Curving Surface Research Articles

A multivariate freezing-thawing depth prediction model for spring load restriction

Road damages induced by heavily loaded truck traffic during the spring thaw are a major road distress in cold regions. To minimize these damages, Spring Load Restriction (SLR) is widely applied in the U.S., Canada, and other countries during the early thawing season by controlling the movement of freight-carrying trucks and heavy equipment travel until the thawing ends. Most SLR policies rely on the Freezing Depth (FD) and Thawing Depth (TD), especially the latter one. Therefore, accurate predictions of FD and TD are important to prevent both the extensive damage to the pavement due to the late placement or early removal of SLR and the economic loss of road users due to an unnecessarily long SLR period. Here, we propose a new multivariate model for predicting FD and TD in support of SLR decision-making. The model gives a curving surface of FD and TD in a 3-dimensional space, instead of 2-dimensional in traditional methods, by considering both the freezing and thawing indices in the entire freeze-thaw cycle. For model evaluations, yearly field data measured at five typical sites from 104 sites in Michigan were adopted. The evaluation results showed that the proposed model is accurate in predicting FD and TD for most sites. Compared to the previous TD predictions in the existing study, the TD predictions with the proposed model have been significantly improved. In addition, this study provides field data that have not been reported earlier in the literature and that can be used for validating other prediction models. The reported work is ready for practice for roadways in cold regions to support SLR decision-making.

Design and Application of CSC-Roll for Heavy Reduction of the Bloom Continuous Casting Process

Center quality control is a key issue affecting large-section bloom production and product quality. The central convex roll could avoid the bloom side part and yield a high reduction amount, which benefit the implement of heavy reduction (HR) for bloom continuous casting process without upgrading the mechanical and hydraulic system of withdrawal and straightening machine. In this work, a curving surface convex roll (CSC-Roll), which could significantly improve bloom center quality, was designed by finite element simulation for a 360 mm × 450 mm #45 steel continuous casting bloom. The optimal roll surface shape of the CSC-Roll was determined based on an analysis of the distribution of the reduction amount in the bloom center and the strain of the bloom centerline and inner surface. The calculation results showed that the optimal size of the CSC-Roll was 200 mm in convex platform region length, 30 mm in convex platform region height, and 80 mm in gradient curvature region length. The bloom heat transfer and deformation behavior in the CSC-Roll reduction process were then analyzed. The results showed that in the CSC-Roll HR process, 61.71 pct of the reduction amount could be transmitted to the inner side of the porosity zone. Macrographs of the 360 mm × 450 mm #45 steel continuous casting bloom proved that the bloom center quality was significantly improved after CSC-Roll HR was applied.

Characterizing free-surface expressions of flow instabilities by tracking submerged features

Under unidirectional flow, complex bottom roughness such as seagrass canopies can induce Kelvin–Helmholtz (KH) shear instabilities, and these vortices can impact the free surface and leave a signature with an inherent frequency. Therefore, one approach to inferring the presence and properties of submerged ecosystems may be to look at the behavior of the water surface. We present an imaging-based laboratory method developed to characterize this canopy-induced shear instability. Much like a lens, a curving free surface refracts light at the interface (Moisy et al., Exp Fluids 46:1021–1036, 2009). Using cameras placed above the length of a flume, the water surface slope is measured by tracking the apparent distortion of submerged model vegetation in a series of images, manifested as a slight shimmering over time. We demonstrate that the synthetic Schlieren technique can: (1) measure the spectral signature of the canopy-induced shear instability on the free surface, (2) provide high-resolution spatial information on the development of the instability over the entire canopy length, and (3) measure the propagation speed and length scale of the coherent KH rollers at the surface and detect distinguishable differences in these properties for varying canopy geometry.

Three-dimensional smoothed-particle hydrodynamics simulation of deformation characteristics in slope failure

This paper presents the development, validation and application of a smoothed-particle hydrodynamics model for three-dimensional (3D) simulation of the evolution of large deformation failure in geo-materials. The Drucker–Prager model with non-associated plastic flow rules is implemented into the smoothed-particle hydrodynamics formulations to describe elasto-plastic soil behaviour. Two typical numerical examples – a two-dimensional (2D) analysis of cohesive slope instability and a 3D simulation for instant collapse of a granular slope – are shown to demonstrate the effectiveness of the method for modelling large deformation of slope failure. Good agreement with experimental observations and previous simulated results is obtained in terms of the profile and internal deformation, respectively. The method is then applied to two special 3D slopes with different geometric configurations, including a curving slope surface and a slope that turns corners. The results suggest that 3D effects should be considered for natural landslides. By influencing the stress status, slope geometries have a significant effect on the final profile, slip surface and distance. The results provide a more accurate and detailed reference for landslide evaluation and foundation ditch design.

Facile One-Step Fabrication of an Undercut Structure by Solution Dewetting on a Water/Ice Mold

This paper reports a facile one-step method for making undercut structures by dewetting of poly(methyl methacrylate) (PMMA) chloroform solution on an ice/water mold. The ice mold is prepared by filling the microchannels with water (micromolding in capillaries (MIMIC) method) and then freezing. The curving surface of water mold stripes and the trapezoidal structure of ice mold stripes work as complementary structures devoted to the formation of undercut structures. The undercut structures with angles of 60° and 40° are obtained, which is determined by the states of ice or water mold. Meanwhile, if the solution concentration is increased, patterned polymer films with different configurations of undercut structures or microchannels would be gained.

On the Active Failure Surface in the Backfilled Clay behind Rigid Retaining Wall in Slope Engineering

In the classical Coulomb’s earth pressure theory, the failure surface in the backfilled clay behind rigid retaining wall in slope engineering is assumed a plane. However, it has been proved by a number of laboratory and field tests that this failure surface is actually a curving surface. In this paper, based on the vertical differential element method and the variational principle, a new analytic solution to determine the actual failure surface in the backfilled clay is derived, and the effects of the backfilled clay’s properties as well as the effects of the retaining wall’s smoothness are discussed. The result obtained from the proposed approach is compared with Coulomb’s earth pressure theory.

Formation of the lower ocean crust and the crystallization of gabbroic cumulates at a very slowly spreading ridge

Ocean Drilling Program Hole 735B was extended to 1508m below the sea floor during Leg 176, atop a shallow bank near Atlantis II Fracture Zone on the very slowly spreading Southwest Indian Ridge. All the drilling was in gabbro, and recovery averaged nearly 87%. The drill penetrated a series of stacked plutons consisting mostly of olivine gabbro, but some with troctolite. Each pluton is some 200–500m thick, each has its own internally coherent stratigraphy, and each apparently represents an individual event of significant magma inflation and addition to the crust. The entire column was extensively deformed along inclined zones of distributed shear before it was completely frozen, this marking the onset of unroofing of the rocks and their ascent to high rift mountains. The deformation mobilized late-stage melts into flow patterns which led to concentration of ilmenite and magnetite in hundreds of seams of oxide gabbro along or near zones of strong crystal–plastic deformation, the highly differentiated melts overall being concentrated by buoyancy forces toward the top of the section, especially in one zone nearly 70m thick. However, upward flow was ultimately blocked or deflected by zones of impermeable rock resulting either from downward freezing or grain-size reduction during shear. A melt lens probably did not form at the base of sheeted dikes, as it does at the East Pacific Rise.Despite this, the rocks are cumulates, and most are adcumulates, with very low residual melt porosities. Cumulate theory based on stratiform, layered intrusions does not entirely apply to these rocks. Instead, all gabbros, including the oxide gabbros, crystallized in a dense crystal mush in patterns dominated by fractures, channelized flow, and intergranular porous flow. Most gabbros are not layered; weak modal layering of uncertain origin is present in <2% of the rocks. Porosity reduction leading to formation of adcumulates at all stages was extremely efficient. This occurred in the course of synkinematic differentiation, also called differentiation by deformation, and involved compaction under conditions of lithostatic loading and shear, emplacement of crystal mushes along inclined, possibly curving faults, dissolution and reprecipitation of minerals along grain boundaries, and pressure solution, which was the final agent in porosity reduction.As the block was lifted from beneath the rift-valley floor, crystal–plastic deformation gave way to brittle fracture, and the now dominantly subsolidus metamorphism shifted from high-temperature assemblages characterized by amphibole near the top of the section, to low-temperature assemblages with smectite–chlorite and zeolite near the bottom. The rocks acquired their stable magnetization during formation of amphiboles and secondary magnetite during this metamorphism. The entire body of rock is reversely stably magnetized at a consistent inclination, and it is rotated to the south, perhaps along a curving detachment surface, away from the ridge segment where it formed, by about 20°. It has an intensity of magnetization sufficient to account for the magnetic anomaly observed over the site.Drilling did not reach ultramafic rock, but dredging indicates that peridotite is probably within a few hundred meters of the bottom of the hole. Seismic Moho, however, is placed at 5km beneath the summit of Atlantis Bank. Much of the rock between Moho and the bottom of Hole 735B must therefore be partially serpentinized peridotite.

Three-dimensional collagen organization of human brain arteries at different transmural pressures.

Measurements on the directional organization of collagen are necessary for relating the structure and mechanical function of blood vessels. The birefringent optical property of collagen has enabled us to assess the collagen architecture for brain arteries, which are prone to spasm and aneurysm formation. Using the universal stage and polarizing microscope, we measured the three-dimensional organization of the collagen of the main layers of the artery wall, and examined the effect of distending pressure on that organization. Adult arteries obtained from autopsy were fixed at one of three distending pressures, 30, 120 and 200 mm Hg; they were embedded in paraffin and sectioned parallel to the vessel axis at 4 microns thickness. Sections were stained with picrosirius red, a birefringent enhancement stain specific for collagen. Orientation data were obtained from tangential sections from thirteen arteries. We chose to use tangential sections that graze the curving surface of individual layers, to permit measurements that are equally sensitive to fibres in the mechanically meaningful range of directions including longitudinal, helical and circumferential. Each measurement was from a single fibre or group of fibres at a specific location; the mean direction and its variation of alignment within each artery layer were calculated. In some arteries, the adventitia and subendothelium measurements were separated into sublayers, distinguishable by the birefringent optical appearance. Main findings included a substantial component of longitudinal fibres in the adventitia and subendothelium, highly varied in coherence and mean direction, and a thin collagen layer of the adventitia, radially outside the medial muscle cells, that was highly organized circumferentially (circular standard deviation of 9 degrees). At higher pressures, the collagen fabric of all the layers was increasingly coherent and more circumferential in direction.