Large Radius Of Curvature Research Articles

Simulation and optimization of microlens hot-melting fabricating process based on finite element method

As an important optical element, the microlens array has received more and more attention. Due to the advantages of a short production cycle, low cost, high efficiency, and easy to transfer, the photoresist hot-melting method has been widely used to fabricate microlens. Fabricating microlenses with large aperture and curvature radius are the basic requirements to ensure image quality. However, due to the limitations of photoresist material properties and the hot-melting process, the shape of the microlens is not easy to control. In this paper, the finite element fluid simulation software Fluent was used to simulate the microlens hot-melting fabricating process. Through the simulation, we could understand the formation process of the microlens. By multiple groups of simulation comparison, the key parameter in the formation of microlens was discussed. Besides, the simulation result shows that when a layer of residual photoresist is left around the original photoresist cylinder, microlens with larger diameter can be easily obtained. The experimental results are in good agreement with the simulation results. The comparison imaging experiment also illustrates that the microlens fabricated by the improved process has better imaging ability. Through simulation, this paper not only explains the mechanism of the hot-melting method, but also optimizes its process. The related research could expand the application range of the hot-melting method in the fabrication of microlens.

Simulation and measurement of systematic errors of stitching interferometry for high precision X-ray mirrors with large radius of curvature.

To accurately measure the surface figure of curved mirrors with large radius of curvature (RoC) using stitching interferometry methods, three types of measurement errors are systematically studied, including retrace error, defocusing error within a single subaperture, and stitching angle error among different subapertures. It was found that part of the retrace error caused by the mismatch between the reference wavefront and reflected wavefront has little effect, while the overall retrace error, including the influence of the imperfect optical elements, will cause an error of 1-2 nm RMS within a single subaperture. Defocusing error will enlarge the error due to amplification of optical path error caused by the deviation of the position of the CCD. Because the error is mainly in the edge area, a slope threshold, which controls the maximum surface slope of each subaperture, can be optimized to reduce the effect of the defocus on stitching measurement error. Constant angle error among neighboring subapertures has the biggest accumulation effect on the final stitched figure. For the spherical mirror with RoC of 100 m of 80mm×40mm, the error of the one-dimensional residual profile is 4.67 nm PV, assuming a constant angle error of 2×10-7rad. For the elliptical mirror with RoC of 60-140 m, it is more than 15 nm peak-to-valley (PV). It is because the profile difference caused by constant angle error is closer to a circle, which can be mostly removed after subtraction of a best-fit sphere. Based on the above error analysis, the developed algorithm-based stitching method was used to measure an elliptical cylindrical mirror of 74mm×40mm with RoC of 60-140 m, and the result was compared with a slope measurement instrument from the Beijing Synchrotron Radiation Facility. After removing the best fitting ellipse profile, the one-dimensional difference between the two results is only 0.77 nm RMS, which demonstrated good measurement accuracy.

Safety Performance of Rural Curved Corner Intersections with Regional Effects

This study evaluates the intersection of rural roads where a curved roadway segment connects the major flow of through traffic from orthogonal directions. A system of up to three intersections in combination can be represented singly by the situation modeled in this paper as a curved corner intersection site. This paper evaluates the application of random intercept negative binomial (NB) regression modeling to produce safety performance functions, and compares the outcome with NB models using fixed regional effects. At curved corner intersections, installing a combined/merged intersection approach near the midpoint of the curve is a potential countermeasure that by comparison with three-leg configurations experienced 20% fewer intersection crashes. A larger radius of curvature along the curved segment at these types of intersections is also very favorable for safety performance. Each 100 ft increase in the radius of a three-leg or four-leg curved corner intersection is estimated to reduce total non-animal crash occurrence by 5% and 7%, respectively. This study can help safety engineers to prioritize the improvement of rural un-signalized intersections.

Cracking Pattern of Indented Ice Sheet Bending Failures

AbstractIce sheet bending failures have been investigated extensively for ice loads on conical offshore structures and icebreakers in arctic regions. Most previous theoretical studies focus on bending failures of semi-infinite level ice, ice wedges, or finite-sized rectangular ice floes. For indented ice sheet bending failures, analytical ice load models have been developed by assuming a radial-before-circumferential cracking pattern. Recently, real-time simulations of ice-structure interactions are gaining increasing traction due to their great application potential. The analytical or semi-analytical models implemented into the real-time simulator significantly influence the accuracy of real-time simulations. Against this backdrop, the cracking pattern assumption needs to be more critically examined, and the criterion for cracking pattern determinations is in demand for utilizing different models for different cracking patterns in real-time simulations. Motivated by this need, the current paper establishes the cracking pattern determination criterion for indented ice sheet bending failures, based on the theory of plates on elastic foundations and normalized formulae. It is found that large indentation lengths and radii of structure waterline curvature induce a circumferential-before-radial cracking pattern. Conversely, small indentation lengths and radii of structure waterline curvature result in a radial-before-circumferential cracking pattern.

Demonstration of Large Curvature Radius Shape Sensing Using Optical Frequency Domain Reflectometry in Multi-Core Fibers

In distributed shape sensing, the shape reconstruction error is more and more sensitive to the strain measuring error along with curvature radius of reconstructed shape increasing, which causes a notable challenge for large curvature radius shape reconstructing. In this paper, we demonstrate a large curvature radius shape sensing using optical frequency domain reflectometry (OFDR) in multi-core fibers. We construct a theoretical model of strain measuring error and curvature radius reconstructing errors under different curvature radius. In the experiment, by this reconstructing error model, we optimally select the measurable strain resolution and the sensing spatial resolution to realize the shape reconstruction with a large curvature radius and reconstruct two-dimensional (2D) circle shapes of curvature radii from 5 cm to 100 cm. To verify the accuracy of three-dimensional (3D) shape reconstruction, we present a 3D shape sensing validation method based on 3D printing technology. We fabricate a 3D phantom containing a groove with a variable curvature radius of 5 cm to 100 cm. The presented distributed shape sensing system realize to reconstruct this complicated 3D shape. The root-mean-square error of curvature radius between the reconstructed and designed 3D space curves is 7.2 mm and the mean Euclidean distance is 3.4 mm.

A simple picture of mantle wedge flow patterns and temperature variation

The solid-state mantle flow is an important factor that controls the mass and heat transfer in the solid Earth. This study aims to provide a simple picture of three-dimensional (3-D) mantle flow patterns in the sub-arc region of subduction zones based on the results of 3-D steady-state numerical models with varying subduction parameters. Here, the mantle wedge flow pattern is evaluated based on the azimuthal directions of the mantle inflow from the back-arc and the down-dip outflow. The outflow direction generally parallels the subduction direction, but the inflow direction relative to the outflow direction depends on the local subduction obliquity – the angle between the subduction direction and the strike-normal axis of the subducting slab. A change in the strike of the slab leads to a change in the obliquity and thus the inflow direction. Such change is common along curved margins as the strike of the slab tends to follow that of the margin, or vice versa. Along convex-arc-ward margins, the mantle inflow is deflected towards the region of lowest obliquity but with reduced vigor due to lower dynamic pressure gradients that partly drive the flow, resulting in a cooler mantle wedge. Along concave-arc-ward margins, the mantle inflow is deflected away from the region of lowest obliquity but with increased vigor, resulting in a hotter mantle wedge. These effects increase with decreasing radius of curvature. Along-margin change in the dip of the subducting slab also affects the inflow direction through its impact on the strike of the slab, but its effect is relatively small. We express the azimuthal inner angle between the inflow and outflow directions as a function of obliquity and apply the function to predict sub-arc mantle inflow directions in the circum-Pacific and neighboring regions. Within and among these margins, the inner angle varies over its full range of 0–180°. Most of the margins that are 1000s of kilometers in length are either straight or curved concave-arc-ward with large radii of curvature, for which small or gradual along-margin changes in the mantle inflow direction and the mantle wedge temperature are predicted. A large drop in the mantle wedge temperature by up to a couple of hundred degrees is predicted at short convex-arc-ward segments, such as at the Kuril-Japan and Bonin-Mariana junctions. The fringes of flat slab segments are curved with small radii of curvature, likely resulting in sharp lateral changes in the inflow direction and the mantle wedge temperature.

Study on the corrosion resistance of sulfonated graphene/aluminum phosphate composites in waterborne polyurethane coatings

Abstract Sulfonated graphene/aluminum phosphate (SG/AlPO4) composites were synthesized by precipitation method, and composites with different mass ratios were added to water-based polyurethane (WPU) resins to prepare coatings. According to tests, composites with the addition of 2 wt% composite coating has good anticorrosion performance, and its protection efficiency is increased by 79.6% compared with pure resin. In the early stage of the corrosion, the SG layer forms the barrier. During the corrosion process, the SG layer was destroyed, the phosphate ions decomposed by the exposed spherical AlPO4 in the corrosive medium and the divalent iron ions on the iron-based surface form a stable precipitation protective layer to achieve the anticorrosion effect. From the EIS test, the coating with 2 wt% composite material has a larger radius of curvature in the Nyquist diagram at different time periods. According to the fitted circuit, it is further confirmed that the precipitation protection layer has a larger resistance value. After soaking for 24 h the resistance value is the largest, which is 1.231 × 104 Ω cm2.

Effect of artery curvature on the coronary fractional flow reserve

Understanding the effect of the artery curvature on the pressure drop inside the arteries is of great importance due to the existence of several curved portions inside the coronary arterial system. In this paper, an experimental model is developed to account for the effect of the curvature of the coronary arteries on the pressure drop and Fractional Flow Reserve (FFR). FFR is an index for the evaluation of the functional significance of coronary stenosis and is defined as the ratio of the coronary pressure downstream of the stenosis to its upstream value. To measure the pressure drop and FFR across curved artery models, three-dimensional-printed curved artery models are fabricated and installed in the test section of the experimental rig. For ratios of curvature radius over the artery diameter ranging from 2 to 7, there are a minimum value for the pressure drop and, hence, a corresponding maximum value for FFR at a ratio of approximately 3. For the curved arteries with larger curvature radii, the pressure drop increases, and consequently, FFR decreases with an increase in the radius. The results showed that an accurate evaluation of the pressure drop and FFR inside a curved coronary artery can only be achieved by accounting for the effect of curvature parameters including the curvature angle and radius, such that neglecting the effect of the artery curvature results in an underestimation of the pressure drop by about 25%–35%. The developed equation is able to determine the pressure drop inside a curved coronary artery model noninvasively.

A Spline Shape Deep Drawing using Finite Element Simulation and Experimental Work Test

In the current research, an analysis study was conducted to process of design of spline cup drawing. Deep-drawing tools (dies and punches) were designed and manufactured to implement the experimental work required to produce a spline cup with inner dimensions are height h=3 mm, width W=9.64 mm, and diameter d=34 mm, drawn from a circular blank of a di ameter D b = 8 0 mm, and thicknes s t = 0 . 7 mm made of low carbon steel (1008-AISI). To simulate the spline shape deep-drawing process, a commercial finite element program code ANSYS 19.0 Workbench was employed. The research aims to produce the spline shape and study the effect of the punch wall curvature radius on the drawing force, thickness distribution, and effective strains across the sidewall, major and minor axis curvature of a completely drawn spline cup using experimental testing and finite element modeling. From the comparisons between the experimental and finite element results, it was shown that the numerical results of a spline cup deep-drawing are good agreement with the results of the experiment and lie within an average of (4% - 8%). The drawing force and thinning for the small punch wall curvature radius is higher than the large punch wall curvature radius. The maximum drawing force and maximum thinning with the smallest punch wall curvature radius (0.5) at the minor axis curvature of a completely drawn spline cup. The maximum effective strain with the smallest punch wall curvature radius (0.5) at the minor axis curvature region at the completely drawn spline cup rim.

Resilient isolation-structure systems with super-large displacement friction pendulum bearings

This paper presents a super-large displacement friction pendulum bearing (SLDFPB) and isolation system with SLDFPB. SLDFPB has one or several spherical shells of large span and large curvature radius as an integrated sliding isolation layer. Superstructure can sustain large horizontal displacement through relative sliding between large spherical shell and sliding blocks. The proposed SLDFPB has two main advantages: 1) avoid damage of isolation layer during super-strong earthquakes owing to large lateral deformation capability; 2) have better isolation effectiveness because of smaller horizontal stiffness and isolation frequency. This study also investigates mechanical property of SLDFPB including equivalent radius and equivalent friction coefficient. Suggested designed method of SLDFPB is given based on seismic mitigation and reset ability of isolation layer. Two isolation structure systems with multi isolation layers are studied. The results show that large ratio of mass and optimised parameters contribute to good control effect.

Tip relief designed to optimize contact fatigue life of spur gears using adapted PSO and Firefly algorithms

This paper examines the dynamic performances of circular profile modifications designed to optimize the contact fatigue life of spur gears. It combines the PSO and Firefly metaheuristics to a gear dynamic/degradation model. The objectives are to analyse the ability of optimal corrections to reduce dynamic loads and dynamic transmission error (DTE), and to describe the influence of the modification variables. To reduce computation efforts, the study modifies the original metaheuristics. In the proposed adaptation of the Firefly algorithm, the particle movement hinges on the brightest firefly perceived through the light-absorbing medium. This change reduces the number of function evaluations per iteration. The analysis shows that while the correction length is more influential, both modification amount and length alter the gear behavior, whereas the curvature radius influence remains modest. Curved corrections are more effective in ameliorating contact fatigue life, whereas larger curvature radii are better at reducing the DTE. Compared to the original gear set, the PSO and Firefly versions showed that optimized modifications engender substantial enhancements of the fatigue resistance. Moreover, optimal profiles also reduce both DTE and dynamic factors, but the inverse cannot be assumed.

Influence of the Solid Shape on the Solution for the Uncoupled Quasi-Static Cyclic Thermoelasticity Problem in a Thermal Layer (Using Regular Solids as Example)

Analytical solutions are obtained for an uncoupled quasi-static cyclic thermoelasticity problem for regular solids: a half-space, a plate, a space with a cylindrical channel, a cylinder, a space with a spherical cavity, and a sphere. The solutions, which are trigonometric Fourier series of temporary variable, are transformed by changing the spatial variable into a form convenient for analysis of temperature oscillations and thermocyclic stresses in the thermal layer. For the solutions found, simple asymptotic dependences are established, suitable for large radii of curvature of the surface and body size. The influence of the solid shape on temperature oscillations and thermocyclic stresses in the thermal layer has been studied.

In Situ Investigation of the Kinematics of Ply Interfaces During Composite Manufacturing

Abstract The kinematics of composite ply interfaces critically affects both the manufacturing processes and deformation mechanisms and is often responsible for the formation of defects such as wrinkles and delamination. In the present work, processing-induced defects in a carbon fiber prepreg composite are evaluated by devising a novel in situ experimental approach. Carbon fiber prepreg laminates are cured in a specially designed autoclave with viewports with plies laid up on a mold with cylindrical tooling set up to maximize the ply-movement. Four-ply layup orientations of [90/90]s, [90/0]s, [90/45]s, and [90/−45]s and three-mold configurations with cylindrical tools of diameter 9.5 mm (3/8 in.), 12.7 mm (1/2 in.), and 15.9 mm (5/8 in.) are used for the parametric study. Strains, ply-movement, and formation of defects are observed in situ using digital image correlation (DIC) during the autoclave cure cycle, through the viewports. The processing-induced defects in the composite are further characterized by X-ray micro-computed tomography (micro-CT). We observed that the mold with the larger radius of curvature (15.9 mm cylinder) leads to higher strains in both in-plane directions and higher displacement in out of plane directions. The maximum average out-of-plane ply movement, as well as the largest wrinkle, are observed for [90/−45]s layup on the mold with the highest radius of curvature.

Variations in Glenohumeral Bony Morphology May Predict Recurrent Instability after Arthroscopic Bankart Repair

Objectives:Variations in bony anatomy may be associated with failure of stabilization surgery. The aim of this study was to develop a method to measure bony morphology on magnetic resonance imaging (MRI) to identify risk factors for failure after Bankart repair.Methods:This was a retrospective case-control study of 118 patients. Cases of postoperative dislocation were compared to matched controls. Demographic data was obtained by chart review and radiographic data from preoperative MRI. Volume was measured using a 3-D model. Radius of curvature of the humeral head and glenoid was measured on axial MRI images. Statistical analysis used student’s t-test for continuous variables and either Fisher’s exact or Chi-squared test for categorical variables; P value < 0.05 was significant. Interrater reliability between reviewers was calculated using interclass correlation coefficients (r).Results:Forty-six patients who had a postoperative dislocation met inclusion criteria and were matched to 72 controls. There was no difference between groups for demographic (age, sex, percentage of contact athletes) or radiographic (glenoid bone loss, off-track Hill-Sachs lesions) parameters. The average number of preoperative dislocations was higher in the case group (3.2 vs. 2.0, p=0.003). The humeral head (68.8 ml vs 62.8 ml, p=0.05) volume was greater in the case group, though this did not reach statistical significance. Glenoid volume (13.5 ml vs 12.8 ml, p=0.31) was similar between groups. The radius of curvature of the glenoid was larger, or shallower, in the case group compared to the control group (23.6 mm vs 22.6 mm, p=0.05), though the difference did not reach statistical significance. A greater percentage of patients with a glenoid radius of curvature > 24.5 mm experienced a postoperative dislocation compared to those who had a smaller radius of curvature (62.0% vs 29.8%, p < 0.01). In fact, patients who had glenoid radius of curvature > 24.5 mm were 5 times as likely to experience a postoperative dislocation compared to those who did not (odds ratio 5.04, 95% CI 2.13 – 11.94, p < 0.01) There was no significant difference between the number of preoperative dislocations between patients with larger or smaller glenoid radius of curvature (2.6 vs 2.3, p = 0.55). There was a strong interrater reliability for measurement of humeral head volume, glenoid volume, radius of curvature of glenoid and radius of curvature of humeral head (r = 0.94, 0.88, 0.89, 0.95).Conclusion:The results of this study demonstrate that a larger radius of curvature, indicative of a shallower glenoid, is associated with failure following primary arthroscopic Bankart. These findings suggest that the bony concavity of the glenoid may play a role in stability.Figure 1.

Numerical Investigation of Water Film Evaporation with the Countercurrent Air in the Asymmetric Heating Rectangular Channel for Passive Containment Cooling System

Passive containment cooling system (PCCS) is an important passive safety facility in the large advanced pressurized water reactor. Using the physical laws, such as gravity and buoyancy, the water film/air countercurrent flow is formed in the external annular channel to keep inside temperature and pressure below the maximum design values. Due to the large curvature radius of the annular channel, one of the short arc segments is taken out, as a rectangular channel, to analyze the main water film evaporation heat transfer characteristics. Two numerical methods are used to predict the water film evaporative mass flow rate during the heat transfer process in the large-scale rectangular channel with asymmetric heating when the water film temperature is not saturated. At the same time, these numerical simulation results are validated by the experiment which is set up to study water film/air countercurrent flow heat transfer on a vertical back heating plate with 5 m in length and 1.2 m in width. It is shown that the maximum deviation between numerical simulation and experiment is 30%. In addition, the influences on these parameters, such as heat flux, evaporative mass flow rate, and water film thickness, are evaluated under the different tilted angles of the rectangular channel and horizontal plane, water/air inlet flow rates, water/air inlet temperatures, heating surface temperatures, and air inlet relative humidities. All these results can provide a good guidance for the design of PCCS in the future.

Improvement of the bending behavior of a flexible riser : Part I – nonlinear bending behavior considering the shear deformation of polymer layers

An un-bonded, multi-layered assembly of heterogeneous materials in the cross-section of flexible risers enables riser systems to withstand a large radius of curvature while preventing structural damage or buckling of many critical areas such as a touch down zone. The contact surfaces between layers exhibit a continuous sliding of metallic components after a certain level of bending, which lowers the bending stiffness of flexible risers. Such interactions are beneficial in order to reduce the stress of tensile wires, but complicate prediction of the limit state and fatigue damage of riser systems in that the sliding of metal layers involves a complex contact phenomenon that is difficult to solve numerically. This series of papers deals with the development of an improved analysis method for flexible risers using theoretical approaches. Part I, as presented in these pages, develops an analytical model that is capable of estimating the cross-sectional stiffness of flexible risers with consideration of external loads and inter-layer interaction. In Part II, the proposed analytical model is applied to a large-scale riser model to achieve an efficient global dynamic analysis of flexible risers.This paper, the first part of a two-paper series, proposes an analytical model that formulates the stress of tensile armor layers through equilibrium equations that take into account the shear and radial deformation of polymer layers. The equilibrium equations are derived under a linear differential equation for each component of flexible risers, so that not only the shear interaction forces but also the contact pressure originating from the bending of layers is considered in the analytical model. The shear interaction forces between two tensile armor layers are formulated through an equivalent shear stiffness by which the shear stiffness of layers is linearly modeled as a series of springs. The proposed model is verified by comparison with the nonlinear bending stiffness from existing bending models and finite element (FE) analysis. For additional verification, the axial stresses of inner and outer tensile armor also are compared. And for further, more in-depth understanding, a case study of various combined load cases is carried out.

An Automatic and Forward Method to Establish 3-D Parametric Scattering Center Models of Complex Targets for Target Recognition

In this article, an automatic and forward method is realized to establish attributed scattering center models directly from the computer-aided design (CAD) model of the complex target. The main steps include the preprocessing of the CAD model, the separation of scattering sources, the selection of strong scattering sources, and the automatic determination of model parameters. With the proposed method, the scattering sources, scattering mechanisms, and model parameters of the scattering centers can be identified and derived, such that the complicated manual intervention is completely avoided. Moreover, the method establishes the distributed scattering center models formed by curved surfaces with large curvature radii. Therefore, the formation mechanism of the distributed scattering center is extended from typical scattering structures to a general case. Thus, the model of the attributed scattering center is extended and can be applied to describe the scattering from the real structures of the complex target. The geometric shape of the scattering source is distinguished based on the principal curvature radii, which are calculated by differential geometry theory. Thus, the frequency dependence parameter is obtained according to its corresponding relationship with the geometric shape. In addition, based on the automatic method, a technology is studied to diagnose and correct the scattering center models of a target whose CAD model is unknown or partially known. Finally, parametric models of several targets in the Moving and Stationary Target Acquisition Recognition (MSTAR) program are established, and then compared with the measured data. The results validate the effectiveness of the proposed method.

Ends and middle: Global force balance and septum location in fission yeast.

The fission yeast cell is shaped as a very regular cylinder ending by hemi-spheres at both cell ends. Its conserved phenotypes are often used as read-outs for classifying interacting genes and protein networks. Using Pascal and Young-Laplace laws, we proposed a framework where scaling arguments predicted shapes. Here we probed quantitatively one of these relations which predicts that the division site would be located closer to the cell end with the larger radius of curvature. By combining genetics and quantitative imaging, we tested experimentally whether altered shapes of cell end correlate with a displaced division site, leading to asymmetric cell division. Our results show that the division site position depends on the radii of curvatures of both ends. This new geometrical mechanism for the proper division plane positioning could be essential to achieve even partitioning of cellular material at each cell division.

Morphology of the Semicircular Canals and Locomotion of Zionodon satanus

Zionodon satanus is a relatively large “insectivore” from the Uinta Formation of Utah, known from associated fragmentary dental, cranial, and postcranial elements. Features of the postcrania, particularly the knee and ankle joints, suggest that this species primarily engaged in swift terrestrial locomotion, but with some climbing and digging capability. Among the cranial fragments of Z. satanus are two petrosal bones preserving portions of the bony labyrinth, particularly the semicircular canals, which are known to vary among extant mammals according to locomotor agility, with more agile animals having semicircular canals with a larger radius of curvature than slower ones. Thus, semicircular canal dimensions can provide insight into locomotion independent of postcranial morphology. Here we compare measurements of the semicircular canals of Z. satanus to other extant and extinct mammals to assess the degree of locomotor agility of this species and compare those results to those obtained by functional analysis of the postcrania.The petrosal bones of the type specimen of Z. satanus were microCT scanned and virtual models of the semicircular canals were extracted with AMIRA 6.5.0 software. One petrosal includes a complete posterior and partial lateral semicircular canal, whereas the other preserves a complete lateral, damaged but complete posterior, and most of the anterior semicircular canal. The height and width of each semicircular canal was measured from the extracted surface models and the radius of curvature was calculated from height and width measurements. The average radius of curvature of the semicircular canals of Z. satanus overlaps with extant mammals of similar body size of “fast” or “medium” agility and lies well outside the range of slow‐moving small mammals. Compared to other fossil “insectivores”, Z. satanus has relatively smaller semicircular canals than Leptictidium from the middle Eocene of Messel, Germany, which has been reconstructed as a bipedal runner and saltator, but larger ones than the North American leptictids Paleictops and Leptictis. These results corroborate observations from the postcranial skeleton, suggesting that Z. satanus likely engaged in frequent, rapid locomotion.

Numerical Study on the Triaxial Stress Condition for Ring-like Fractures around Deep Underground Openings

Abstract The fracture pattern of rock mass surrounding a deep tunnel is closely related to the in situ stress, which is generally quite anisotropic. This study focuses on the triaxial stress condition for the formation of ring-like fractures around tunnels through three dimensional numerical modeling. The fracture patterns around both the tunnel and ahead of the tunnel face under different anisotropic triaxial stresses were analyzed, and the influence of tunnel shape on the formation of ring-like fractures was also discussed. A conceptual criterion for the formation of ring-like fractures was proposed based on the simulations. It was found that the ring-like fractures can be expected when the axial pressure coefficient is less than 0.3, regardless of the tunnel shape. Ring-like fractures are more likely to be located near tunnel-free surfaces with a larger radius of curvature. The aim of this article is to shed some light on the interpretation of failure phenomenon in deep underground excavations.