Аnalysis of methods of calculating road structures based by shear resistance in the soil

Introduction. Checking the soil of the subgrade and the layers of road pavement made of loosely cohesive materials by shear resistance is one of the three mandatory conditions for calculating road clothing according to strength criteria. The methodology for checking the soil of the subgrade and the sandy layers of the road pavement is constantly being modified, which is why changes concerning certain calculation details appear in each new version of the regulatory document. The purpose of this work is to analyze the advantages of the classical solution of A.M. Krivissky and to reveal the essence of the errors made in subsequent modifications of this calculation.Materials and methods. The analysis of solutions is carried out from the standpoint of compliance with the basics of mechanics. It is shown that the calculation of the total shear stress in the classical solution of A.M. Krivissky is performed in accordance with the principle of force superposition, which consists in calculating the components of the stress tensor from each force (time load and the own weight of the layer materials) separately, followed by summing the corresponding components. In this case, the active shear stresses from the temporary load and the own weight of the materials are calculated as the equivalent stress of the Mohr-Coulomb criterion. The calculation of these two components of the total shear stress is performed at the same value of the internal friction angle. Since the angle of inclination of the sliding surface to the main axes is determined by the sum or difference of 45 degrees and half of the internal friction angle, the tangential and normal stresses, which are components of the active shear stress, both from the temporary load and the own weight of the materials, are determined for the same shear surface rotated to the main axes at the same angle. In the current normative calculations, the active shear stresses from the temporary load and the own weight of the materials are determined at different angles of internal friction. This means that the active shear stresses from the temporary load and the own weight of the materials act on two different shear surface rotated to the main axes at different angles. Such stresses cannot be summed up or compared with each other. In addition to this error of the normative calculation methods, their other disadvantages are given.Results. As a result of a detailed analysis of the known modifications of the classical solution, obvious contradictions to the principles of continuum mechanics are established. As an alternative to modern calculation criteria for shear resistance, the article presents criteria for soil strength in which the shear stress exceeds the equivalent stress in the Mohr-Coulomb criterion. The principle of deducing formulas for calculating the first critical load and the total shear stress from the strength criteria under consideration is shown.Conclusion. Conclusions are drawn about the need to return to the classical solution obtained by specialists of the Leningrad School of the USSR, or to develop a fundamentally new solution based on a new plasticity condition in which the total shear stress exceeds the similar characteristic of the stress state of the original Mohr - Coulomb criterion.

Comprehensive shear stress analysis of turbulent boundary layer profiles

Motivated by the need for accurate determination of wall shear stress from profile measurements in turbulent boundary layer flows, the total shear stress balance is analysed and reformulated using several well-established semi-empirical relations. The analysis highlights the significant effect that small pressure gradients can have on parameters deduced from data even in nominally zero pressure gradient boundary layers. Using the comprehensive shear stress balance together with the log-law equation, it is shown that friction velocity, roughness length and zero-plane displacement can be determined with only velocity and turbulent shear stress profile measurements at a single streamwise location for nominally zero pressure gradient turbulent boundary layers. Application of the proposed analysis to turbulent smooth- and rough-wall experimental data shows that the friction velocity is determined with accuracy comparable to force balances (approximately 1 %–4 %). Additionally, application to boundary layer data from previous studies provides clear evidence that the often cited discrepancy between directly measured friction velocities (e.g. using force balances) and those derived from traditional total shear stress methods is likely due to the small favourable pressure gradient imposed by a fixed cross-section facility. The proposed comprehensive shear stress analysis can account for these small pressure gradients and allows more accurate boundary layer wall shear stress or friction velocity determination using commonly available mean velocity and shear stress profile data from a single streamwise location.

Turbulent structure inside and above shallow to deep canopies

Multi-plane PIV measurements were performed in an open-channel flume filled with elongated prisms of height k and width l to investigate the effect of the deepening of the canopy on the flow structure. Velocity measurements were performed both inside the canopy and above it. Analysis of the spatial convergence for the double-averaged quantities shows that for canopy flow investigations (z < k), at least 5 measurement planes are required to obtain a relative spatial convergence error below 3% for the dispersive shear stress, the quantity the most sensible to spatial sampling. With only three measurement planes, the spatial convergence is below 1% only in the flow region above the canopy (z > k). Three canopy aspect ratios, k/l = [1, 3, 6] were investigated for a fixed modified-submergence ratio β = (h - k)=l = 3 where h is the water depth. As the canopy deepens, the hydraulic roughness decreases and the velocity near the bottom of the canopy becomes gradually constant, as expected for deep canopies. We show how the highly converged (both in space and time) profiles of double-averaged longitudinal velocity and total shear stress can be used to calculate the vertical distribution of drag in the canopy. With this methodology, values of the drag coefficient CD(z) can be calculated, and are found to be always close to unity, even in the upper part of the canopy.

Establishing the generality of three phenomena using a boundary layer with free-stream passing wakes

Direct numerical simulation was performed on an incompressible, smooth flat-plate boundary layer at unit molecular Prandtl number and constant surface temperature under free-stream periodically passing turbulent planar wakes over the momentum thickness Reynolds number range of 80 ≤ Reθ ≤ 1850. This inhomogeneous free-stream wake perturbation source with mean deficit differs markedly from the isotropic turbulent patch used in the previous studies of Wu & Moin (J. Fluid Mech., vol. 630, 2009, p. 5; Phys. Fluids, vol. 22, 2010, 085105). Preponderance of hairpin vortices is observed in both the transitional and turbulent regions of the boundary layer. In particular, the internal structure of merged turbulent spots is a hairpin forest; the internal structure of infant turbulent spots is a hairpin packet. Although more chaotic in the turbulent region, numerous hairpin vortices are readily detected in both the near-wall and outer regions of the boundary layer up to Reθ = 1850. This suggests that the hairpin vortices in the higher-Reynolds-number region are not simply the aged hairpin forests convected from the upstream transitional region. Temperature iso-surfaces in the companion thermal boundary layer are found to be a useful tracer in identifying boundary-layer hairpin vortex structures. Total shear stress overshoots wall shear stress in the transitional region and the excess relaxes gradually in the downstream turbulent region. This overshoot is shown to be associated with a localized streamwise acceleration of the streamwise velocity component. Breakdown of the wake-perturbed laminar boundary layer is closely related to the formation of hairpin packets out of quasi-streamwise vortices. Mean and second-order statistics are in good agreement with previous data on the standard turbulent boundary layer. Downstream of transition, normalized root-mean-square (r.m.s.) wall-shear-stress intensity shows almost no variation with Reθ, whereas normalized r.m.s. wall-pressure intensity increases slightly. Taken together with the previous results of Wu & Moin, the generality of the following three phenomena in quasi-standard boundary layers can be reasonably established, namely, preponderance of hairpin vortices in the transitional as well as in the turbulent regions up to Reθ = 1850, transitional total shear stress overshoot, and a laminar-layer breakdown process closely tied to the formation of hairpin packets.

Mechanism for initiating secondary currents in channel flows

This study investigates the underlying mechanisms that initiate secondary flow in developing turbulent flow along a corner. This is done by theoretical examination of the total shear stress, which is the time-averaged product of instantaneous streamwise velocity U and the velocity Vn normal to the interface. The study shows that lines of zero total shear stress exist in the flow region, which delineate the region of secondary flow. Therefore, the flow region is dividable and eight vortices occur in a duct flow. The theoretical and experimental results show that the division line, separating the neighboring secondary currents in a corner, is not always identical to the bisector of the corner, but deviates from the corner bisector if the aspect ratio is b/h ≠ 1. By simplifying Reynolds equation in the near-bed region, we find that theoretically a lateral variation of streamwise velocity initiates the wall-tangent flow that drives the vortex in the region bounded by zero total shear stress. A simplified method for estimating the vortex center, near-bed secondary velocity, and shape of secondary currents has been proposed, and a good agreement between the measured and predicted features is achieved.

Determination of Total Shear Stress and Polymer Stress Profiles in Drag Reduced Boundary Layer Flows With Polymer Injection

Two methods of recovering the entire total shear stress profile from incomplete velocity data in turbulent boundary layers are presented and validated for both DNS simulations and experimental measurements. The first method, an exponential-polynomial curve fit, recovers the whole total shear stress profile well by using the data from the outer part of the boundary layer (y/δ > 0.3). However, this curve fit is sensitive to the quality of the data. The second method, a new (1−y) weighted straight line fit, which is very simple and accurate, has been applied to current experiments of drag reduction in zero pressure gradient turbulent boundary layers with polymer injection. The total shear stress profile obtained from this fit is used to estimate the contribution of the polymer stress to the total shear stress.

Drag and shear stress partitioning in sparse desert creosote communities

Most research to characterize the wind-erosion susceptibility and the degree of surface roughness required to suppress erosion on erodible surfaces has been empirical. However, a recently proposed shear velocity ratio model attempts to place shear stress partitioning in an entirely theoretical framework. The purpose of this study was to directly measure components of shear stress in a sparsely vegetated environment in order to evaluate the model. For the field study, new instrumentation was developed to measure drag on a creosote shrub, and Irwin sensors were modified to measure surface shear stress in the field. Simultaneous measurements of total shear stress and surface shear stress were taken at four sites of different roughness densities, in the Eldorado Valley, Nevada. Results indicate that porous shrubs had greater drag coefficients (Cd = 0.485) than did solid elements (sphere Cd = 0.3) and are more effective at protecting a surface. Values of β, the ratio of element to surface drag coefficients, were therefore higher than previously published values. Surface and total shear stress scaled consistently with each other at a range of wind speeds, and varied according to the roughness density of the surface. Shear stress partitioning values agreed well with previously published field data and some wind-tunnel data. The theoretical model predicted the results successfully when m = 0.16, where m is an empirical constant that accounts for the difference in average stress and the maximum surface stress in initiating erosion. The wide applicability of the model is likely due to the inclusion of the adjustable m, which accommodates all values of β and σ (ratio of roughness element basal area to frontal area).

Structure of Turbulence Close to the Interface in the Liquid Phase of a Co-Current Stratified Two-Phase Flow

Turbulence data are presented which were measured by hot-film anemometry in the liquid phase of a two-phase co-current stratified flow of air and water in a rectangular channel. Mean velocity profiles, u', v', and u' v' intensity distributions were measured across the liquid phase, with special attention being given to the vicinity of the interface. Distributions of total shear stress, eddy viscosity and turbulent energy have been calculated.

The effect of pressure gradient on the law of the wall in turbulent flow

The effect of a streamwise pressure gradient on the velocity profile in the viscous sublayer of a turbulent flow along a smooth wall in two-dimensional flow is estimated. In the analysis, a similarity argument is used and the necessary empirical information obtained from a constant pressure flow. An allowance is made for the departure from the wall value of the gradient of total shear stress normal to the wall. The results of analysis were used to generate new additive constants for use with Townsend's modified law of the wall velocity profile and subsequently Townsend's profile is found to be in good agreement with the measured velocity profiles in an adverse pressure gradient.