Stepped Slope Research Articles

Effects of Stepped Chute Slope and Slit Location on a Jet from Abrupt Contraction Aerator

Effects of Stepped Chute Slope and Slit Location on a Jet from Abrupt Contraction Aerator

Convection heat transfer of stepped basin single slope solar still: A numerical investigation

Solar-powered desalination is a quick and easy way to make drinking water. Numerous solar distillation systems have been investigated for various parameter modifications based on local resource availability. In this work, a solar still with a modified stepped basin is investigated to raise the rate of internal evaporation and, therefore the output yield of the solar still. Stepped basin solar stills are taken into consideration for the study since they are very effective because the water's surface exposure to radiation is greater. Thus, increasing the rate of internal water evaporation enhances the rate of convective heat transfer between the evaporating and condensing surfaces, leading to improved and consistent output. The two-dimensional stepped basin single slope solar still was investigated and contrasted with the traditional single slope still in terms of heat transfer and fluid dynamics. To optimize the configuration for better performance in various types of climatic and operational circumstances that imitate the scenario of daily life, design elements such as the number of steps and the different heights of the basin are also taken into account. Each step was added with far more success than the one before it, up until the length was reduced to 1.16% of the entire shorter length. This numerical study enables us to draw the conclusion that the rise in natural heat transfer rate with the addition of steps is mostly caused by the increased surface area and the inherently restrictive nature within the domain. Additionally, with an increase in Rayleigh number, Ra, the gradient variations of the traditional single slope solar still overheat transfer features have been greatly regulated and successfully raised for the modified stepped basin Solar still.

Advances in Spillway Hydraulics: From Theory to Practice

Over the past decades, significant advances have been achieved in hydraulic structures for dams, namely in water release structures such as spillway weirs, chutes, and energy dissipators. This editorial presents a brief overview of the eleven papers in this Special Issue, Advances in Spillway Hydraulics: From Theory to Practice, and frames them in current research trends. This Special Issue explores the following topics: spillway inlet structures, spillway transport structures, and spillway outlet structures. For the first topic of spillway inlet structures, this collection includes one paper on the hydrodynamics and free-flow characteristics of piano key weirs with different plan shapes and another that presents a theoretical model for the flow at an ogee crest axis for a wide range of head ratios. Most of the contributions address the second topic of spillway transport structures as follows: a physical modeling of a beveled-face stepped chute; the description and recent developments of the generalized, energy-based, water surface profile calculation tool SpillwayPro; an application of the SPH method on non-aerated flow over smooth and stepped converging spillways; a physical model study of the effect of stepped chute slope reduction on the bottom-pressure development; an assessment of a spillway offset aerator with a comparison of the two-phase volume of fluid and complete two-phase Euler models included in the OpenFOAM® toolbox; an evaluation of the performance and design of a stepped spillway aerator based on a physical model study. For the third topic of spillway outlet structures, physical model studies are presented on air–water flow in rectangular free-falling jets, the performance of a plain stilling basin downstream of 30° and 50° inclined smooth and stepped chutes, and scour protection for piano key weirs with apron and cutoff wall. Finally, we include a brief discussion about some research challenges and practice-oriented questions.

Stability analysis of nonhomogeneous and anisotropic stepped slopes under the influence of earthquakes

There have been many studies related to the stability of single-step slopes, but there have been few studies on the stability of stepped slopes. Based on the limit analysis method and the strength reduction method, the stability factor FS of a stepped slope in nonhomogeneous and anisotropic soils is calculated. Then, the calculation method in this paper is compared with previous studies to verify the correctness of the calculation method. Finally, the parametric analysis of the stepped slope is also carried out. The results show that the maximum error obtained by the calculation method of this paper does not exceed 5%, which verifies the rationality and effectiveness of the method in this paper. The ratio B/H of slope width to slope height significantly affects the stability of the slope. When B/H < 3, FS decreases sharply with increasing B/H; when B/H > 3, FS decreases slowly with increasing B/H. When the inclined angle, anisotropy parameter and seismic parameter of the slope increase, the stability of the stepped slope decreases; when the platform width parameter and soil nonhomogeneity parameter of the slope increase, the slope stability is also improved.

Fill‐and‐Spill, Tilt‐and‐Repeat (FaSTaR) cycles: Stratigraphic evolution above a dynamic submarine stepped slope

AbstractThe classic fill‐and‐spill model is widely applied to interpret topographic controls on depositional architecture and facies distributions in slope successions with complicated topography. However, this model implies a constant topographic configuration over the lifespan of a turbidite system. In contrast, the impact on patterns of erosion and deposition above dynamic slopes whose topographic configuration varies spatially over time remains poorly investigated. Here, using high‐resolution 3D seismic reflection data and more than 100 wells from a 40 km long stepped slope system (Campos Basin, offshore Brazil), we document the evolution of a sand‐prone turbidite system active during the Oligocene–Miocene transition. This turbidite system was influenced by vertical and lateral deformation, and we propose a new stratigraphic model to explain the resultant depositional architecture. Two depocentres were identified as steps, with channels on the proximal step, and channel–lobe complexes on the distal step, bounded by sediment bypass‐dominated ramps. Lateral stepping of channels on the proximal step, and oblique stacking of the down‐dip lobe complexes, each cut by through‐going channels, indicate multiple fill‐and‐spill cycles. A persistent north‐east‐ward stepping and thickening on the steps are interpreted to reflect lateral tilting of the seafloor driven by salt tectonics. The dynamic substrate prevented the establishment of a single long‐lived conduit across the proximal step, as recorded in systems with fixed topographic configurations. The filling of through‐going channels with mud at the end of each cycle suggests waxing‐to‐waning sediment supply cycles and periods of sand starvation when the lateral tilting dominated and drove avulsion of the feeder channels towards topographic lows. This study demonstrates that subtle dynamic slope deformation punctuated by discrete sediment supply cycles results in complex stratigraphic patterns with multiple phases, and multiple entry and exit points. Repeated cycles of fill‐and‐spill, tilt‐and‐repeat are likely to be present in other stepped slope systems.

Research on influence of anchor cable failure on slope dynamic response

Anchor cables are an important branch of geotechnical engineering and are widely used in slope reinforcement. The Wenchuan earthquake showed that the anchor cable fracture can cause the instability of the slope. The anchor cables in the numerical software obey the ideal elastic-plastic law and cannot simulate fracture and failure. To achieve the fracture effect, the anchor cable model is modified. Based on stepped slopes, the dynamic response characteristics are analyzed, and the effect of pre-tension is discussed. The results show that: 1) The influence of anchor cable failure on slope safety cannot be ignored. After the failure conditions are met, the free segment no longer transmits tension, and the anchored segment degenerates into soil nails. 2) When the slope is unstable, the anchor cable will show a continuous fracture phenomenon. The fracture first occurred in the dangerous parts such as the slope toe, and then turned to the top. 3) The fracture of the anchor cable will lead to the release of the soil stress, accompanied by the change of the acceleration amplitude and frequency, and finally manifested as a larger residual displacement. Slope reinforcement not only needs to consider the anchoring force, but also the coordination relationship.

Experimental investigation of a stepped solar still employing a phase change material, a conical tank, and a solar dish

The configuration of an external solar dish improves the performance of stepped slope solar still (SS) in an experimental setting. The use of an external solar dish raises the effects of the water basin, resulting in a higher rate of evaporation. The stepped still was designed, built, and tested in Ismailia, Egypt, using local weather conditions. The proposed SS had a 1 m2 base area and eight steps, a solar dish with a concentration ratio of 80, a cone tank, two centrifugal pumps, four photovoltaic modules totaling 1000 W, a control unit, and solenoid valves. The impact of utilizing the storage material during the phases was investigated. A nozzle was installed at the top of the cone tank. Four mass flow rates of circulated water were examined 250, 350, 450, and 550 mL/min. The control unit receives inputs from the photovoltaic output, photodiodes, and water temperature inside the cone. The control unit outputs the signal for the two solar dish motors, centrifugal pumps, and solenoid valves. First, a standard stepped SS, second, a stepped SS using phase change material (PCM), and finally, a stepped SS using PCM combined with a solar dish were investigated. The conventional stepped SSs with PCM had an optimal mass flow rate of 250 mL/min, whereas the stepped SS integrated with the solar dish had 550 mL/min of mass flow rate (an optimum value). The highest daily freshwater productivity was 7.63, 9.18, 11.23, and 13.9 kg/d for water spraying mass flow rates of 250, 350, 450, and 550 mL/min, respectively, with 0.0161 $/L/m2 of a maximum projected cost, according to data from an integrated stepped SS.

Numerical Simulation of Solitary Waves Propagating on Stepped Slopes Beaches

The objective of the current paper is to study the propagating and breaking of solitary waves on stepped slopes beaches, to simulate the shoaling and breaking, specifically the location of breaking point Xb, and solitary wave height at breaking Hb of solitary waves on the different stepped slopes. Ansys Fluent is used to implement the simulation, a two-dimensional volume of fluid (VOF) which is based on the Reynolds-Averaged Navier–Stokes (RANS) equations and the k–ε turbulence closure solver. The obtained results were firstly validated with existing empirical formulas for solitary wave run-up on the slope without stepped structure and are compared with the experimental and numerical results. The numerical computation has been carried out for several, configurations of beach slopes with tan ß= 1:15, 1:20, 1:25, wave height H0= 0.04, 0.06, 0.08m, water depth h0= 0.15, 0.2, 0.25m, and step height Sh= 0.025, 0.05, 0.075m. A set of numerical simulations were implemented to analyze shoaling and breaking of solitary waves, wave reflection, wave transmission, and wave run-up with various parameters wave heights, water depth, beach slopes, and Sh step height.

Kinematic limit analysis of unsaturated stepped excavation slopes under surcharge loads

Stability assessments and design of stepped excavation slopes are of great practical significance and require explicit consideration of the three-dimensional (3D) effect and suction-related effects. In the realm of 3D kinematic limit analysis, this paper presents a semi-analytical method to quantify the impact of suction in stability assessments of stepped excavation slopes. The influences of surcharge load and seismic excitation are both considered from a kinematic perspective. Numerical experiments were conducted regarding the roles of soil suction, 3D effects, surcharge loads and seismic actions in safety assessments. An example is presented to show the practical use of the proposed method in engineering practice with respect to determination of the optimum shape of a stepped excavation slope characterised with a fixed slope toe and slope crest positions. The results demonstrate that the stability of stepped excavation slopes can be improved by 10–25% compared with the stability of a single-stage slope and the optimum depth coefficient (αopt) falls in the range 0.55–0.70 in most cases. For steeper excavation slopes, αopt might exceed this range while, for gentler slopes, αopt tends to be smaller than this range. The critical slip surface and 3D effects tend to be more pronounced with an increase in surcharge load.

Kinematics and Sediment Dispersal Pattern of Multi-Stage Mass Transport Deposits on a Stepped Slope with Numerous Elliptical Depressions, Northwestern South China Sea

Kinematics and Sediment Dispersal Pattern of Multi-Stage Mass Transport Deposits on a Stepped Slope with Numerous Elliptical Depressions, Northwestern South China Sea

Analytical approach for stability of 3D two-stage slope in non-uniform and unsaturated soils

In geological engineering, the unsaturation and non-uniformity of soil have significant influence on slope stability. However, they were common neglected in published literature. Based on the three-dimensional (3D) rotational failure mechanism, this paper introduces a method that combines the gravity increase method and the upper bound theorem, to evaluate the factor of safety (FS) of 3D stepped slope in non-uniform and unsaturated soils. The soil cohesion increases linearly with depth, and three nonlinear unsaturated shear strength models are adopted in this study. After the calculations of internal energy dissipation rate and external work rate, the analytical formula of FS is derived, and the lowest FS value is obtained through optimization. To prove the validity of the proposed method, the present results are compared with previously published solutions. A parametric study is carried out, and the influences of a number of factors on FS are discussed. For non-uniform and unsaturated soils, the new formula for calculating the FS of 3D two-stage slopes is presented for practical use in geological engineering.

Stepped Spillway Slope Effect on Air Entrainment and Inception Point Location

Spillway is a crucial hydraulic structure used to discharge excess water from the dam reservoir. Air entrainment is essential to prevent cavitation damage on the spillway, however, without air entrainment the risk of cavitation over the spillway increases. The most important parameter for the determination of air entrainment in stepped spillways is the inception point. The inception point is the location where the air starts to inter into the water flow surface over the spillway. It occurs when the turbulent boundary layer meets the free surface. The location of the inception point depends upon different parameters like flow rate, geometry, step size, and slope of the spillway. The main aim of this study was applying numerical simulation by using the realizable k-ϵ model and the volume of fluid (VOF) method to locate the location of the inception point. For this purpose, by using different stepped spillways with four different slopes (12.5°, 19°, 29°, and 35°) different flow rates were simulated, which gives the location of the inception point of different channel slopes of stepped spillways at different flow rates. The results demonstrated that the inception point location of mild slopes is farther from the crest of the spillway than the steep slope stepped spillway. Non-aerated flow zone length increases when the channel slope decreases from steep to mild slope.

Experimental Study and Performance Analysis of Phase Change Material Integrated Stepped Slope Solar Still

The major challenge in developing countries is to provide drinking water to the people, several techniques are employed but the challenge is to make cost effective and its sustainability over a period. Most of the developing countries work on saline water conversion to neat drinking water, distillation is one of the old and handy techniques in this conversion; where sunlight is used as energy drive for the process because elevating the temperature of saline water is enough for distillation and also for its free of cost availability. Solar still distilled water costs very less than the conventional method of deriving water from saline water and also people need not to worry about the purification of obtained water. Hence various analysis on increasing the performance of solar stills is required to increase the productivity to meet the rising demand for clean drinking water. The experimental work is carried out with three stepped solar stills, one without phase change material, one with paraffin wax as phase change material and other with calcium nitrate as phase change material. Solar stills are integrated with phase change materials to increase the productivity of clean drinking water by storing the solar energy in the form of latent heat to release in the dark hours for enabling solar sill distillation even during night time. There will be change in the total productivity based on the size of solar still, phase change material used, basin design and exergy efficiency, therefore these parameters have to optimized for better yield of neat drinking water from saline water. Experimentation was carried in the month of February and March of 2020 to estimate and compare the yield of three solar stills for the time period of 24 hours, certainly solar stills equipped with phase change materials resulted in higher total production than solar still without phase change material though their day time productivity was low. Solar still equipped with calcium nitrate as phase change material yielded 8.17 % more clean drinking water than the solar still equipped with paraffin as phase change material, though calcium nitrate is economical than paraffin wax but maintenance of solar still with calcium nitrate as phase change material is a hefty task.

Deep-lacustrine sediment gravity flow channel-lobe complexes on a stepped slope: An example from the Chengbei Low Uplift, Bohai Bay Basin, East China

Many stepped slopes are present at deep-lacustrine basin margins in China, especially in the Paleogene rift basin margins of East China. Sediment gravity-flow deposits on these stepped slopes have the potential to form excellent reservoir quality sediments that are targeted for hydrocarbon exploration, but still remain poorly understood. In this study we use the Ed3 member of Oligocene-aged Dongying Formation deposited over the Chengbei Low Uplift, as an example for investigating facies types, distribution and main controlling factors of sediment gravity-flow deposits on stepped slopes at deep-lacustrine basin margins. Paleotopographical reconstructions indicate that the study area displayed a three-level stepped slope that were dissected by three large canyons and many associated smaller-scale channels prior to the deposition of the Ed3 member. On the basis of facies identification, six facies associations are further distinguished: (1) fan valley fills, (2) confined channel deposits, (3) poorly confined channel deposits, (4) levee deposits, (5) interchannel deposits, and (6) lobe deposits. These facies associations are grouped into four systems, namely fan valley fills, confined channel-levee, poorly confined channel-levee and lobe systems, as architectural elements constituting two types of channel-lobe complexes in the study area, namely anastomosing channel-lobe complexes and meandering channel-lobe complexes. The interaction between paleotopography and lake level fluctuations likely represented the direct control on the morphology, pattern and spatial-temporal distribution of channel-lobe complexes in the study area. Moreover, lake level fluctuations can also influence the volume and grain size of sediment supply to the stepped slope systems. Hyperpycnal flood events, as trigger factors, caused the generation of subaqueous sediment gravity flows that fed the stepped slope systems. Climate variations appear to be a contributing driver of lake-level fluctuations, and also indirectly control sediment supply into the deep lake and development scale of the stepped slope systems. These controls therefore determined the sediment supply, trigger and spatial-temporal variations of the stepped slope systems. This study improves the understanding of facies types and their distribution across stepped slopes at deep-lacustrine basin margins, as well as the controlling factors on the development of these sediment gravity-flow deposits.

The role of large-scale mass wasting processes in changing the sediment dispersal pattern in the deep-water Central Canyon of the northwestern South China Sea

Large-scale mass transport complex (MTC) (usually covering hundreds to thousands of km2 with a volume of tens to hundreds of km3) resulting from slope failures, can change the overall sediment dispersal pattern in deep-water canyon. However, the causal mechanisms remain enigmatic. We investigate the large-scale MTCs in the Central Canyon that are imaged in 3D by high-resolution seismic reflection data from the northwestern South China Sea. Our results indicate that a total volume of 435.3 km3 of sediments related to large-scale mass wasting processes were dumped into the Central Canyon from its side direction between 5.7 and 4.2 Ma. This led to adjustments of the geomorphology of the thalweg slope, which changed from a simply stepped slope (2 steps separated by 1 ramp) into a complexly stepped slope (3 steps separated by 2 ramps). The adjustments are argued to be caused by the thickness variations of MTCs1-4 that also ponded the axial turbidity flows at their up-dip directions. And then, the adjusted thalweg slope controlled the formation of a multi-stage submarine fan, which is proved to be an important hydrocarbon exploration target within the Central Canyon. Besides the first step in the canyon where sediments were mainly transported downslope due to the initially large velocities of turbidity flows, the following ramps were also considered as sediment bypass zones due to the further accelerated flows. Whereas, the subsequent steps became sediment deposition dominated zones as turbidity flows decelerated abruptly. Slope overstepping resulting from high sediment supply that was controlled by the East Asia summer monsoon, together with seismicity caused by the structural inversion of the Red River Fault were responsible for the occurrences of the large-scale mass wasting processes. We highlight how the large-scale mass wasting processes change the sediment dispersal pattern in the deep-water canyon for the first time. This study is of great significant to identify the locations of hydrocarbon reservoirs and evaluate the spatial variability in depositional reservoir qualities within the deep-water canyon.

Research on stepped cohesive joint repair slope of composite laminates based on finite element numerical simulation

Research on stepped cohesive joint repair slope of composite laminates based on finite element numerical simulation

Performance enhancement of stepped double slope solar still by using nanoparticles and linen wicks: Energy, exergy and economic analysis

This work aims to improve the thermal and economic analysis of stepped double slope solar still (SDSSS) that integrated with linen wicks (LWs) and carbon black nanoparticles (CBNs). The LWs and CBNs were used to increase the evaporation surface area and enhance heat transfer of basin saline water. The SDSSS with LWs and LWs with CBNs were evaluated, and compared with traditional solar still (TSS). The energy and exergy for convection and evaporation and exergy efficiency for different modifications were analyzed, and its costs were discussed. Results indicated that adding LWs and CBNs to SDSSS increased the freshwater productivity and energy efficiency by 80.57 and 110.5%, respectively, compared to TSS. The SDSSS fractional exergy of evaporation was the highest in the case of integrating LWs and CBNs with the solar still due to the high basin water temperature. This modification caused the highest exergy efficiency for SDSSS because of enhanced photo-thermal properties of CBNs, and heat storage characteristic of LWs. Economic analysis indicated that the total costs per liter of produced freshwater for SDSSS without any modifications, SDSSS with LWs, SDSSS with CBNs, and SDSSS with LWs and CBNs were lower than TSS by 13.73, 19.91, 23.83, and 47.22%, respectively.

Uniform flow and energy dissipation of hydraulic-jump-stepped spillways

Abstract In skimming flow, a uniform flow can be achieved and the flow depth, velocity and air concentration remain constant if a stepped spillway is sufficiently long. In this study, physical model experiments were performed to investigate the uniform characteristics and energy dissipation of a hydraulic-jump-stepped spillway, which is a new type of stepped spillway for increasing the unit discharge capacity and energy dissipation. Based on the redefinition of uniform flow, experimental results show that at a given stepped spillway slope, a smaller height for the beginning of the uniform flow region, a greater uniform aerated flow depth and a greater uniform equivalent clear water flow depth can be obtained as compared with the traditional stepped spillway due to strong aeration in the aeration basin. Under the condition of uniform flow, the energy dissipation rate of stepped spillways can be estimated by the equivalent clear water flow depth with given inflow conditions. Compared with the traditional stepped spillway, the uniform flow over the hydraulic-jump-stepped spillway has a smaller specific energy, revealing that the hydraulic-jump-stepped spillway is more advantageous for dissipating energy, especially at large unit discharges.

Mesozoic tectono-sedimentary evolution of the Trapanese SouthernTethyan margin (NW Sicily) integrating facies and stratigraphic analysis with subsidence history

Several Mesozoic successions of the Southern Tethyan margin were accumulated on a carbonate platform evolving to pelagic plateau depositional systems. Rifting paleotectonics was the main process conditioning their tectono-sedimentary evolution. The well-exposed outcrops in the NW Sicilian fold and thrust belt of the so-called Trapanese carbonate platform to pelagic succession highlight the occurrence of lateral facies and thickness changes, paleofaults, volcanics, and resedimented deposits. The integration of facies analysis, stratigraphic data, and subsidence history have permitted to decipher the polyphase tectono-sedimentary evolution and to distinguish different depositional settings. Structural lows, filled with up to 100m of pillow lavas and reworked deposits, appear as intraplatform basins bordered by structural highs, as horst ridges, characterised by condensed sedimentation, and isolated seamounts. These sectors were linked among them by stepped fault margins, scalloped margins and depositional slopes. The tectonic history, highlighted by the backstripped sections, reveals superimposed evolutionary stages reflecting rifting and rapid tectonic subsidence, leading to continental break-up (Late Triassic-Early Jurassic stage); the Middle Jurassic stage reflects slow thermal subsidence in the basin shoulders and higher rates in the intervening depressions; the Late Jurassic-Early Cretaceous regional uplift interrupts the thermal subsidence curve trend. The tract of the Late Cretaceous-Eocene curve suggests again slow thermal post-rift subsidence, also influenced by sediment load. The different subsidence curves, reconstructed from different positions in the sedimentary basin, demonstrate that its evolution could be driven by the identified syn-sedimentary faults that were formed and/or re-activated during several tectonic events encompassing the whole Jurassic-Cretaceous time period. The regional significance of this tectonics indicates that the Sicilian sector of the Southern Tethyan continental margin was tectonically active for the whole Mesozoic.The reconstructed paleophysiography of the Trapanese continental margin, during the Mesozoic, appears characterised by a segmented and drowned carbonate platform with morphostructural highs separated by deep channels. The comparison with the present-day morphostructural setting of some regions of the Atlantic continental margins (e.g. Caribbean, Brazilian equatorial margin), suggests also for the study region that the occurrence of transcurrent/transform faults and stretching of the continental lithosphere can have played an important role in determining the physiographic conformation.

3D stability assessment of stepped slopes in inhomogeneous soils

Stability assessment of slopes has historically been performed assuming soils to be homogeneous in two-dimensional (2D) cases. In real cases, soils are usually inhomogeneous, and each slope collapse indicates a three-dimensional (3D) nature. Based on a 3D rotational failure mechanism, this work develops an approach to account for the impact of the vertical strength inhomogeneity on the 3D stability of stepped slopes. Seismic actions are taken into account by introducing the concept of a horizontal seismic coefficient. An upper-bound expression for stability factors is derived in the light of the kinematic approach, and the most critical solution is obtained from an optimization programming. In comparison with the previously published solutions, the validity of the proposed method is shown. A sensitivity analysis is carried out to discuss parametric effects on the stability of 3D stepped inhomogeneous slopes.