Principal Stress Research Articles

Three-dimensional peridynamic simulation on triaxial compression failure mechanical behavior of cylindrical marble specimen containing pre-existing fissures

A series of triaxial compression experiments and analyses were conducted out by using the three-dimensional bond-based peridynamics (BB-PD) model to investigate the mechanical behavior, deformability, and failure behavior of marble samples under different confining pressures. This study assessed the impact of confining pressure on mechanical performance of the intact marble, calibrated PD model micro-parameters using experimental data, and predicted the fissure behavior of marble specimens with single or parallel fissures. Through detailed analysis of crack evolution, crack pattern, displacement fields, and principal stress fields, the research revealed that the ductility of marble depended on the confining pressure, especially in the presence of fissures. Increasing confining pressure facilitated a transition from splitting failure to conjugate shear failure modes and induced stress concentration at fissure tips, leading to wing cracks and secondary cracks initiation. The presence and number of fissures were found to directly influence the mechanical behavior and failure process complexity of marble. A higher number of fissures reduced brittleness and strength while enhancing ductility and variety of failure modes. Seven distinct failure patterns of marble were identified under triaxial compression, illustrating the combined effect of confining pressure and fissures on marble specimen failure modes. This work can provide a theoretical and numerical basis for fissured rocks fracture in deep engineering

Nucleation of fracture: The first-octant evidence against classical variational phase-field models

Abstract As a companion work to [1], this Note presents a series of simple formulae and explicit results that illustrate and highlight why classical variational phase-field models cannot possibly predict fracture nucleation in elastic brittle materials. The focus is on “tension-dominated” problems where all principal stresses are non-negative, that is, problems taking place entirely within the first octant in the space of principal stresses.

Evaluation of the Biomechanical Effects and Stability of Titanium and Carbon Fiber-Reinforced Polyetheretherketone Mini Plates in Le Fort I Advancement Osteotomy Fixation Using Finite Element Analysis.

This study aimed to investigate the biomechanical properties of 60% carbon fiber-reinforced polyetheretherketone (Cfr-PEEK), which exhibits high mechanical strength and can address the limitations of titanium mini plates used in Le Fort I osteotomy. Models were created using the FEA method based on tomography images of adult individuals. A 5 mm maxillary advancement was applied to the models following Le Fort I osteotomy. Mini plates made of titanium and 60% Cfr-PEEK were used. Support was provided by the nasomaxillary and zygomaticomaxillary buttresses to fix a total of four L-shaped mini plates. Oblique loads of 125 N, directed from palatal to buccal, and a total of 250 N compression loads were applied to the central fossa of the premolar and molar teeth in the maxillary model at a 30° angle relative to the long axis of the teeth. Displacement values at the osteotomy line, Von Mises stresses in the mini plate-screws, and principal stresses in the bone were compared. Examination of stress values in the fixation systems of the models revealed higher stress values in the Cfr-PEEK model compared to the titanium model. However, these stresses did not reach levels that would deform the Cfr-PEEK fixation systems. Stress and displacement values in the bone were lower in the Cfr-PEEK model compared to the titanium model. According to the findings of our study, Cfr-PEEK represents a viable alternative to titanium for mini plate material in Le Fort I osteotomy, offering biomechanical advantages.

Stress Zoning Characteristics of Goaf Side and Quantitative Evaluation of Surrounding Rock Stability

Aiming to maintain the stability of the mining roadway and the next working-face roadway in the goaf side of a coal mine, a systematic study was carried out, through theoretical analysis, numerical simulation, field case analysis, and other methods, of the synergistic change mechanism in the stress distribution and plastic zone development morphology of the roadway’s surrounding rock in the goaf side under mining disturbance. It was revealed that, under the influence of mining, the goaf side will form a high-deviatoric-stress environment, which directly affects the shape and stability of the plastic zone of the roadway’s surrounding rock. Based on the characteristics of the principal stress ratio and the morphological development law of the plastic zone of the surrounding rock, the side of the goaf is divided into four regions: unloading zone, high-deviatoric-stress zone, low-deviatoric-stress zone, and original-stress zone. And the corresponding mine pressure behavior zoning is proposed: fracture zone, butterfly failure zone, elliptical failure zone, and circular failure zone. A quantitative evaluation method for the stability of the roadway surrounding rock based on the plastic zone morphology criterion was established, and combined with the division of mine pressure, the stability of the surrounding rock on the side of the goaf was quantitatively evaluated.

Analytical study on plastic loosening zone of weak surrounding rocks tunnel in high cold areas

AbstractThe analysis of plastic loosening zone of tunnels with cold condition, high in situ stress, and weak stratum is the key scientific problem of tunnel construction in cold areas. Based on the unified strength theory and considering the coupling effect of high in situ stress and low‐temperature field, the analytical model of the plastic loosening zone of tunnel surrounding rocks was proposed, and the influence laws of physical parameters (initial ground stress, freezing temperature, excavation radius, and intermediate principal stress) was explored. The results illustrate that: (1) with the coupling of low temperature and stress fields, the in‐situ stress has a more significant effect on the radius of the plastic loosening zone of the tunnel surrounding rocks, showing a nonlinear correlation. When the in situ stress is small, the influence of the temperature field on the radius of the plastic loosening zone is more obvious. (2) The radius of the plastic loosening zone of the tunnel surrounding rocks increases synchronously with the excavation radius and gradually decreases with the increase of the intermediate principal stress. (3) The greater the temperature difference in the low‐temperature field, the tunnel stability has a more significant response to the intermediate principal stress and is positively correlated with the coefficient of the intermediate principal stress. (4) In the actual project, the proposed model can well describe the mechanical behavior and deformation characteristics of tunnel surrounding rocks in low‐temperature environment, showing applicability. The research results are expected to provide a theoretical basis for the study of tunnel stability in cold areas.

Developing a geomechanical model to predict breakdown pressure in a vertical borehole using failure analysis: a case study

Breakdown is an important process in geomechanics; a very complex process in hydraulic fracturing which has been the subject of extensive research in the literature. There exist several models in the literature for predicting the breakdown pressure. In this research, the breakdown pressure for hydraulic fracturing in a vertical borehole was modeled using 2D and 3D failure analysis. In the geomechanical model constructed in this case study, elastic moduli were obtained using petrophysical data as well as data extracted from core analysis. The in-situ stress state of the reservoir was obtained by poroelastic horizontal strain model and was then validated by field data. To test the accuracy of the horizontal strain model, several models were used to obtain the minimum horizontals stress. At the end, the induced principal stresses inside the borehole were modeled by Kirch Equations. Four failure criteria, namely Mohr–Coulomb, 2D Hoek–Brown, Hubbert-Willis and 3D Mogi-Coulomb were used to obtain the breakdown pressure for the target reservoir. Based on the prediction results of these failure criteria, it was obtained that 2D Hoek–Brown, Hubbert-Willis, and 3D Mogi-Coulomb criteria resulted in seemingly unrealistic breakdown pressures with respect to the minimum horizontal stress gradient. The Mohr–Coulomb criterion produced lower breakdown pressure gradients, yet closer to the minimum horizontal stress values, even though it neglects the effect of intermediate stress.

Shear stress-strain relationships and anisotropy in silty soil: The role of principal stress rotation

Shear stress-strain relationships and anisotropy in silty soil: The role of principal stress rotation

Continuous fiber printing path generation based on Euler diagram division

Continuous fiber printed structures are widely used in aerospace applications because of their excellent performance and high design freedom. Existing path planning methods optimize the continuous fiber printing direction by stress lines or discrete angles, but these methods are far from perfect printing paths and lack planning for connectivity relations. In this study, a planning method for continuous fiber printing paths based on constructing Eulerian circuits from a weighted undirected graph is proposed. The principal stress lines are transformed into a weighted undirected graph, which divides the Eulerian subgraph by splitting the common nodes to plan the continuous fiber printing path circuit. Subsequently, the printing structure parameters are optimized based on simulation analysis. The experimental results, taking MBB (Messerschmitt-Bolkow-Blohm) beams as an example, show that the printing path designed in this paper improves the structural strength by 52.9% and the structural stiffness by 81.7% compared with the conventional printing path.

Evaluation of Steel Slag as a Sustainable Alternative Aggregate for Railway Ballast: A Shakedown Theory-Based Approach

Recent advancements in railway construction have emphasized environmental sustainability, integrating considerations of environmental impact into the planning and execution of infrastructure projects to reduce costs and mitigate adverse effects. This study investigates the use of steel slag as a sustainable alternative for railway ballast, grounded in shakedown theory. The characterization of the aggregates was performed in accordance with NBR 5564 and AREMA standards, confirming that the material meets most requirements. The mechanical behavior of the ballast was analyzed under cyclic loading conditions, assessing permanent deformation and the material’s ability to achieve stability (shakedown). Triaxial tests with repeated loading simulated real railway conditions, applying vertical stresses up to 600 kPa and confining pressures ranging from 35 to 200 kPa. The results indicate that steel slag aggregates exhibited promising performance, with seven specimens achieving stable deformation levels, characterized by residual deformations of less than 2.5 mm. Notably, these specimens approached deformations on the order of 10−7, indicating stability under cyclic loading. Furthermore, a comparative analysis of shakedown criteria proposed by various authors revealed variations in limits for granular materials, enhancing the understanding of steel slag aggregate behavior. The experimental results were validated through numerical simulations conducted with Systrain software 2.0, which simulated a loading condition of 32.5 tons per axle, confirming the observations with maximum principal stresses ranging from 166 to 184 kPa in the ballast. The analysis showed that steel slag aggregates can withstand stress levels higher than those of granodiorite, reinforcing their viability as a sustainable alternative for railway ballast.

Asymmetric deformation and failure behavior of roadway subjected to different principal stress based on biaxial tests

The magnitude and direction of stress will affect the failure of roadway. The impact of stress magnitude and direction on roadway failure was investigated using a rock failure system equipped with true triaxial loading, acoustic emission (AE), and digital image correlation (DIC) technologies. The system allowed for the simulation of rock sample failures under various three-dimensional stress conditions, while real-time monitoring was conducted using a high-precision microseismic system. By prefabricating rectangular holes at different angles in sandstone specimens, roadways under different stress effects in engineering can be simulated. Biaxial loading tests were then performed on these prefabricated sandstone cube specimens to observe external fracture characteristics and internal fracture information using acoustic emission equipment. The peak strength of samples with holes is approximately 38–56% of that of intact samples. In the early and middle loading stages, the strain on the surface is on the order of 10-3. In the later loading stage, the strain on the surface is on the order of 10-2. The findings indicate that roadway failure primarily involves local particle ejection, fragment spalling, large-scale particle ejection, plate crack buckling, and eventual failure. The ultimate failure mode varies based on stress deflection angles: with no included angle, the roadway exhibits a ’V’ shaped failure zone on both sides, predominantly experiencing tensile failure. At included angles of 30°, 45°, and 60° between stress and roadway axis, the roadway displays a “—” failure pattern along the diagonal, characterized by a combination of tension and shear failure. The extension angle of the“—” failure zone varies depending on the stress deflection angle. At a 90° included angle, the roadway shows a ’V’ shaped failure in the roof and floor, primarily undergoing tensile failure. Real-time monitoring of the strain field evolution around the roadway during failure using DIC method revealed valuable insights. AE events at different deflection angles reflect the progression of micro cracks in the specimen, showing a strong correlation with macro failure. The research outcomes elucidate the mechanisms behind various forms of roadway failure induced by stress deflection and shed light on the failure mechanism at different stress deflection angles.

Intelligent Inversion Analysis of Surrounding Rock Parameters and Deformation Characteristics of a Water Diversion Surge Shaft

The water diversion surge shaft is vital for a hydropower station. However, the complex geological properties of the surrounding rock make it challenging to obtain its mechanical parameters. A method combining particle swarm optimization (PSO) and support vector machine (SVM) algorithms is proposed for estimating these parameters. According to the engineering geological background and support scheme, a three-dimensional model of the water diversion surge shaft is established by FLAC3D. An orthogonal test is designed to verify the accuracy of the numerical model. Then, the surrounding rock mechanical parameter database is established. The PSO-SVM intelligent inversion algorithm is used to invert the optimal values of the mechanical parameters of the surrounding rock. The support for excavating the next layer depends on the mechanical parameters of the current rock layer. An optimized design scheme is then compared and analyzed with the original support scheme by considering deformation and plastic characteristics. The research results demonstrate that the PSO-SVM intelligent inversion algorithm can effectively improve the accuracy and efficiency of the inversion of rock mechanical parameters. Under the influence of excavation, the surrounding rock in the plastic zone mainly fails in shear, with maximum deformation occurring in the middle and lower parts of the excavation area. The maximum deformation of the surrounding rock under support with long anchor cables is 0.6 cm less than that of support without long anchor cables and 4.07 cm less than that of support without an anchor. In the direction of the maximum and minimum principal stress, the maximum depth of the plastic zone under the support with long anchor cables is 1.3 m to 2.6 m less than that of the support without long anchor cables and the support without an anchor. Compared with the support without long anchor cables and support without an anchor, the support with long anchor cables can effectively control the deformation of the surrounding rock and limit the development of the plastic zone.

Three-Dimensional Discontinuum Modeling and Rigid Block Stability Analysis of a Group of Three Caverns for Hydroproject in Northeast India

Abstract This paper presents various methods for calculating the factor of safety (FOS) and utilizes the Isoblock method to analyze the stability of underground powerhouse caverns located in the North-East state of India. A three-dimensional discontinuum analysis simulates the stability of the downstream sidewall, upstream sidewall, and crown of the caverns. The results indicate that the powerhouse cavern contains approximately 2.36% unstable blocks, while the Main Inlet Valve (MIV) and Transformer Caverns exhibit 0.14% and 0.84% unstable blocks, respectively. A comprehensive parametric analysis investigates the impact of joint stiffness, joint friction angle, in-situ stress, cover depth, and the orientation of the cavern's longer axis on stability. The findings reveal that the cavern's stability is significantly influenced by variations in lateral stress ratio and the direction of in-situ principal stress. Stability is optimized at stress ratios between 1.2 and 1.8, with maximum instability observed in the powerhouse cavern, correlating with its larger size. Notably, the stability of the crown is greater than that of the sidewalls, particularly when the cavern orientation is aligned between N68°E and N78°E. The study underscores the importance of these factors in the design and stability assessment of underground structures, providing valuable insights to enhance their safety and reliability. This analysis highlights the necessity for considering joint stiffness and in-situ stress orientations in future designs to mitigate risks associated with instability.

Permanent deformation and particle crushability of calcareous sands under cyclic traffic-induced loadings through simple shear apparatus

This study focuses on investigating permanent deformations, encompassing normal and shear strains, of calcareous sandy soils subjected to drained cyclic traffic-induced loadings. The investigation utilizes a Simple Shear (SS) apparatus allowing for variations in both normal and shear stress components over each cycle and incorporates Principal Stress Rotation (PSR), a feature not replicable in conventional cyclic uniaxial triaxial tests which is the key aspect of this research. The study also accounts for the harmonically changing the effective horizontal stress resulting from cyclic variations of effective vertical stress, conducted under a horizontally constrained boundary condition with zero lateral strain. A series of drained cyclic simple shear experiments is carried out, implementing a heart-shaped stress path, encompassing up to 1000 cycles. The objective of the study is to analyze permanent normal and shear deformations, along with associated total particle crushing, using both sieving analyses and 2D image processing of particles. The study also evaluates the impact of an initial static shear stress originating from the longitudinal slope of roads. The findings highlight the influences of induced cyclic amplitudes of stress components, principal stress and strain rate rotation, and initial static shear stress on the development of permanent strains. Furthermore, the research characterizes particle crushability in terms of total crushability over such loading, examining its dependency on relative density and variations in both shear and normal stress components.

Asymmetric sample shapes complicate planar biaxial testing assumptions by intensifying shear strains and stresses

Planar biaxial testing offers a physiologically relevant approach for mechanically characterizing thin deformable soft tissues, but often relies on erroneous assumptions of uniform strain fields and negligible shear strains and forces. In addition to the complex mechanical behavior exhibited by soft tissues, constraints on sample size, geometry, and aspect ratio often restrict sample shape and symmetry. Using simple PDMS gels, we explored the unknown and unquantified effects of sample shape asymmetry on planar biaxial testing results, including shear strain magnitudes, shear forces measured at the sample’s boundary, and the homogeneity of strains experienced at the center of each sample. We used a combination of finite element modeling and experimental validation to examine PDMS gels of varying levels of asymmetry, allowing us to identify effects of sample shape without confounding factors introduced by the nonlinear, spatially variable, and anisotropic properties of soft tissues. Both biaxial simulations and experiments, which showed strong agreement, revealed that sample shape asymmetry led to significantly larger shear strains, shear forces, and overestimation of principal stresses. Excluding these shear forces resulted in an underestimation of shear moduli during inverse mechanical characterizations. Even in the simplest of deformable biomaterials, sample shape asymmetry should be avoided as it can induce drastic increases in shear strains and shear forces, invalidating traditional planar biaxial testing analyses. Alternatively, sample shape asymmetry may be exploited to generate more robust estimates of constitutive parameters in more complex materials, which could lead to a refined understanding and inference of mechanical behavior.

Study on micromechanical behavior and energy evolution of granular material generated by latent diffusion model under rotation of principal stresses

In this study, advanced image processing technology is used to analyze the three-dimensional sand composite image, and the topography features of sand particles are successfully extracted and saved as high-quality image files. These image files were then trained using the latent diffusion model (LDM) to generate a large number of sand particles with real morphology, which were then applied to numerical studies. The effects of particle morphology on the macroscopic mechanical behavior and microscopic energy evolution of sand under complex stress paths were studied in detail, combined with the circular and elliptical particles widely used in current tests. The results show that with the increase of the irregularity of the sample shape, the cycle period and radius of the closed circle formed by the partial strain curve gradually decrease, and the center of the circle gradually shifts. In addition, the volume strain and liquefaction strength of sand samples increase with the increase of particle shape irregularity. It is particularly noteworthy that obvious vortex structures exist in the positions near the center where deformation is severe in the samples of circular and elliptical particles. However, such structures are difficult to be directly observed in sample with irregular particles. This phenomenon reveals the influence of particle morphology on the complexity of the mechanical behavior of sand, providing us with new insights into the understanding of the response mechanism of sand soil under complex stress conditions.

Biomechanical evaluation of implant options for unilateral maxillary defects: a finite element analysis

ObjectiveThis study aimed to evaluate stress distribution in unilateral maxillary defects using finite element analysis (FEA) to compare subperiosteal (SI) and zygomatic implants (ZI).Materials and methodsA 3D model of a unilaterally atrophied maxilla was reconstructed from CT scans. Five scenarios were simulated: (1) quad zygoma implants (SC1), (2) zygoma and conventional implants (SC2), (3) two-piece SI and conventional implants (SC3), (4) one-piece SI and conventional implants (SC4) and (5) one-piece SI implant (SC5). Mechanical properties were assigned based on data in the literature; a 450 N force for occlusal loading and a 93 N force for oblique loads were applied.ResultsUnder vertical loading, SC2 exhibited the highest tensile stress (Pmax) in the atrophic region (R-AM), while SC4 showed the lowest Pmax across the entire maxilla, indicating better stress distribution. Under oblique forces, SC2 also showed the highest Pmax in R-AM, while SC5 had the lowest Pmax overall. Minimum principal stress (Pmin) followed similar patterns, with SC4 and SC5 demonstrating lower stress levels than the other scenarios. Abutment stresses were highest in SC2 and lowest in SC4. Overall, the SI scenarios (SC3–SC5) exhibited lower stress transmission to the alveolar bone than the ZI scenarios (SC1 and SC2), with SC4 providing the most balanced stress distribution across all regions.ConclusionsSI implants, mainly the one-piece SI (SC4), offered a more favourable stress distribution than ZI implants in unilateral maxillary defects, reducing the risk of excessive bone stress. This finding suggests that SI implants may be superior for such cases, although individual patient anatomy should guide implant selection. Further clinical studies are necessary to confirm these biomechanical findings in vivo.Clinical relevanceThis study underscores the crucial role of implant selection in minimising stress on the alveolar bone in unilateral maxillary defects. Based on these findings, we recommend personalised implant strategies based on biomechanical insights to enhance outcomes in maxillofacial reconstruction.

An exact implementation of the generalized Zhang-Zhu criterion for elasto-plastic finite element calculations

The generalized Zhang-Zhu (GZZ) strength criterion was proposed as an extension to the Hoek-Brown criterion and the Mogi criterion. The introduction to mean normal stress results in a non-smooth and non-convex yield surface, which presents a challenge for updating plastic stress. Current research primarily focuses on modified smooth GZZ criteria or approximate solutions, which inevitably lead to increased computational costs or inaccuracies. In this paper, an accurate stress updating algorithm is proposed based on the original GZZ criterion. The algorithm operates entirely in the principal stress space, where numerical singularities at the intersection of yield surfaces are avoided by defining four different types of stress updating. This approach simplifies the GZZ criterion compared to its formulation in general stress space. The return mapping is employed to compute the updated stress and consistent stiffness matrix, facilitating calculations using both finite element implicit and explicit algorithms. Finally, the accuracy of the proposed method is validated using rock true triaxial test data and semi-analytical solutions for stresses and displacement around a circular opening under the GZZ criterion.

Pseudo-dynamic stability analysis of 3D rock slopes considering tensile strength-modified Hoek–Brown failure criterion: Seismic UBLA implementations

The Hoek-Brown (HB) criterion has found extensive application in the stability analysis of intact or jointed rock slopes, in both two-dimensional (2D) and three-dimensional (3D) contexts. In the early days, the assessment of Hoek-Brown slopes rarely incorporated tensile strength until, recently, limited studies examined the tension-controlled toppling failure at the sliding head. Nevertheless, the adapted tensile strength, which is extrapolated from the HB envelope the tensile regime, has been found overestimate experimental results. Thus, for more realistically representing the influence of rock tensile strength, the present study introduces a novel procedure for assessing the seismic stability of 3D HB slopes. In this study, the tensile strength-modified HB envelopes considering cut-off effects are derived in the principal stress space and Mohr space. To assess the slope stability, the obtained HB envelope is employed in a multi-cone mechanism based on upper bound limit analysis (UBLA). Specifically, the counter of this mechanism is determined by 10 optimized dependent rupture angles, highly considering the nonlinearity of the Hoek-Brown envelope compared to the traditional linearization strategies. As an improved seismic stability analysis, the seismic load is characterized by a modified pseudo-dynamic method. Analytical expressions for two stability indicators, i.e., the stability number and safety factor, are derived. Comparisons with numerical simulations demonstrate the rationality of the proposed procedure. Parametric analysis indicates the significant effect of the tension cut-off on the HB rock slope stability and the contour of the sliding surface.

Experimental investigation of cyclic responses of frozen soil under principal stress rotation induced by wave loads

Experimental investigation of cyclic responses of frozen soil under principal stress rotation induced by wave loads

Optical and stress properties of ZrO2/SiO2 and TiO2/SiO2 anti-reflective coatings deposited by ion-beam-assisted deposition on a flexible substrate

Dielectric films of ZrO2,TiO2, and SiO2 were deposited on flexible polycarbonate (PC) and polyethylene terephthalate (PET) substrates by using ion-beam-assisted deposition (IBAD). Each layer had a thickness ranging from 30 to 210 nm. The optical and anisotropic stress properties were investigated. Two anti-reflective coatings (ARCs), ZrO2/SiO2 and TiO2/SiO2, were selected and deposited on the PET flexible substrate. The anisotropic stresses of the single layer and ARCs were measured using a phase-shifting moiré interferometer. Experimental results showed that the optimal oxygen flow rates for the ZrO2,TiO2, and SiO2 films deposited with IBAD were 10, 10, and 15 sccm, respectively. The refractive index (n) was TiO2(2.37)>ZrO2(2.05)>SiO2(1.46), and the extinction coefficient (k) for all samples was below 10−3. The thermal expansion coefficient of the PC substrate was three times that of the PET substrate, and the high-refraction ZrO2 and TiO2 single-layer films presented cracks and distortions on the PC substrate. Only the low-refractive-index SiO2 sample did not present cracks. The three dielectric films did not crack or distort when deposited on the PET substrate. The anisotropic stress analysis provided the maximum principal and shear stresses for the three dielectric films on the PET substrate. Therefore, the maximum principal stress of the 210 nm single-layer film on a PET substrate is TiO2>ZrO2>SiO2. It was also discovered that the principal stress of the AR multilayer film is significantly decreased due to the damping stacking effect (DSE) of the high- and low-refractive-index materials, ZrO2/SiO2 ARC (−297.3MPa)>TiO2/SiO2ARC(−132.6MPa). Thus, the high packing density of TiO2 gives a better DSE than ZrO2.