Uniform Slope Research Articles

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The research on two-wheeled inverted pendulum (TWIP) mobile robots has been ongoing in a number of robotic laboratories around the world. In this paper, we consider a robust controller design for the TWIP mobile robot driving on uniform slopes. We use a 2 degree-of-freedom (DOF) model which is obtained by restricting the spinning motion in a 3 DOF motion dynamic equation. In order to design the robust controller guaranteeing stability of the TWIP mobile robot driving on inclined surface, we propose a sliding mode control based on the theory of variable structure systems and design a sliding surface using the theory of the linear quadratic regulation (LQR). For simulation, the dynamic model of the TWIP mobile robot is constructed using Mathworks` Simulink and the sliding mode control is also implemented using Simulink. From simulation results, we show that the proposed controller effectively controls the TWIP mobile robot driving on slopes.

Dynamics of laterally confined marine ice sheets

We present an experimental and theoretical study of the dynamics of laterally confined marine ice sheets in the natural limit in which the long, narrow channel into which they flow is wider than the depth of the ice. A marine ice sheet comprises a grounded ice sheet in contact with bedrock that floats away from the bedrock at a ‘grounding line’ to form a floating ice shelf. We model the grounded ice sheet as a viscous gravity current resisted dominantly by vertical shear stresses owing to the no-slip boundary condition applied at the bedrock. We model the ice shelf as a floating viscous current resisted dominantly by horizontal shear stresses owing to no-slip boundary conditions applied at the sidewalls of the channel. The two shear-dominated regions are coupled by jump conditions relating force and fluid flux across a short transition region downstream of the grounding line. We find that the influence of the stresses within the transition region becomes negligible at long times and we model the transition region as a singular interface across which the ice thickness and mass flux can be discontinuous. The confined shelf buttresses the sheet, causing the grounding line to advance more than it would otherwise. In the case that the sheet flows on a base of uniform slope, we find asymptotically that the grounding line advances indefinitely as $t^{1/3}$, where $t$ is time. This contrasts with the two-dimensional counterpart, for which the shelf provides no buttressing and the grounding line reaches a steady state (Robison, J. Fluid Mech., vol. 648, 2010, pp. 363–380).

A novel algorithm for slope stability analysis

A concise algorithm is introduced to perform slope stability analysis to determine the geometry of the critical slip circle and the corresponding factor of safety without the need for iterative calculations. An optimisation process is performed using the developed algorithm for various soil properties and slope geometries to determine the critical slip circle within all possible slip circles and obtain the factor of safety. The performance of the algorithm is compared with three-dimensional finite-element analysis using the strength reduction method and benchmark studies conducted previously. It is found that the developed algorithm shows good agreement with the previous studies and three-dimensional finite-element analysis. The factors of safety are calculated for a wide range of parameters and variations in these factors are expressed using linear and quadratic equations to establish a correlation between factor of safety and five parameters: cohesion, friction angle and unit weight of soil, as well as slope height and slope angle. The correlation coefficients introduced in this study provide a convenient way for practising engineers to estimate factors of safety that are applicable to uniform slopes.

PSI in the case of internal wave beam reflection at a uniform slope

Two-dimensional numerical simulations are performed to examine internal wave reflection at a sloping boundary. Owing to reflection, the reflected wave amplitude and wavenumber increase. At low values of the incoming wave amplitude, the reflected wave beam is linear and its properties agree well with linear inviscid theory. Linear theory overestimates the reflected wave Froude number, $Fr_{r}$, for higher values of incoming wave amplitude. Nonlinearity sets in with increasing value of incoming wave Froude number, $Fr_{i}$, leading to parametric subharmonic instability (PSI) of the reflected wave beam: two subharmonics emerge from the reflection region with frequencies $0.33{\it\Omega}$ and $0.67{\it\Omega}$ and wavenumbers that add up to those of the reflected wave. The amplification of Froude number due to reflection must be sufficiently large for PSI to occur implying that the off-criticality in wave angle cannot be too large. The simulations also show that, all other parameters being fixed, a threshold in beam amplitude is required for the onset of PSI in the reflected beam, consistent with results from a previous weakly-nonlinear asymptotic theory for a freely propagating finite-width beam. Growth rates of subharmonic modes at moderate reflected wave amplitude are in reasonable agreement with that theory. However, for $Fr_{r}>0.5$, small scale fluctuations becomes prominent and the subharmonic energy growth rates saturate in the simulations in contrast to the theoretical prediction. Increasing the incoming beam thickness (number of carrier wavelengths) increases the strength of PSI. Keeping the incoming Froude number constant and increasing the incoming Reynolds number by a factor of 50 does not have an effect on the unequal division of frequencies among the subharmonic modes that is found in the simulations.

Application and comparison of stability analysis of slope using circular arc method and strength reduction method

In order to evaluate the accuracy of strength reduction method using FEM, the safety factors of the uniform clay slope and sand slope are investigated by Fellenius’s method, Bishop’s method using traditional limit equilibrium method and strength reduction method respectively. The limit equilibrium method is carried out based on the code for foundations in port engineering and the FE analysis is based on Plaxis3D. The results show that the safety coefficient obtained by strength reduction method of FEM is larger than that obtained by limit equilibrium method and the errors are 6.03% and 1.61% for clay slope and 8.54% and 3.99% for sand slope.

Influence of strength parameters of soil on the slope stability

The stability analysis of uniform clay and sand slope is carried out using traditional limit equilibrium method and strength reduction method. In order to evaluate the influence of strength parameters including friction angle and cohesive strength, the errors among Fellenius’s method, Bishop’s method and strength reduction method are calculated in detail. The results are: 1) the safety factor obtained from Fellenius’s method is smaller than that obtained from Bishop’s method; 2) the error between Bishop’s method and strength reduction method usually firstly increases and then decrease as the friction angle/cohesive strength becomes larger.

Simple Relationships for the Optimal Design of Paired Drip Laterals on Uniform Slopes

AbstractMicroirrigation plants, if properly designed, allow water use efficiency to be optimized and quite high values of emission uniformity to be obtained in the field. It is known that disposing...

Effects of nonlinear failure criterion on the three-dimensional stability analysis of uniform slopes

This paper presents a kinematic approach of limit analysis to evaluate the effects of nonlinear failure criterion on the three-dimensional (3D) stability analysis of uniform slopes. For slopes in various clays, the upper bounds on the critical heights associated with the linear and nonlinear failure criteria are obtained and comparisons of the linear and nonlinear results are made to investigate their differences. The differences between the linear and nonlinear solutions change with varying slope inclination, resulting in two critical values on the slope inclination angle. In the intermediate range of slope inclinations, the critical heights associated with the linear failure criterion are smaller than the nonlinear results, and the underestimation by using the linear failure criterion cannot be neglected. For other cases, the analyses based on the linear failure criterion will overestimate the stability of actual slopes obeying the nonlinear failure criterion. Meanwhile, the 3D effects have insignificant influences on the two critical slope inclination angles. However, the sensitivity of the critical heights to the nonlinearity of soil strength envelope appears to be more pronounced for slopes with a smaller width.

New Software (Multi-flowCAD) Development for Sub-Main Line Hydraulic Design: Computational Algorithm, Computer Visualization and Implementation

Hydraulic design of multiple outlets sub-mains in a distribution network system, often referred to as manifolds, laterals or gated pipes, which are extensively used in practice, has been a major problem tackled by many authors. The increasing progress in computer technology has led to the development of the improved solutions of analytical and numerical methods. This paper aims to present the new software simulation model based on the stepwise computation algorithm with software application. This model is based on discrete nonuniform outflow distribution approach for evaluating different forms of pressure head-discharge distributions along the sub-main line. In the procedure, the required hydraulic flow characteristics along the energy-grade line, the velocity head change and variation of the Reynolds number, which affects the selection of the proper friction coefficient formula to be applied along the different reaches of the pipeline, are sensitively determined. Based on certain hydraulic parameters and uniformity criteria, an improved user-friendly computer program in Visual Basic 6.0 language named “Multi-flowCAD” was developed for hydraulic analysis and design of multiple outlets sub-main lines. The present computer-aided computing technique was successfully implemented with the highest accuracy for different forms of pressure head profiles covering various design configurations regarding different flow regimes and uniform line slope situations with respect to alternative computing techniques. In professional practice, the present improved software simulation model is the most suitable, because only the basic equations of the hydraulics of steady-state pipe flow condition were sensitively used in each pipe section between successive outlets. The present model can be efficiently used for hydraulic analysis and design of various types of multiple outlets pipelines in sub-main distribution networks, for all performed simulations.

Assessment of rock slope stability using GIS-based probabilistic kinematic analysis

Instability in a rock slope is highly dependent on unfavorable orientations of the discontinuities in the rock mass. Therefore, kinematic analysis has been used to analyze the structural condition of unfavorably oriented discontinuities using the stereographic projection method. In this analysis, the orientation of a discontinuity is compared with the slope orientation and friction angle by plotting the orientation of a discontinuity onto a stereonet. This stereonet-based kinematic analysis assumes that a uniform slope orientation and a tightly clustered orientation of the discontinuities exist. However, the slope orientation, represented by the slope aspect and slope angle, cannot be uniform if the slope faces are rugged, as in many natural rock slopes, or if the slope was created by deficient blasting. Moreover, the orientation of discontinuities measured in the field is often scattered, even in a same discontinuity set. However, such variations cannot be included in traditional kinematic analysis and representative values of the slope orientation and mean orientation of a discontinuity are used, which creates uncertainties. To overcome these problems, a GIS-based methodology using grid-based data on the slope orientation data and a probabilistic approach is proposed. To take into account variations in the slope orientation, a digital elevation model (DEM) of the slope face was used and the topographic data of the slope face was derived from the DEM. The slope faces were divided into 2×2m2pixels, and the orientation of the slope face was evaluated based on the grid cells. In addition, the orientation of a discontinuity was treated as a random variable, thereby accounting for natural variability, and a probabilistic analysis approach was adopted to deal with uncertainties and variability. Therefore, a grid-based probabilistic analysis module for the kinematic analysis was developed and used on a cell-by-cell basis to predict instability in spatially distributed slope faces. This probabilistic kinematic analysis was performed in a GIS environment because GIS provides an excellent platform for management and manipulation of raster-based spatial data. We applied this approach to the spatially distributed steep rock slopes in the Baehuryeong area, Korea, located along a tortuous mountain road.

Facies and Sedimentary Environment of the Late Cretaceous Units at Abegarm(Avaj) Area

An investigation was made on the facies and sedimentary environment of upper cretaceous rocks at north west of Abegarm(Avaj) area. This study has also covered carving lime sediments mainly being micritic and sparits with fossil(bioclast) markings, such as: Echinoderm, alga, lamelibransch, brachiopodo and berizoa. Field and microscopic studies led to recognition and separation of 10 carbonate and carving facies as follow: Group of open marine facies that include 1- Bioclastic mudstone, 2- Bioclastic wackstone, 3- Bioclastic packstone, Group of barrier facies that include 4- Bioclastic grainstone, 5- Grainstone packstone, Group of lagoon facies that include 6- Bioclastic packstone, 7- Peloid wackstone Group of continental facies that include, 8- Litharenite, 9- Sublitharenite and 10- Gerywacki. By interpretation and analysis of these microfacies and their related environment we shall be able to recognize the old geographical(palaeobiogeographic) condition in this region which has proven to have been a ramp type carbonate platform with a nearly uniform slope(homodinal ramp).

Separation of upslope flow over a uniform slope

Motivated by the importance of understanding mountain weather during periods of thermal convection, a laboratory study was conducted to investigate the separation of an upslope (anabatic) flow on a two-dimensional heated mountainous slope in the absence of a background mean flow. Three flow regimes were identified. In the first, at slope angles${\it\beta}$larger than a critical value${\it\beta}_{c}\approx 20^{\circ }$, the separated flow generated a rising plume completely fed by the anterior upslope flow. For this case, a simple model based on a balance between the opposing vorticities of baroclinicity and shear was proposed to predict the location of the separation point relative to the mountain base. The model also predicts the velocity and length scales at separation as well as those of the rising plume after separation. In the second regime,$10^{\circ }<{\it\beta}\leqslant {\it\beta}_{c}$, the volume flow of the separated plume was not fully supplied by the upslope flow, requiring entrainment of additional ambient fluid at the base of the plume source. The third regime occurred when${\it\beta}\leqslant 10^{\circ }$, wherein the plume almost completely engulfed the slope, similar to a buoyant plume emanating from a source of finite dimensions, thus overshadowing the upslope flow. Measurements of the separation point conducted during the MATERHORN field research program were consistent with the results of the laboratory experiments and modelling.

Effects of microtopography on spatial point pattern of forest stands on the semi-arid Loess Plateau, China

Microtopography may affect the distribution of forests through its effect on rain redistribution and soil water distribution on the semi-arid Loess Plateau, China. In this study, we investigated the characteristics of microtopography on two shady slopes (slope A, 5 hm2, uniform slope; slope B, 5 hm2, microtopography slope) and surveyed the height, the diameter at breast height and the location (x, y coordinates) of all selected individual trees (Robinia pseudoacacia Linn., Pyrus betulifolia Bunge, Populus hopeiensis Hu & Chow, Armeniaca sibirica Lam., Populus simonii Carr. and Ulmus pumila Linn.) on slope A and slope B in the watersheds of Wuqi county, Shaanxi province. Subsequently, the effects of microtopography on the spatial pattern of forest stands were analyzed using Ripley’s K(r) function. The results showed that: (1) The maximal aggregation radiuses of the tree species on the uniform slope (slope A) were larger than 40 m, whereas those of the tree species on the microtopography slope (slope B) were smaller than 30 m. (2) On slope B, the spatial association of R. pseudoacacia with P. betulifolia, A. sibirica, P. simonii and U. pumila varied from being strongly negative to positive at microtopography scales. The spatial association of Populus hopeiensis Hu & Chow with U. pumila also varied from being strongly negative to positive at microtopography scales. However, there was no spatial association between P. betulifolia and P. hopeiensis, P. betulifolia and A. sibirica, P. betulifolia and P. simonii, P. betulifolia and U. pumila, P. hopeiensis and A. sibirica, P. hopeiensis and P. simonii, A. sibirica and P. simonii, A. sibirica and U. pumila, and P. simonii and U. pumila. On slope A, the spatial association between tree species were strongly negative. The results suggest that microtopography may shape tree distribution patterns on the semi-arid Loess Plateau.

Direct Numerical Simulation of Three-dimensional Gravity Current on a Uniform Slope

Gravity currents occur when fluids of different density are brought together. When gravity currents travel down a uniform slope, buoyancy effects become more important and changes the physical dynamics of its motion. In the present paper, we report data from full three-dimensional direct numerical simulation of gravity currents propagating down a uniform slope. Our data shows that in most cases, the gravity current evolve to a shape that is similar to a triangular wedge. The physical mechanisms leading to formation of this triangular shape and the dynamics of such a structure is presented

An Assessment for Hydraulically Efficient Design of Uniformly Sloping Submain Lines

AbstractDetermining the actual pressure head profiles along the submain lines with a uniform slope is very important for proper hydraulic design of water distribution systems. In practice, there are three general pressure head profiles (Type I, Type II, and Type III) along submain lines depending on different uniform line slope situations. Of all types of pressure profiles, the Type IIb profile is considered the optimal (or ideal) pressure profile which can produce the minimum pressure head difference for a given pipe length. This profile occurs when the total energy loss by friction is just balanced by the total energy gain due to uniform downslope. This paper presents a comprehensive analysis based on the energy–gradient ratio (EGR) approach to identify the optimal (or ideal) pressure profile (Type IIb), to achieve the minimal point of the relative maximum pressure variation, ΦH, which can be defined as the ratio of the maximum allowable pressure head difference (∆Hmax) to the total friction drop (hf(L)). This minimal point is regarded as 'the most efficient pressure profile' or 'ideal hydraulic design' in the existing literature. For this purpose, an illustrative figure (Figure 4) was developed to compare values of the relative maximum pressure variation versus the dimensionless EGR (KS = S0/Sf) for all types of pressure profiles. In this figure, the present ϕH curve versus KS values allows the design engineer to make a decision for the best alternative for selecting the KS value, where for a given pipe slope (S0) the KS value can be selected to meet the minimum pressure variation [KS =1, (ϕH)min =0.36] or the range of pressure variation as close to the minimum point as possible. The present design technique may provide a useful decision support tool for achieving a good design solution among hydraulically possible alternatives with minimal pressure head difference, and results in a higher level of water application uniformity along the multi‐outlet pipeline system. Copyright © 2014 John Wiley & Sons, Ltd.

An analysis of dam-break flow on slope

The one-dimensional steep slope shallow water equations are used to model the dam-break flow down a uniform slope with arbitrary inclination, and analytical solutions are derived by the hodograph transformation and the Riemann's method in terms of evaluated integrals. An implicit analytical solution is obtained to evaluate the spatio-temporal distributions of dam-break flood hydrographs along the slope. For convenience, the solution for representative wave profiles and velocity distributions is shown in charts. Comparing with the Dressler's solution and WES experimental data, the analytical solution is seen reasonable.

New Insights on using Fallout Radionuclides to Estimate Soil Redistribution Rates

The fallout radionuclides such as ¹³⁷Cs have been widely accepted and used in the past 40 yr to provide quantitative soil redistribution estimates at a point scale. Recently their usefulness has been questioned by a few researchers challenging the validity of the key assumption that the spatial distribution of fallout radionuclides in soil is initially uniform. The objective of this work is to reconcile the opposing views by examining the assumption and by developing a new concept for correctly interpreting soil redistribution rates estimated with the tracing technique. This review shows that the spatial uniformity assumption is invalid due to ¹³⁷Cs redistribution caused by spatial variations in rainfall interception, vegetation type and cover, surface residue cover, water infiltration rates, and micro-topography. Thus, the commonly used method of comparing a point ¹³⁷Cs inventory with the reference mean inventory for estimating soil redistribution rate for that point is flawed. Soil redistribution rate estimated for a sampling point is not the true erosion rate because random spatial variation of the radionuclide inventory at the point is erroneously attributed to an effect of soil redistribution. Fortunately, such spatial variations at points are typically random in nature, and therefore can be resolved statistically by increasing independent sample number and by interpreting soil redistribution rate in terms of mean value for a uniform area or slope position, as the random spatial errors of the radionuclide inventories tend to be averaged out.

Building a Pre-Calculated Quick Forecast System for Tsunami Run-Up Height

The main purpose of this study is to build a run-up database using an analytical Green's function of 1D fully nonlinear shallow water equations over a uniform constant slope. The total mechanical energy, tsunami run-up height and inundation distance can be quickly derived once a submarine earthquake occurs. Only fast fourier transformation (FFT), multiplication and superposition are employed in the present algorithm. The in situ investigations of the 2004 Indian Ocean Tsunami and 2011 Tohoku Tsunami are used to validate the present methodology. Most calculated run-up heights are on the safe side and the inundation distance is reasonable. The computational procedure can be efficiently finished within a few seconds so that complete tsunami information can be provided after integrating the existing numerical Green's function database.

Discussion of “Design of Nonzero Uniformly Sloping Laterals in Trickle Irrigation Systems” by Zayani Khemaies, Hammami Moncef, Alouini, Aws, and Souissi Adarrazak

Discussion of “Design of Nonzero Uniformly Sloping Laterals in Trickle Irrigation Systems” by Zayani Khemaies, Hammami Moncef, Alouini, Aws, and Souissi Adarrazak

Discussion of “Stability assessment of slopes with cracks using limit analysis”

The discusser has recently published a paper in Geotechnique titled “Investigation by limit analysis on the stability of slopes with cracks” (Utili 2013) that includes, for the first time (to the discusser’s knowledge), a systematic investigation of the influence of the presence of cracks in uniform slopes for rotational failure mechanisms via the limit analysis upper bound approach. Looking at the discusser’s paper and the paper under discussion (Michalowski 2013), a reader may note that the aim of the two papers is the same, namely, to assess quantitatively the effect of the presence of cracks on the stability of slopes employing the upper bound approach of limit analysis. The discusser’s paper was sent to Geotechnique when the discusser had no knowledge of either the author’s conference paper (Michalowski 2012) or of the paper under discussion published in July 2013. On the other hand, the discusser’s paper was published after the publication of the author’s conference paper (Michalowski 2012). Hence, it can be concluded that the discusser and the author had independently developed an original formulation for the calculation of upper bounds based on rotational failure mechanisms for cracked uniform slopes at similar times.