock failure becomes more pronounced with increased stress, primarily manifesting as shear failure. Internal cracks in the specimen lead to stress concentration and marked plastic deformation under compression, yet do not result in macroscopic surface cracks. The fracture angle θ of specimens post-failure generally exceeds 45° and varies with stress changes; at consistent burial depths, the angle of the sandstone failure surface increases with intermediate principal stress. This paper preliminarily establishes the informational linkage between rock failure and energy release, analyzing the rock samples over time and space. This research offers insights for analyzing and mitigating sudden rock instability.

The shrinkage behavior of boreholes drilled through deepwater creeping salt formations in West Africa

Introduction: Salt formations are complex and pose significant risks during oil and gas drilling. Creep behavior in salt formations under geostress can jeopardize drilling safety.Methods: This study analyzes the shrinkage behavior of boreholes drilled through salt formations in West Africa’s Block B, with emphasis on the differential creep rates in two horizontal principal stress directions and the evolution of wellbore shape over time. The impact of drilling fluid density on shrinkage rates is also investigated.Results: After drilling through salt formations, the creep rates differ between the two horizontal principal stress directions. Shrinkage is faster in the direction of minimum horizontal principal stress and slower in the direction of maximum horizontal principal stress. Over time, shrinkage rates converge, resulting in a transition from elliptical to circular wellbore shape. Higher drilling fluid density leads to reduced shrinkage rates.Discussion: These findings contribute to the theoretical guidance for drilling fluid density selection in salt formations.

Experimental Study of Macro- and Micro-Scopic Damage in Red Sandstone under Dry and Wet Cycling

The high-strength red sandstone in its natural state is subjected to significant strength deterioration under alternating wet and dry conditions, which can cause many catastrophic problems in the process of engineering construction. It is important to deeply understand the damage mechanism of red sandstone under the action of dry and wet cycles. Therefore, this paper explores the mechanism of red sandstone’s uniaxial deformation and failure through indoor uniaxial compression tests, studies the damage to the microstructure of red sandstone under wet–dry cycles using scanning electron microscopy, and establishes a damage variable based on fractal dimension. The results show that with the increase of wet–dry cycles, the peak stress of red sandstone shows a decreasing trend, and the minimum peak stress is 17.3 MPa, which is a 46.62% decrease compared to the sample with 0 wet–dry cycles. During the wet–dry cycle process, there are four deformation characteristics of red sandstone samples, namely, crack compression, crack extension, progressive fracture, and crack penetration. SEM images show that the porosity, pore area, and fractal dimension all show a nonlinear increase, and the maximum damage variable can reach 10.41%. The research results can provide guidance for engineering design and slope failure mechanism research in red sandstone areas.

Investigation of the dense granular soil behaviour inside and outside the shear band: a three-dimensional DEM-FDM study

The present paper aims to compare the behaviour of dense granular soils inside and outside the Shear Band (SB) during the Plane Strain Compression (PSC) test using the Discrete Element Method (DEM). The flexible membrane in the PSC test was modelled by adopting a discrete element–finite difference (DEM-FDM) hybrid approach. In contrast with previous 2D studies, the present study employed 3D simulations to consider the effects of out-of-plane characteristics such as the intermediate principal stress. According to the findings, the minimum and intermediate principal stresses outside the SB were twice as high as those inside at the residual state. It was also found that mechanical coordination numbers and redundancy indexes both inside and outside the SB decreased up to the onset of the residual phase, with a higher reduction rate inside the SB. As far as fabric anisotropy is concerned, the degree of anisotropy increased both in and out the SB until the peak state, with a somewhat higher rate inside the SB. A further finding was that the distribution of normal contact forces outside the SB remained symmetrical around the vertical axis after shear banding, however, it became asymmetrical inside the SB.

Multiscale modeling of gas-induced fracturing in anisotropic clayey rocks

In the context of repositories for nuclear waste, understanding the behavior of gas migration through clayey rocks with inherent anisotropy is crucial for assessing the safety of geological disposal facilities. The primary mechanism for gas breakthrough is the opening of micro-fractures due to high gas pressure. This occurs at gas pressures lower than the combined strength of the rock and its minimum principal stress under external loading conditions. To investigate the mechanism of microscale mode-I ruptures, it is essential to incorporate a multiscale approach that includes subcritical microcracks in the modeling framework. In this contribution, we derive the model from microstructures that contain periodically distributed microcracks within a porous material. The damage evolution law is coupled with the macroscopic poroelastic system by employing the asymptotic homogenization method and considering the inherent hydro-mechanical (HM) anisotropy at the microscale. The resulting permeability change induced by fracture opening is implicitly integrated into the gas flow equation. Verification examples are presented to validate the developed model step by step. An analysis of local macroscopic response is undertaken to underscore the influence of factors such as strain rate, initial damage, and applied stress, on the gas migration process. Numerical examples of direct tension tests are used to demonstrate the model's efficacy in describing localized failure characteristics. Finally, the simulation results for preferential gas flow reveal the robustness of the two-scale model in explicitly depicting gas-induced fracturing in anisotropic clayey rocks. The model successfully captures the common behaviors observed in laboratory experiments, such as a sudden drop in gas injection pressure, rapid build-up of downstream gas pressure, and steady-state gas flow following gas breakthrough.

An integrated geomechanical and petrophysical multiparameter approach for gas reservoir evaluation

Integrating petrophysical and geomechanical parameters is an efficient approach to evaluating shale gas reservoir potential. The high cost of corings and their limited number, coupled with time-intensive investigation, led researchers to use this alternative combination approach. In the Jiaoshiba area, from single-pilot well core data and log measurements, petrophysical and geomechanical parameters such as shale volume, total organic carbon, gas content, as well as pore pressure, stress components, and mineral brittleness were first estimated using established methods. In the second phase, based on logging curves, the reservoir electro-facies (EF) classification was performed using the unsupervised multi-resolution graph-based clustering method on a series of twenty wells, identifying five EF with different intrinsic characteristics. Unsupervised analyses were developed using the multilayer artificial neural network while incorporating the K-nearest neighbors and graphical classification algorithms. The results from the first and second phases indicate reservoir richness in organic matter, with the best reservoir exhibited by EF2 and EF3. In addition, effective stress components (SV, SH, and Sh) evaluation shows a normal stress regime with hydraulic fracture systems perpendicular to the minimum horizontal stress at each measured depth of the reservoir (Sv > SH > Sh). This research workflow can efficiently evaluate shale reservoirs with a realistic approach for identifying favorable fracturing positions while reducing errors due to human interference.

Propagation and complex morphology of hydraulic fractures in lamellar shales based on finite-discrete element modeling

We explore the controls of stress magnitude and orientation relative to bedding on the resulting morphology/topology of hydraulic fractures using a combined finite-discrete element method (FDEM). Behavior is shown conditioned by the ratio of principal stresses λ=σ3/σ1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda ={\\sigma }_{3}/{\\sigma }_{1}$$\\end{document} and relative inclination of the bedding. When the lateral pressure coefficient (λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda$$\\end{document}) is less than 0.67, hydraulic fractures predominantly initiate as tensile fractures along the wellbore, aligning with the maximum principal stress direction. Conversely, for λ≥0.67\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda \\ge 0.67$$\\end{document}, shear cracks are favored to initiate for the minor stress difference, leading to a less predictable initiation and extension direction. Simultaneously, diminished stress differences correspond to elevated reservoir breakdown pressures, displaying a linear correlation with lateral pressure coefficients and little influenced by equivalent bedding orientation. Bedding plane orientation significantly impacts the mode and morphology of hydraulic fracture propagation. Bedding parallel to the direction of the minimum principal stress (σ3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\sigma }_{3}$$\\end{document}) favors layer-penetrating and bifurcated fractures, whereas inclined bedding facilitates the emergence of numerous steering-type and capture-type fractures. Especially at steeper inclinations (β=60∘\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta =60^\\circ$$\\end{document}), hydraulic fractures readily extend along the bedding surface, inducing macroscopic shear slip failure. Under high-stress disparities, the breakdown pressure exhibits greater sensitivity to bedding inclination, and its influence pattern aligns with the variations in tensile strength, typically reaching maximum and minimum values at bedding inclination angles of 0° and 60°, respectively.

An Improved Continuum Approach for Unconsolidated Formations on the Field Scale

Summary With the development of unconventional resources, such as oil sands and methane hydrate reservoirs, the importance of the mechanical performance model for underground unconsolidated rocks has increased significantly. The commonly used numerical approach for unconsolidated rocks is the discrete-element method (DEM). However, the extensive calculations required by the DEM make it inadequate for simulating unconsolidated rock behavior on a field scale. An alternative is the continuum approach, used to simulate the behavior of unconsolidated rocks on the field scale. In previous continuum approaches, unconsolidated rocks have been modeled as a visco-plastic fluid (i.e., Bingham fluid). The continuum approach based on visco-plastic fluid uses pressure (scalar) to describe the stress state of the particles. However, this approach does not account for the difference between the maximum and minimum principal stresses of the in-situ stress field when simulating the mechanical performance of unconsolidated rocks. Here, we developed an improved continuum approach for unconsolidated rocks and used the finite-element method as a numerical approach. Our improved model can consider the difference between the maximum and minimum principal stresses of the in-situ stress field and the pore pressure of the unconsolidated formation. We validated our numerical model with the angle of repose test, a benchmark problem for unconsolidated rocks. The validation results confirm the accuracy of our unconsolidated model. For the coupled model between the unconsolidated model and the flow model, we used an analytical solution to verify its reliability. Unconsolidated rock performances in an unconsolidated reservoir with fluid injection have been investigated based on our coupled model. The simulation results show that injection can activate the movement of unconsolidated rock particles, leading to changes in the distribution of effective stress and permeability. Our model has the potential to address large-scale unconsolidated rock issues and contribute to energy extraction.