Deformation Amplitude Research Articles

Factors affecting corneal deformation amplitude measured by Corvis ST in eyes with open-angle glaucoma.

To evaluate the factors affecting corneal deformation amplitude (DA) measured using Corvis ST in eyes with open-angle glaucoma. This prospective, longitudinal study included 48 eyes with open-angle glaucoma who required additional intraocular pressure (IOP)-lowering drops. All eyes underwent a complete eye examination at baseline, including a Corvis ST, which was repeated 4-8 weeks after the change in therapy. Factors affecting the corneal biomechanics, namely the DA, were determined using mixed effect models. The mean age of the cohort was 65.0 ± 7.9 years. The mean IOP reduced from 23.4 ± 5.4 mmHg to 17.9 ± 5 mmHg after the change in glaucoma treatment ( P < 0.001). The DA increased from 0.89 ± 0.16 mm to 1.00 ± 0.13 mm after IOP reduction ( P < 0.001). On mixed effect model analysis, IOP (-0.02 ± 0.001, P < 0.001) and corneal pachymetry (-0.0003 ± 0.0001, P = 0.02) affected the change in the DA. IOP and corneal pachymetry affect the DA and must be accounted for when using Corvis ST to evaluate corneal biomechanics in glaucoma.

ПИРИТНЫЕ ОГАРКИ КАК НАПОЛНИТЕЛЬ КОМПОЗИЦИОННОГО МАТЕРИАЛА НА ОСНОВЕ БУТАДИЕН-СТИРОЛЬНОГО КАУЧУКА

Currently, recycling waste from various types of production, as well as finding the possibility of reusing it, is a very relevant topic. In the modern world, rubbers make a tremendous contribution to the development of the industrial sector. In order to study the possibility of using pyrite cinders as a filler for a rubber mixture based on styrene-butadiene rubber, the elastic-strength and rheological characteristics of the finished composite mixtures were studied, and the contact angle of wetting was determined to assess the interaction of the compositions with other materials. It was established that there was no influence of pyrite cinders on the nature of the surface of the rubber mixture. The dependence of the storage modulus on the deformation amplitude for different types of fillers has been established, which makes it possible to evaluate the qualitative and quantitative distribution of the filler in the polymer and the interaction of the polymer and the filler. It was revealed that pyrite cinders and chalk have a weak interaction with the polymer, from which it follows that they behave as a non-reinforcing filler, but their introduction into the polymer matrix does not deteriorate the elastic-strength properties of the rubber. The dependence of stress on deformation for mixtures with different types of fillers has been established. It was established that in terms of technological characteristics, no deviations in the material from the generally accepted patterns of introducing fillers into the polymer matrix were found. The values remain at the level of unfilled rubber and rubber filled with technical chalk. The general complex of properties of the composition based on styrene-butadiene rubber with pyrite cinders allows it to be recommended, after modification, for use in the production technology of rubber products.

Effect of intrastromal corneal ring segments on in vivo corneal biomechanics in keratoconus: 1-year results.

To evaluate the 1-year effects of the implantation of intrastromal corneal ring segments (ICRS) in keratoconus (KC) on the dynamic corneal response (DCR) parameters obtained with the Corvis. Fernández-Vega Ophthalmological Institute, Oviedo, Spain. Prospective, single-center, clinical study. Included were patients who underwent ICRS implantation for KC over a period of 1 year. On the day of the surgery and at least 6 months after ICRS implantation, the following measurements were made: corrected distance and uncorrected distance visual acuity, corneal tomography indices with the Pentacam, biomechanically corrected intraocular pressure and the Corvis DCRs (integrated inverse concave radius, deformation amplitude ratio, stiffness parameter at first applanation, stress-strain index [SSI] and the highest concavity radius). 30 eyes were included with a mean follow-up time of 15 months. Statistical analysis showed that ICRS implantation induced significant improvements in corneal biomechanics measurements between preoperative and long-term follow-up as demonstrated by a significant increase in SSI (P = .003). To confirm that this difference was actually induced due to a stiffening between early postoperative (previously published) and long-term an additional t-test was done between month 1 and late follow-up which confirmed a significant stiffening in the value of SSI (P = .01). Patients implanted with ICRS alone for KC showed a significantly stiffer response due to increased structural support compared with preoperative values and 1 month postoperative.

Characterisation of the transverse shear behaviour of binder-stabilised preforms for wind turbine blade manufacturing

Binder-stabilised preforms are being used increasingly in the production of large composite structures, such as wind turbine blades, to increase the throughput. The transverse shear behaviour of the preform is one of the driving factors in the development of wrinkling during manufacturing but has not previously been characterised in the literature. In this paper, the combined intra- and inter-ply deformations during transverse shearing of a binder-stabilised preforms for wind turbine blade manufacturing are characterised by a new test methodology. The results from two experimental campaigns are presented. In the first campaign, preform specimens are subjected to monotonic loading to a nominal transverse shear angle of 18.0° with three different deformation rates. The results show an increase in maximum load levels with greater deformation rates. In the second campaign, preform specimens are subjected to deformation-controlled cyclic loading with two different deformation amplitudes corresponding to a nominal transverse shear angle of 1.5° and 12.2°, respectively. During cyclic loading, permanent deformation is observed in all preform specimens and the maximum load at the 19th cycle is reduced to 48% of the maximum load at the first cycle for the tests with deformation amplitudes of 12.2°. The data generated in this study is freely available at https://doi.org/10.17632/9m78sg3zwn.1.

Corneal biomechanics in normal and subclinical keratoconus eyes

BackgroundThe diagnosis of keratoconus, as the most prevalent corneal ectatic disorder, at the subclinical stage gained great attention due to the increased acceptance of refractive surgeries. This study aimed to assess the pattern of the corneal biomechanical properties derived from Corneal Visualization Scheimpflug Technology (Corvis ST) and evaluate the diagnostic value of these parameters in distinguishing subclinical keratoconus (SKC) from normal eyes.MethodsThis prospective study was conducted on 73 SKC and 69 normal eyes. Subclinical keratoconus eyes were defined as corneas with no clinical evidence of keratoconus and suspicious topographic and tomographic features. Following a complete ophthalmic examination, topographic and tomographic corneal assessment via Pentacam HR, and corneal biomechanical evaluation utilizing Corvis ST were done.ResultsSubclinical keratoconus eyes presented significantly higher Deformation Amplitude (DA) ratio, Tomographic Biomechanical Index (TBI), and Corvis Biomechanical Index (CBI) rates than the control group. Conversely, Ambrósio Relational Thickness to the Horizontal profile (ARTh), and Stiffness Parameter at the first Applanation (SPA1) showed significantly lower rates in SKC eyes. In diagnosing SKC from normal eyes, TBI (AUC: 0.858, Cut-off value: > 0.33, Youden index: 0.55), ARTh (AUC: 0.813, Cut-off value: ≤ 488.1, Youden index: 0.58), and CBI (AUC: 0.804, Cut-off value: > 0.47, Youden index: 0.49) appeared as good indicators.ConclusionsTBI, CBI, and ARTh parameters could be valuable in distinguishing SKC eyes from normal ones.

Improvement of the thermodynamic properties of lithium borohydride LiBH4 by mechanical treatment for hydrogen storage applications: A DFT investigation

In the present work, single, double and triaxial (tensile/compression) strains were applied to lithium borohydride LiBH4 using Density Functional Theory (DFT) based on Perdew-Burke-Ernzerhor for solids (PBEsol) approach. The results show that the structural properties change with the deformation amplitude. The total density of state (TDOS) and partial density of state (PDOS) studies show that the LiBH4 complex hydride is an insulator with an energy band gap of 6.73 eV and the width of the valence and conduction bands vary with the change of the strain amplitude. The deformation energy shows that triaxial deformation on LiBH4 complex hydride requires more energy than single and double strains. Hence, these deformations are found responsible for the decrease of the thermodynamic properties of LiBH4 hydride. Specifically, under a maximum uni/bi/triaxial compressive strain of ε = −9%, the enthalpy of formation and decomposition temperature decrease by 3.25 %, 7.59 %, and 36.54 %, respectively. While, under a maximum uni/bi/triaxial tensile strain of ε = +9 %, the enthalpy of formation and decomposition temperature decrease by 3.85 %, 11.83 %, and 26.44 %, respectively, compared to unstrained hydride. Consequently, the findings are in excellent agreement with the standards of the U.S. Department of Energy (DOE) (ΔHf = −40 Kj/mol.H2 and Td = 289–393 K) for hydrogen storage in the solid state.

The corneal biomechanical differences after wearing orthokeratology lenses and multifocal soft lenses in children: A self-control study

BackgroundTo compare the changes in corneal biomechanics after orthokeratology (OK) lens and Defocus Incorporated Soft Contact (DISC) lens treatment. MethodsOf 28 myopic children were recruited, with one eye wearing OK lens and the other eye wearing DISC lens for one year, and the data after discontinued for 4 weeks were also collected. Major outcomes were corneal biomechanics and axial length (AL) elongation. ResultsThroughout the follow-up period, the DISC group had longer the first applanation (A1) time, larger A1 deformation amplitude, A1 deflection length (A1 DLL), and A1 deflection amplitude than the OK group. AL elongation was less in the OK group at each visit (all P < 0.05) but faster in the OK group than in the DISC group after discontinuation (P = 0.006). Moreover, AL elongation was related to baseline A1 time, A1 velocity and whole eye movement max in the DISC group, and in the OK group, was related to the baseline the second applanation (A2) DLL, A2 delta arc length and stiffness parameter A1 (all P < 0.05). ConclusionsThe cornea was more deformable after wearing DISC lens than OK lens, and corneal biomechanical parameters were associated with AL elongation. Eyes showed less AL elongation during OK lens treatment while faster AL elongation after discontinuation than DISC lens. The baseline corneal biomechanics may help to predict AL elongation in myopic control strategies.

Study on deformation theory and resonance frequency of circular-plane PVC actuator

The polyvinyl chloride (PVC) gel actuator has the advantages of low mass density, large actuation strain, good compliance, and simple fabrication. It deforms when excited by a voltage, and the deformation amplitude of the actuator is higher when an alternating current voltage of a specific frequency causes the actuator to resonate. In this paper, a circular-plane actuator based on PVC gel film and flexible electrodes was developed. Then, a theoretical model is established based on the Yeoh strain energy density function model and the mechanical analysis of deformation region-boundary constraints, the key parameters affecting the deformation are obtained. Subsequently, finite element simulation tests were done on the basis of this model, and the values of uniaxial stretching were highly consistent with the previous actual experimental results, which verified the reasonableness of the model and simulation method. Then, we focus on the analysis of the resonance frequencies of PVC actuators with different plasticizer content, electrode diameter, and pre-stretching degree. Finally, we compare the differences in time-domain characteristics of PVC actuators in the resonant and non-resonant states.

Consistent C-bar radial-basis Galerkin method for finite strain analysis

For finite-strain problems of quasi-incompressible materials, with hyperelastic and hyperelasto-plastic behavior, we develop a mixed polynomial-enriched radial-basis function (RBF) interpolation. It is characterized by decoupling quadrature and polynomials for the deviatoric and volumetric terms of the right Cauchy–Green tensor. With an enriched interpolation, first and second derivatives of the deformation gradient are continuous. A finite-element mesh is employed for quadrature purposes with the corresponding distribution of Gauss points. In terms of discretization, linear, quadratic and cubic polynomials are combined and function support is established from the number of pre-assigned nodes. Due to the adoption of a Lagrangian kernel, finite strain elasto-plastic constitutive developments are based on the Mandel stress. Combined with the C¯ technique, these developments are found to be convenient from an implementation perspective, as RBF formulations for finite strain plasticity have been limited in terms of generality and amplitude of deformations in the quasi-incompressibility case. Three benchmark tests are successfully solved, and it was found that a combination of reduced integration with a deviatoric cubic basis and volumetric quadratic basis provides superior results in the quasi-incompressible case. Numerical testing shows very good convergence behavior of the results. Besides absence of locking with selective interpolation, outstanding Newton convergence was observed regardless of strain levels.

Implantation of Intracorneal Ring Segments in Keratectasia: Effects on Corneal Biomechanics in 112 Eyes.

The aim of this study was to analyze changes in corneal biomechanical properties after implantation of intracorneal ring segments (ICRSs) in keratectasia. This retrospective single-center study included 112 patient eyes that underwent femtosecond laser-assisted ICRS implantation (Intacs SK; Addition Technology Inc, Des Plaines, IL) for keratectasia. Biomechanical analysis was performed using the Ocular Response Analyzer (ORA; Reichert Inc, Depew, NY), with determination of corneal resistance factor, corneal hysteresis, and Keratoconus Match Index, as well as by Corvis ST (OCULUS, Wetzlar, Germany), with determination of stiffness parameter A1, Ambrosio relational thickness to the horizontal profile (Arth), integrated radius, deformation amplitude ratio, and stress-strain index as well as Corvis Biomechanical Index and Tomographic Biomechanical Index. Data collection was performed preoperatively and 6 months postoperatively for ORA and Corvis ST and additionally after 1 and 2 years for ORA. The corneal resistance factor decreased significantly postoperatively (5.8 ± 1.7 mm Hg) compared with preoperatively (6.75 ± 3.7 mm Hg; P = 0.021) and increased again during follow-up (6.2 ± 1.9 mm Hg; P = 0.024), without regaining preoperative values. Corneal hysteresis and Keratoconus Match Index did not change significantly. Stiffness parameter A1 ( P = 0.045) increased significantly after ICRS implantation and Arth decreased significantly from 181 ± 85 to 150 ± 92 ( P = 0.016). However, there was no significant postoperative change for others Corvis parameters. Corneal biomechanical properties showed inconsistent changes after ICRS implantation. Classical corneal biomechanical parameters (using single central air-puff tonometers) do not seem to be suitable for follow-up after ICRS implantation.

Contribution Factor Analysis of the Wuhan Yangtze River Bridge Deformation Using Sentinel-1A SAR Imagery and In Situ Data

Bridges play a crucial role in the development of the national economy and transportation industry, and their deformation monitoring is vital for ensuring their health. Therefore, it is necessary to conduct long-term monitoring of bridges’ deformation. This study monitored the deformation of the Wuhan Yangtze River Bridge using the SBAS-InSAR technology and Sentinel-1A data. The deformation results were analyzed in combination with bridge structure, human activity, temperature and stratigraphy. The results were as follows: (1) The vertical deformation rate of the bridge was between −15.6 and 10.7 mm/year, and part of the deformation belonged to rebound deformation; (2) The middle span deformation is the largest and the uplift and lowering alternate; (3) The reduction in human activity is the reason for the lower deformation amplitude from January to October 2020 compared to after October 2020; (4) A positive correlation between deformation and temperature was observed only along a portion of the bridge; (5) There is no direct correlation between observed lowering and stratigraphy under the bridge piers, as the sinking is presumably absorbed by the bridge structure.

Effect of corneal flap thickness on opaque bubble layer formation in Visumax FS-LASIK using GEE analysis

IntroductionThis study aimed to investigate two types of corneal flap thickness on opaque bubble layer (OBL) formation in Visumax femtosecond laser-assisted stromal for situ keratomileusis (FS-LASIK). MethodsThis retrospective study analyzed 203 eyes of 103 patients (32 men and 71 women) who underwent Visumax FS-LASIK between January 2020 and June 2020, and according to corneal flap thickness, they were divided into the 100-μm group (64 eyes) and the 110-μm group (139 eyes). Anterior-segment examination revealed no abnormal findings. Preoperatively, intraocular pressure (IOP), central corneal thickness (CCT), residual stromal thickness (RST), spherical power, cylindrical power, flat keratometry (K1), steep keratometry (K2), and biomechanical parameters including deformation amplitude (DA) ratio, Integrated Radius, stiffness parameter at first applanation (SP-A1), and Ambrosio relational thickness to the horizontal profile (ARTh) were evaluated. Primary outcomes were the incidence of OBL formation in the two groups compared by the Chi-square test and the correlation between the incidence of OBL and the above preoperative data by Spearman's Rho test. Secondary outcomes were the comparisons corrected by the generalized estimating equation (GEE) model. ResultsThe incidence of OBL formation in the 100-μm group was 59.4 %, which was higher than that in the 110-μm group (23.0 %) with a significant difference (χ2 = 25.635, P < 0.001). The thinner corneal flap thickness (r = −0.355, P < 0.001) and higher spherical power (r = −0.142, P < 0.05) correlated with OBL formation. Higher K1 (r = 0.217, P < 0.01) and K2 (r = 0.198, P < 0.01) also correlated with OBL formation. The results of the GEE correction analysis showed higher rates of OBL formation in the 100-μm group (odds ratio [OR] = 4.704, 95 % CI 1.681–13.161, P < 0.01). ConclusionsOBL was more likely to occur with the 100-μm corneal flap than with the 110-μm corneal flap in Visumax FS-LASIK. The risk of OBL formation in the 100-μm group was 4.704 times higher than that in the 110-μm group.

Stretching-Induced 2D-to-3D Shape Transformation of an Elastic Composite for Sensitivity-Tailorable Soft Electronics.

The shapes of rubbers and elastomers are challenging to alter, and current methods relying on permanent plasticity and dynamic cross-linking strategies are usually laborious and can inevitably compromise the network elasticity. Here, we report a photoresponsive elastic composite that can be programmed into 3D shapes by first UV light irradiation and then stretching. The composite comprises ethylene propylene rubber as the elastic substrate and photoliquefiable azobenzene small molecules as the responsive filler. Upon UV light irradiation, the liquefication of the filler induces the destruction of the crystalline aggregates near the irradiated surface, and after stretching and subsequent stress release, the irradiated part bends to the irradiated side based on a gradient network orientation mechanism. The position and amplitude of bending deformation can be controlled to realize a 2D-to-3D shape transformation. We further show that the resulting 3D-shaped elastomer can integrate with silver conductive paste to develop soft conductive lines with tailorable strain-sensitive conductivities. This study may open a new door for the development of shape-tailorable elastomers and soft electronics with designable strain-sensitive conductivities.

High-speed shock–boundary-layer interaction over deformed surfaces

This paper concerns the interaction of an oblique shock wave with a supersonic turbulent boundary layer over a thin panel surface, leading to shock–boundary layer interaction and panel buckling. We have performed high-order numerical simulations featuring various static two-dimensional surface deformations typically encountered in experiments. The deformation amplitudes we examined were at least half the height of the incoming turbulent boundary layer thickness. The results show that along the panel midspan, where the maximum deformation amplitude is located, the mean and root mean square pressure are affected by about 10%. Cases for which the pressure at the shock–boundary layer interaction was increased relative to the planar case showed to decrease downstream, and vice versa. Despite the weak response to the mean pressure amplitude, the mean pressure surface contour plots reveal that the streamwise, particularly the spanwise distribution, is affected more noticeably. For example, the surface deformation modes are shown to disrupt the spanwise constant mean pressure, forming higher (or lower) values at either the panel's midspan or edges, depending on the mode. Moreover, the surface curvature leads to a characteristic bending of the spanwise distribution, which can be concave or convex depending on the deformation mode. Analysis of the Reynolds stress anisotropy componentality at different heights from the buckled surface reveals a similar spanwise response of the turbulent velocity fluctuations. The results suggest that the deformation rate plays an important role alongside the deformation amplitude in the turbulent layer and shock–boundary layer interaction.

Evaluation of the effect of the corneal suture removal on corneal biomechanics with Corneal visualization Scheimpflug technology (Corvis ST) after penetrating keratoplasty (PKP)

Background The cornea is a part of the anterior segment of the eye, which plays an important role in the refraction of light rays on the retina. Cornea also maintains the shape of the eyeball and constitutes a mechanical barrier, protecting the eye against external environmental factors. For the determination of corneal biomechanics, it requires application of an air puff and simultaneous imaging of the response of the tissues to the stimulus. Available methods include ocular response analyzer (ORA) and corneal visualization Scheimpflug technology (CORVIS ST). Aim To evaluate the effect of the corneal suture removal on the corneal biomechanics with CORVIS ST after penetrating keratoplasty. Patients and methods In this prospective study, the corneal biomechanics of 30 patients who had penetrating keratoplasty were evaluated before removal of the corneal sutures at least 6 months and after 3 months of removal of sutures with CORVIS ST. Results In this study, the CORVIS ST parameters were evaluated with significant reduction of the central corneal thickness, peak distance, deformation amplitude, and Ambrosio’s relational thickness to the horizontal profile. There was significant increase in the radius of curvature and stiffness parameters at first applanation. Conclusion Good corneal biomechanics in the period after 3 months of removal of the corneal sutures and weak corneal biomechanics in the period before removal of the corneal sutures at least 6 months after penetrating keratoplasty and the measured corneal parameters have potential benefits for monitoring postoperative wound healing.

Identification of the model parameters in cornea with keratoconus in terms of the numerical-experimental study of corneal geometry and mechanical behavior

The aim of this work is to derive a computational technique for model parameter es-timation of corneal mechanical behavior basing upon the following input clinical bi-omarkers: the real-time amplitude of corneal deformations, measured in course of non-contact pneumotonometry, intraocular pressure and geometric features of the patient’s cornea, revealed during his tomographic examination. The developed technique of corneal properties prediction within the area of kerato-conus and beyond it, is based upon the data resulting from finite element modeling of a non-contact tonometric test, and upon the procedure of multi-parameter optimization (minimization) of the deviation of the calculated results from the amplitude of corneal deformation measured by means of pneumotonometer Corvis ST. The simulation is based on the results of a survey of 78 patients of a real clinical database, taking into account the geometry of the cornea, the size and position of the keratoconus zone, the intraocular pressure, and the deformation parameters of the material during the pneumotest, which are specific for each patient.

On the Influence of the Surface Electric Charge on the Regularities of the Formation of Faraday Ripples on the Surface of a Low-Viscosity Liquid

The purpose of the study is to analyze the effect of a surface electric charge on the formation conditions of the Faraday ripples on a horizontal surface of a low-viscosity liquid in a vibration field.Methods. The problem is solved analytically in the limit of small amplitude deformation of the free surface of the liquid. The final relation is derived under the condition that the dissipation is small. The liquid was considered ideally conductive with a surface-distributed electric charge. Results. A simple analytical expression is derived that quantitatively describes the effect of suppression of the Faraday ripple if the surface density of the electric charge increases. It is shown that the increase in the surface density of the electric charge significantly enlarge the threshold value of the vibration field amplitude, the excess of which leads to the formation of ripples. The threshold value of the vibration amplitude is proportional to the viscosity of the liquid and depends on its density, surface tension coefficient and the specific horizontal scale of the ripple.Conclusion. The Faraday’s ripple formed on the surface of a liquid in a vertically oscillating container is very sensitive to the value of the surface density of the electric charge. An increase of the surface charge density leads to suppression of the ripple formation. The effect can be used to prevent the appearance of parasitic convective flows that arise in liquid layers placed in vibration fields. The physical mechanism of Faraday ripple suppression is the rivalry between two qualitatively different types of flows near the liquid surface. Increasing the surface charge density changes the balance of surface forces in such a way as to promote the appearance of aperiodic motions and suppress oscillatory ones. In particular, oscillatory motions responsible for the development of Faraday instability caused by vertical vibrations of the liquid container are suppressed.

Autocollimators: plane angle measurand ambiguities and the impact of surface form

Abstract A phase shifting interferometer and a deformable mirror were used to study the impact of surface form on autocollimators, which detect the orientation of a plane reflecting surface. As real surfaces are not strictly planar, autocollimators must reduce a distribution of local surface orientations to a single reported angle, implicitly defining a measurand. Plausible choices of the summary statistic used to collapse an angle distribution to a single number can disagree by \SI{4}{\arcsecond} for a surface with a \SI{35}{mm} diameter and \SI{130}{nm} standard deviation from the best-fit plane. Combining a general framework for specifying autocollimator measurand definitions with Monte-Carlo simulation of random test surfaces yields estimates of the plausible differences between autocollimator measurands as a function of surface deformation amplitude, and shows the existence of three separate classes of measurands according to their sensitivity to subsets of the Zernike polynomials. Uncertainties due to surface form and measurand ambiguity can be eliminated by explicitly specifying a plane angle measurand for imperfect surfaces, such as a least-squares plane fit realized using an interferometer.

Marangoni stability of a thin liquid film falling down above or below an inclined thick wall with slip

AbstractThe linear and nonlinear instability of a thin liquid film flowing down above or below (Rayleigh-Taylor instability) an inclined thick wall with finite thermal conductivity are investigated in the presence of slip at the wall-liquid interface. A nonlinear evolution equation for the free surface deformation is obtained under the lubrication approximation. The curves of linear growth rate, maximum growth rate and critical Marangoni number are calculated. When the film flows below the wall it will be subjected to destabilizing and stabilizing Marangoni numbers. It is found that from the point of view of the linear growth rate the flow destabilizes with slip in a wavenumber range. However slip stabilizes for larger wavenumbers up to the critical (cutoff) wavenumber. From the point of view of the maximum growth rate flow slip may stabilize or destabilize increasing the slip parameter depending on the magnitude of the Marangoni and Galilei numbers. Explicit formulas were derived for the intersections (the wavenumber for the growth rate and the Marangoni number for the maximum growth rate) where slip changes its stabilizing and destabilizing properties. From the numerical solution of the nonlinear evolution equation of the free surface profiles, it is found that slip may suppress or stimulate the appearance of subharmonics depending on the magnitudes of the selected parameters. In the same way, it is found that slip may increase or decrease the nonlinear amplitude of the free surface deformation. The effect of the thickness and finite thermal conductivity of the wall is also investigated.

Numerical Investigation on the Yield Pillar Bearing Capacity under the Two-End-Type Cable Reinforcement

For underground coal mining techniques such as gob-side entry retaining (GER) or gob-side entry driving (GED), the stability of yield pillars is paramount. A well-designed yield pillar aims to withstand mining-induced stresses. This study delves into the impact of bi-terminal cable support on the stability of such pillars. Utilizing 30 distinct numerical models, each with varying pillar width/height (w/h) ratios and diverse cable support methodologies, our findings suggest an upward trend in both peak and residual strength in response to heightened support strength. Notably, pillars with a wider configuration exhibited a more pronounced increase in peak strength compared to their narrower counterparts, while the latter showcased a more pronounced residual strength enhancement. Additionally, the residual/peak strength ratio was smaller in narrower pillars and increased with the increase in the cable support strength. In view of the surrounding rock mass’s support stress distribution, numerical modelling was adopted to analyze the underlying support mechanism. The results showed the support stress zones extended farther on both sides of pillars with the decrease in the row spacing, which made the radial stresses rise effectively and ameliorated the coal pillar’s stress state. Finally, with the 8311 operation advancing towards the station, the deformation amplitude of the coal pillar was only 2.28%, and the stability of the coal pillar was effectively maintained.