Triangular Aperture Research Articles

Unveiling the reinforcement benefits of innovative textured geogrids

The smooth surface texture of the commercially available geogrids limits the shear strength mobilization at the interfaces. This study presents the design, manufacturing, and interface performance evaluation of innovative textured geogrids. Geogrids with square, triangular, and hexagonal apertures with and without inherent surface texture were manufactured through additive manufacturing (3D printing) technique, using PLA (Poly Lactic Acid) filament. The texture includes elevated pins of 3 mm height at the junctions and inherent diamond pattern of 1 mm height on the ribs. The individual and combined effects of surface texture and aperture shape on the stress–displacement relationship, dilation angle, and the thickness of shear zone are quantified using large-scale direct shear tests and Particle Image Velocimetry (PIV) analysis. Results showed that the textured geogrid with hexagonal aperture has exhibited the maximum interface coefficient of 0.96 with sand followed by the geogrids with triangular and square apertures. Irrespective of the aperture shape, provision of the surface texture resulted in an overall increase of interface shear strength by more than 13%. Further, PIV analysis revealed that the shear zone is 25% thicker for textured geogrids of different aperture shapes, suggesting higher interlocking and passive resistance offered by their textured surfaces.

Large-scale direct shear testing for assessing interfacial parameters of natural and recycled sand with geosynthetic reinforcements

The demand for infrastructure projects is being driven by urbanization, which led to scarcity of natural sand (NS), which prompts exploration of alternative sustainable construction materials due to environmental concerns. Recycled sand (RS), processed from construction and demolition waste (C&DW), is an alternative material in infrastructure applications. Investigating interfacial shear behaviour between geosynthetic reinforcements with RS as a sustainable alternative material is crucial for infrastructure projects. This study presents the comprehensive large-scale direct shear testing (LSDST) on RS, NS, and its interfaces with ten types of geosynthetic reinforcements (i.e., polypropylene geogrids (GRD1 – GRD3), polyester geogrids (GRD4 – GRD6), and geotextiles (GT1 – GT4). LSDST were carried out using self-fabricated direct shear testing equipment of size equal to 500 mm x 500 mm x 300 mm (L x B x H). The findings indicate that the RS and NS exhibit similar shear strength parameters, sand-GRD interface demonstrates greater resistance compared to the sand-GT interface. RS and NS-GRD4 - GRD6 interfaces with transverse ribs and rough texture and NS-GRD1 interface with triangular apertures, exhibit significant shear strength parameters than the unstabilized case due to the mobilization of passive thrust. Interfacial shear coefficients for NS and RS range from 0.94 – 1.27 and 0.80 – 1.15 for GRD interfaces, and 0.89 – 1.06 and 0.86 – 0.99 for GT interfaces, respectively. Therefore, the RS can be a sustainable alternative for NS.

Vortex position detection using a scanning triangular aperture in a digital micromirror device

Optical vortices, as solutions to the wave equation, remain stable under ideal theoretical conditions. However, in experiments where beams produced with holograms and spatial light modulators introduce perturbations, their phase structures can be disrupted, leading to instability. Specifically, higher-order optical vortices (with topological charge |ℓ|>1 ) are inherently unstable in that they tend to separate in a series of optical vortices with unit topological charge (|ℓ|=1) even with small perturbations. In this work, we demonstrate a technique to detect the positions of optical vortices using a scanning triangular aperture in a digital micromirror device and a digital pinhole. We observe the diffraction patterns of a vortex through the triangular aperture, and we show that we can determine the center of an optical vortex (OV) by measuring the intensity at the center of a pattern using a digital pinhole. We investigate the changes in the measured signal for different triangular apertures and pinhole sizes. We observe that while smaller pinholes lead to a decrease in light intensity, the detected position of a single OV with unit topological charge is similar for all pinhole sizes. We also find that the triangular aperture size becomes important when locating vortex pairs. Using a triangular aperture with a radius R = 0.52 mm, we can resolve OV pairs at least 86.4μ m apart in our experiments. Our methods help pave the way to understanding the fundamental behavior of multiple vortex interactions in optical beams and also can be used when determining the position of an OV in metrology.

Taxonomy of hybridly polarized Stokes vortex beams.

Structured beams carrying topological defects, namely phase and Stokes singularities, have gained extensive interest in numerous areas of optics. The non-separable spin and orbital angular momentum states of hybridly polarized Stokes singular beams provide additional freedom for manipulating optical fields. However, the characterization of hybridly polarized Stokes vortex beams remains challenging owing to the degeneracy associated with the complex polarization structures of these beams. In addition, experimental noise factors such as relative phase, amplitude, and polarization difference together with beam fluctuations add to the perplexity in the identification process. Here, we present a generalized diffraction-based Stokes polarimetry approach assisted with deep learning for efficient identification of Stokes singular beams. A total of 15 classes of beams are considered based on the type of Stokes singularity and their associated mode indices. The resultant total and polarization component intensities of Stokes singular beams after diffraction through a triangular aperture are exploited by the deep neural network to recognize these beams. Our approach presents a classification accuracy of 98.67% for 15 types of Stokes singular beams that comprise several degenerate cases. The present study illustrates the potential of diffraction of the Stokes singular beam with polarization transformation, modeling of experimental noise factors, and a deep learning framework for characterizing hybridly polarized beams.

Classification of geogrid reinforcement in aggregate using machine learning techniques

The present study proposes a novel ML methodology for differentiating between unstabilized aggregate specimens and those stabilized with triangular and rectangular aperture geogrids. This study utilizes the compiled experimental results obtained from stabilized and unstabilized specimens under repeated loading into a balanced, moderate-sized database. The efficacy of five ML models, including tree-ensemble and single-learning algorithms, in accurately identifying each specimen class was explored. Shapley’s additive explanation was used to understand the intricacies of the models and determine global feature importance ranking of the input variables. All the models could identify the unstabilized specimen with an accuracy of at least 0.9. The tree-ensemble models outperformed the single-learning models when all three classes (unstabilized specimens and specimens stabilized by triangular and rectangular aperture geogrids) were considered, with the light gradient boosting machine showing the best performance—an accuracy of 0.94 and an area under the curve score of 0.98. According to Shapley’s additive explanation, the resilient modulus and confining pressure were identified as the most important features across all models. Therefore, the proposed ML methodology may be effectively used to determine the type and presence of geogrid reinforcement in aggregates, based on a few aggregate material properties and performance under repeated loading.

Higher-order fractal transverse modes observed in microlasers

Two classes of higher-order, fractal spatial eigenmodes have been predicted computationally and observed experimentally in microlasers. The equatorial plane of a close-packed array of microspheres, lying on one mirror within a Fabry-Pérot resonator and immersed in the laser gain medium, acts as a refractive slit array in a plane transverse to the optical axis. Edge diffraction from the slit array generates the high spatial frequencies (>104 cm−1) required for the formation of high-order laser fractal modes, and fractal transverse modes are generated, amplified, and evolve within the active medium. With a quasi-rectangular (4-microsphere) aperture, the fundamental mode and several higher-order eigenmodes (m = 2,4,5) are observed in experiments, whereas only the m = 1,2 modes are observed experimentally for the higher-loss resonators defined by triangular (3-microsphere) apertures. The fundamental and 2nd-order modes (m = 1,2) for the 4-sphere aperture are calculated to have qualitatively similar intensity profiles and nearly degenerate resonant frequencies that differ by less than <0.1% of the free-spectral range (375 GHz) but exhibit even and odd parity, respectively. For all of the observed fractal modes, the fractal dimension (D) rises rapidly beyond the intracavity aperture array as a result of the high spatial frequencies introduced into the mode profile. Elsewhere, D varies gradually along the resonator axis and 2.2 < D < 2.5. Generating fractal laser modes in an equivalent optical waveguide is expected to allow the realization of new optical devices and imaging protocols based on the spatial frequencies and variable D values available.

Life cycle costs and mid-term performance of a geogrid-stabilized pavement section, an economical and sustainable approach, case study, RN-39 Honduras

When we talk about mechanical stabilization of granular layers with geogrids in roadway applications, we often mention that these pavements have a better performance along the time and a reduced cost along the whole life cycle. In the last years we have been measuring the International Roughness Index (IRI) of a segment of multi-axial with triangular aperture geogrid-stabilized road of 45.6 km of length and comparing it with a non-stabilized segment of 30.7 km of length, which was constructed in the same period and was commissioned the same year, for the same traffic. In terms of deterioration based on the International Roughness Index (IRI) for each segment, the mechanically stabilized road has shown a better performance than the non-stabilized segment, this publication seeks to show the tendency of the IRI curve for both sections, and the differences in their behavior. In addition, an analysis with the software; Highway Development and Management, version 2.0 (HDM-4) will be conducted to estimate the impact in the road user’s costs which are part of the life cycle cost and compare both sections, as well as an attempt to emulate and calibrate the IRI curve for the stabilized road section. This publication will help pavement engineers, designers, asset managers, highway engineers, departments of transportation and any people involved on roads, to better understand the economic advantages and performance benefits of mechanically stabilized granular layers with multi-axial geogrids on pavements and how they can help building resilient, durable, and sustainable road infrastructures.

Local Stiffness Assessment of Geogrid-Stabilized Unbound Aggregates in a Large-Scale Testbed

This paper integrates and extends an earlier article presented at the 20th International Conference on Soil Mechanics and Geotechnical Engineering. The generation of a stiffened zone in the proximity of a geogrid is one of the primary mechanisms of mechanical stabilization of pavement unbound aggregate layers using geogrids. This paper focuses on the quantification of the stiffened zone through a local stiffness assessment using bender element (BE) sensors. Unbound aggregate base layers were constructed in a large-scale laboratory testbed. Geogrid-stabilized layers had geogrids with different-sized triangular apertures contributing to the geogrid-stiffened zone. Shear wave velocities were measured at three different heights using BE sensors, and the vertical stiffness profiles of the mechanically stabilized aggregate layers were evaluated. In addition, the conversion method between small-strain stiffness and large-strain stiffness was established from the repeated load triaxial tests with BE pairs to transform the vertical stiffness profile into that of the resilient modulus. Furthermore, dynamic cone penetration (DCP) and light-weight deflectometer (LWD) tests were performed at multiple locations into the stabilized and unstabilized unbound aggregates. From the large-scale experimental study, the local stiffness improvement owing to the geogrid enhancement was up to 16.2% in the vicinity of the geogrid location, and the extent of the local stiffened zone evaluated through various test methods was between 15.2 cm (6 in.) and 25.4 cm (10 in.) above the geogrid.

Pore size effect of zirconium-based metal-organic frameworks for encapsulation and release of volatile monoterpenes

In this work the sorption properties of three isoreticular Zr-based MOFs, viz., UiO-66, UiO-67, and UiO-68 as adsorbents of active organics were examined and especially the pore size effects are discussed using d-limonene, myrcene, α-terpinene, and α-pinene as probe molecules. Results indicated that the terpene uptake and release are highly dependent on both the MOF pore size and the geometric feature of guest molecules themselves. The shape selective property of UiO-66 holds for the tested terpenes, where the adsorption capacity of d-limonene, myrcene, and α-terpinene in equilibrium with the liquid phase (0.43–0.46 g g−1) was approximately 5-times larger than that of α-pinene with 0.56 nm kinetic diameter (0.09 g g−1). The narrow triangular apertures of UiO-66 act as the permeation-limiting barrier for guest molecules with the dimension close to the pore size. Except for α-pinene, the loading fraction for other terpenes decreased with an increase in the MOF pore diameter. For example, the uptake of UiO-66, UiO-67, and UiO-68 for myrcene reached up to 90 %, 81 %, and 76 % of their theoretical maximum loading, respectively. Differential scanning calorimetry revealed that the melting point of both d-limonene and α-terpinene confined in the 0.71 nm pores of UiO-67 shifts to a higher temperature relative to that in the bulk phase. In contrast, no obvious phase transition was observed for the terpene composites with either UiO-66 or UiO-68 (0.94 nm pore size) under identical conditions. Consistent with the thermal analysis results, the monoterpenes entrapped in the UiO-67 showed a much lower release rate than their counterparts in the other two frameworks.

Characteristics of a Gaussian focus embedded within spiral patterns in common-path interferometry with phase apertures

A phase-only method is proposed to transform an optical vortex field into desired spiral diffraction–interference patterns. Double-ring phase apertures are designed to produce a concentric high-order vortex beam and a zeroth-order vortex beam, and the diffracted intensity ratio of two beams is adjustable between 0 and 1. The coherent superposition of the two diffracted beams generates a brighter Airy spot (or Poisson spot) in the middle of the spiral pattern, where the singularity for typical vortex beam is located. Experiments employing circular, triangular, and rectangular phase apertures with topological charges from 3 to 16 demonstrate a stable, compact, and flexible apparatus for vortex beam conversion. By adjusting the parameters of the phase aperture, the proposed method can realize the optical Gaussian tweezer function and the optical vortex tweezer function simultaneously along the same axis or switch the experimental setup between the two functions. It also has potential applications in light communication through turbulent air by transmitting an orbital angular momentum-coded signal with a concentric beacon laser.

The computation of the average speckle size from the point spread function for triangular apertures

We suggest triangular aperture modeling for the computation of speckle size using the point spread function (PSF) concept. The fast Fourier transform (FFT) algorithm indicates three models of triangular apertures in the point spread function (PSF) computation. We calculated for the first time the average speckle size from the full width at half maximum (FWHM) for the triangular apertures in the PSF. The results are compared with the speckle sizes results obtained from the autocorrelation of speckle images corresponding to the considered models showed an agreement. In the analysis, I consider the 1st model with four equilateral triangular apertures, each of equal sides (b), along the Cartesian coordinates at equal distances from the center (xd). In the 2nd model, I assume 16 triangular apertures in a circular contour. In contrast, in the 3rd model, a sequence of six equilateral triangular black and white (B/W) zones is shown where the central triangle is black. I consider central obstruction to attenuate the low spatial frequency in the PSF. I take a transparent triangular aperture for comparison. Also, the PSF corresponding to the circular aperture is given for comparison. In addition, reconstructed images of apertures from the speckle images are obtained. We considered MATLAB codes for all the computations and plots.

Sand-geogrid interfacial shear response revisited through additive manufacturing

Though it is known that the geometric features of geogrids are crucial for deriving optimal interface shear strength, not much work is done to optimize the size and shape of the apertures relative to the particle size of the soils in contact. Most of the commercial geogrids have rectangular or square apertures, which are many times bigger than the soil particles. The present study explores the effects of aperture size and shape of geogrids relative to the size of the sand particles on their interface shear response through direct shear tests and digital image analysis. Geogrids of different aperture sizes and shapes were manufactured using a 3D printer. Shear tests were carried out on three sands of different grain sizes interfacing with geogrids of five different aperture sizes and three different aperture shapes. Through these tests, interface shear response with a wide range of aperture ratio and different shapes of geogrids is understood. Shear zone thickness of different sand-geogrid interfaces was computed through Particle image velocimetry (PIV). Based on the tests and analyses, triangular apertures are found to be more efficient compared to other apertures. The optimal range of aperture ratio is found to be 2–11.29.

Mode characteristics of VCSELs with different shape and size oxidation apertures

Vertical cavity surface emitting laser (VCSELs) as the ideal light source for rubidium (Rb) and cesium (Cs) atomic clocks is analyzed for its mode and polarization control. We fabricated three kinds of shapes: triangular, elliptic, and circular oxidation apertures which also have different sizes. We formed three different shape oxide apertures by wet-oxidation with 36 μm–39 μm circular mesa. Our results show that triangular oxidized-VCSEL has the advantages of mode and polarization selection over elliptic and circular oxide apertures. When triangular oxide-confined VCSELs emit in single mode, the measured side mode suppression ratio (SMSR) is larger than 20 dB and orthogonal polarization suppression ratio achieves 10 dB. Resonant blueshift of VCSELs with triangular and elliptic apertures is observed with the decrease of aperture size.

Role of particle breakage on damping, resiliency and service life of geogrid-reinforced ballasted tracks

A series of cyclic loading tests were performed to establish the effect of particle breakage on the damping, resiliency and serviceability of railroad ballast. Five geogrids of triangular, square and rectangular apertures with different sizes were used to stabilize the ballast having the mean diameter (D50) of 42 mm. It was established that the particle breakage that occurs during cyclic loading helps in energy dissipation and also enhances the track resiliency. Further, the quantum of particle breakage is governed by the extent of lateral and vertical strains in ballast. Accordingly, empirical relationship has been established between breakage reduction index, BRI with the lateral and vertical spread reduction indices, LSRI and VSRI. The damping ratio (Dr) and resilient modulus (Mr) is shown to increase with the increase in particle breakage (Bg). Furthermore, the volumetric (εvol) and shear strains (εs) in ballast at the end of testing was found to be influenced by the particle breakage (Bg). Further, the track life enhancement factor (Lef), defined as the ratio of number of load cycles (N) required to attain a given extent of strains in ballast in case of geogrid-reinforced ballast (Grb) to that of unreinforced ballast (Urb), is found to vary from 500 to 1 for 0.3 and 0.5 % lateral strain and 12.50 to 1 for 2 and 3 % vertical strain. The Lef was found to be highest in case of geogrid G1. In addition, a unique relationship is established between Bg and Lef wherein it was found that as the particle breakage increases, the service life of track reduces.

Pupil dilation and constriction in the skate Leucoraja erinacea in a simulated natural light field.

The skate Leucoraja erinacea has an elaborately shaped pupil, whose characteristics and functions have received little attention. The goal of our study was to investigate the pupil response in relation to natural ambient light intensities. First, we took a recently developed sensory-ecological approach, which gave us a tool for creating a controlled light environment for behavioural work: during a field survey, we collected a series of calibrated natural habitat images from the perspective of the skates' eyes. From these images, we derived a vertical illumination profile using custom-written software for quantification of the environmental light field (ELF). After collecting and analysing these natural light field data, we created an illumination set-up in the laboratory, which closely simulated the natural vertical light gradient that skates experience in the wild and tested the light responsiveness - in particular the extent of dilation - of the skate pupil to controlled changes in this simulated light field. Additionally, we measured pupillary dilation and constriction speeds. Our results confirm that the skate pupil changes from nearly circular under low light to a series of small triangular apertures under bright light. A linear regression analysis showed a trend towards smaller skates having a smaller dynamic range of pupil area (dilation versus constriction ratio around 4-fold), and larger skates showing larger ranges (around 10- to 20-fold). Dilation took longer than constriction (between 30 and 45 min for dilation; less than 20 min for constriction), and there was considerable individual variation in dilation/constriction time. We discuss our findings in terms of the visual ecology of L. erinacea and consider the importance of accurately simulating natural light fields in the laboratory.

Evaluation of Hexagonal Multi-Shape, Multi-Axial Geogrids in Unsurfaced Road Applications

A full-scale unsurfaced test section was constructed to evaluate the performance of two recently developed innovative geogrids, referred to as NX-1 and NX-2, having a unique combination of hexagonal, trapezoidal, and triangular aperture shapes, rib aspect ratios greater than 1.0, and a coextruded, composite polymer sheet designed to improve aggregate and geogrid interaction. The test section consisted of a 25-cm-thick crushed aggregate surface layer placed over a weak clay subgrade. Simulated truck traffic was applied using a load cart outfitted with a single-axle dual-wheel truck gear. Rutting performance and instrumentation response data gathered from earth pressure cells and single-depth deflectometers were monitored at multiple traffic intervals. It was found that the geogrids improved rutting performance when compared with an unstabilized test item, and NX-1 was found to be the best performer of the two geogrids. Calculated traffic benefit ratios ranged from approximately 1.2 at low levels of rutting up to approximately 13.0 at higher levels of rutting. Instrumentation response data indicated that the geogrids reduced measured pressure and deflection near the surface of the subgrade layer. Pressure response data in the aggregate layer suggested that the geogrids redistributed applied pressure higher in the aggregate layer, effectively changing the measured stress profile with depth.

3D-Printed Quasi-Cylindrical Bragg Reflector to Boost the Gain and Directivity of cm- and mm-Wave Antennas.

We demonstrate a concept for a large enhancement of the directivity and gain of readily available cm- and mm-wave antennas, i.e., without altering any property of the antenna design. Our concept exploits the high reflectivity of a Bragg reflector composed of three bilayers made of transparent materials. The cavity has a triangular aperture in order to resemble the idea of a horn-like, highly directive antenna. Importantly, we report gain enhancements of more than 400% in relation to the gain of the antenna without the Bragg structure, accompanied by a highly directive radiation pattern. The proposed structure is cost-effective and easy to fabricate with 3D-printing. Our results are presented for frequencies within the conventional WiFi frequencies, based on IEEE 802.11 standards, thus, enabling easily implementation by non-experts and needing only to be placed around the antenna to improve the directivity and gain of the signal.

Galerkin finite element study for mixed convection (TiO2\u2013SiO2/water) hybrid-nanofluidic flow in a triangular aperture heated beneath

Fluidity and thermal transport across the triangular aperture with lower lateral inlet and apply placed at the vertical outlet of the chamber which filled with efficient TiO2–SiO2/water hybrid nanofluid under the parametrical influence. Several parameters are tested like the numbers of Hartmann (0 le Ha le 100), Richardson (0 le Ri le 5), and Reynolds (10 le Re le 1000) were critiqued through streamlines, isotherms, and Nusselt number (Nu). Numerical model has to be developed and solved through the Galerkin finite element method (GFEM) by discretized with 13,569 triangular elements optimized through grid-independent analysis. The Hartmann number (Ha), exerts minimal impact over the flow and thermal aspects while the other parameters significantly manipulate the physical nature of the flowing and thermal aspects behaviors.

Calibration of pavement ME rutting model for geogrid stabilized roadways

Many transportation agencies started implementing Mechanistic-Empirical (ME) approach for designing and analyzing new and rehabilitated pavements. Although the widely popular empirical design approach based on 1993 AASHTO Design Guide is still in practice, the need for performance-based design and accurate prediction of pavement distresses throughout the service life led to the adoption of the ME approach. The two major steps associated with the ME approach are the computation of pavement stress–strain responses using mechanistic analysis and estimation of pavement distresses using empirical analysis. Layered Elastic Analysis (LEA) or Finite Element Analysis (FEA) is normally utilized for mechanistic analysis whereas regression analysis is typically used for empirical analysis. Although the empirical models (i.e., transfer functions) were calibrated using the Long Term Pavement Performance (LTPP) dataset, these models do not consider the benefits of geogrid stabilization. Research and field studies had shown improvement in pavement performance when the pavement is stabilized with geogrids. This paper aims at incorporating the effect of geogrid in one of the distress models – more specifically, the rutting model – of AASHTOWare Pavement ME. Model calibration factors were developed based on the recent full-scale accelerated pavement test conducted at the research facility of the US Army Corps of Engineers. Two types of punched and drawn triangular aperture geogrids were utilized in the full-scale test. Pavement surface deformations measured during the trafficking period were used for calibrating the rutting model. The calibrated rutting model was validated with the LTPP and Louisiana Transportation Research Center (LTRC) dataset.

DEM-FDM Coupled Numerical Study on the Reinforcement of Biaxial and Triaxial Geogrid Using Pullout Test

The key to modeling the interlocking of geogrid-reinforced ballast is considering both the continuous deformation characteristics of the geogrid and the discontinuity of the ballast particles. For this purpose, pullout tests using biaxial and triaxial geogrids were simulated using the coupled discrete element method (DEM) and finite difference method (FDM). In this coupled model, two real-shaped geogrid models with square and triangular apertures were established using the solid element in FLAC3D. Meanwhile, simplified shaped clumps were used to represent the ballast using PFC3D. The calibration test simulation showed that the accurately formed geogrid model can reproduce the deformation and strength characteristics of a geogrid. The pullout simulation results show that the DEM-FDM method can well predict the relationship between pullout force and displacement, which is more accurate than the DEM method. For ballast particles of 40 mm in size, both the experiment and simulation results showed that the triaxial geogrid of 75 mm is better than the 65-mm biaxial geogrid. In addition, the DEM-FDM method can study the interaction mechanism between the particles and the geogrid from a microscopic view, and also reveal the similar deformation behavior of the geogrid in the pullout process. Therefore, the DEM-FDM coupled method can not only investigate the interlocking mechanism between the ballast and particles but can also provide a great method for evaluating the performance of different types of geogrids.