Effect of roughness on water flow through a synthetic single rough fracture

A single fracture is usually idealized theoretically as smooth parallel plates, but the real fractures are rough-walled with points of contact. Though relative roughness is considered in quantifying the flow through a single rough fracture (SRF) previously, additional factors such as the distribution of rough elements and bending degree of streamlines should be considered in order to obtain more accurate results. Semiempirical friction factor (f) and discharge per unit width (q) equations are first deduced taking relative roughness, roughness elements distribution and streamline reattachment length into consideration. A horizontal SRF model was then set up and a series of experiments and simulations were performed. Main conclusions are drawn: Recirculation of streamlines arises in the rough element and the intensity of the recirculation increases with the angle from which the streamlines enter into the rough elements and Reynolds number (Re); streamlines are discontinuously distributed when asperity height is large and nonlinear flow occurs; the nonlinearity of the flow increases with the increasing the asperity height and Re; the critical value of related roughness used to judge whether the influence of roughness on water flow through a SRF can be ignored or not should be much lower than 0.033; the revised f and q equations under laminar flow through a SRF are proved to be better when calculating the f and q values.     

Friction Factor of Water Flow Through Rough Rock Fractures

Fluid flow through rock joints occurs in many rock engineering applications. As the fluid flows through rough-walled rock fractures, pressure head loss occurs due to friction drag of the wall and local aperture changes. In this study, the friction factor was experimentally investigated by performing flow tests through sandstone fractures with joint roughness coefficient ranging from 5.5 to 15.4 under changing normal stress from 0.5 to 3.5 MPa. According to the experimental results, the friction factor was formulated as a function of two-independent variables—Reynolds number and relative roughness. Relative roughness is defined as the ratio of maximum asperity height to equivalent hydraulic aperture. The experimental results show that the proposed predictor of the friction factor fits the data with a coefficient of determination R ² > 0.93. Sensitivity analyses indicate that in general, the proposed friction factor increases with the relative roughness of confined fractures. The large difference of friction factor induced by relative roughness occurs when the Reynolds number is lower than unity, especially for Re < 0.2. For Reynolds numbers greater than unity, the difference of friction factor induced by relative roughness is smaller. Inclusion of joint roughness in calculating the friction resistance to fluid flow in rough rock joints and the influence of normal stress to the joints is a major step towards more accurate predictions for fluid flow in underground joint networks. This study provides a significant improvement in fundamental understanding of fluid flow in the jointed strata.     

Sedimentation by river-induced turbidity currents: field measurements and interpretation

Turbidity currents, initiated from spring runoffs of an influent river, were observed in the upper region of a reservoir in Hokkaido, Japan, by measuring water temperature, velocity and suspended-sediment concentration. Their profiles offer some physical parameters for the sedimentary conditions, assuming the turbidity currents to be quasi-uniform. The bottom sediment deposited by the turbidity currents was then collected by a portable core sampler. The bottom sediment consists of more than 90% silt and clay, and thus offers a hydraulically smooth bed for shear flow; a plane bed as a bed configuration was formed on the reservoir bed, probably because of the low shear velocity and small grain size of sediment. Using a graphic method with log-normal probability paper, the bottom sediment is divided into several overlapping log-normal subpopulations. Grain-size analysis indicates that the bottom sediment may be regarded as cohesionless; criteria for ‘complete deposition’ of transported grains can then be incorporated into the ‘extended Shields diagram’ giving the minimum shear stress to erode bottom sediment. Applying the new diagram to the grain size distribution of the bottom sediment, it is suggested that each of the log-normal subpopulations was deposited in each of four different ‘modes of deposition’, i.e. ‘traction’, ‘saltation (or intermittent suspension)’, ‘suspension’ and ‘suspension under equilibrium’. The last mode may be observed under a sedimentary condition where upward flux of suspended sediment by eddy diffusion is almost equal to its depositional flux due to gravity. The mean and critical grain sizes for bottom sediment and each of the corresponding subpopulations decrease consistently with an increase of Ψ=F_d² log₁₀Re (F_d is the densimetric Froude number and Re is the flow Reynolds number). Ψ correlates inversely with shear velocity, which bears a linear relationship to mean velocity. These results lead to the conclusion that relatively fine suspended sediment is deposited as a result of decreasing bottom friction with a relative decrease of turbulent energy.     

Experimental study of free-surface flow instability and bedforms in shallow flows

To test erosion and development of bed sculpture in unstable, pulsating shallow flow, three series of experiments were performed in a 10-m flume with flows of Reynolds Number (Re) up to 10³, Froude Number (Fr) up to 3.0, and slope up to 2%. In the first series of experiments (59 runs), the bed was rigid (glass flume-bottom), in the second (50 runs) and third (10 runs) series, planar beds were made from well-sorted and poorly sorted sand, respectively. Development of flow surface instability above the rigid bed showed the following stages: smooth surface; small wavelets; well-developed waves; and rough flow. Development of bedform morphology in the second series of tests showed the following sequence: smooth bed; flow-aligned ridge and trough pattern; combined ridge and rhomboid pattern; and rhomboid configuration. In presence of flow instability, ridge patterns form in flows with mean values indicative of laminar-subcritical regime, combined ridge and rhomboid patterns in laminar-supercritical regime, and rhomboid patterns in flows with mean values indicative of transitional turbulent-supercritical regime. The third series of experiments demonstrated transverse segregation of the bed material across the ridges.The results, in line with stability theory, show that laminar and transitional flows already become unstable when $\text{Fr}\text{=}\text{1}\text{2}$ and suggest that pulsations may appear in sheet-floods and overland flow, intensifying erosion and transport of sediment. The precise mechanism of origin of the parent kinematic flow configurations instrumental in generation of the ridge and the rhomboid patterns is not yet clear. It may be related to the mechanism operating in transition and generation of turbulence in parallel flows, or flows with a superimposed fluctuation, but other types of hydrodynamic instability are also possible.     

床面粗糙度和底床渗透率对泥-水界面物质交换特性的影响

泥-水界面物质交换过程对自然水体中污染物的迁移转化起重要作用,粗糙底床界面物质交换过程涉及到床面粗糙度和底床渗透率的影响。通过实验室环形水槽实验测量得到水力粗糙砂质底床条件下界面物质交换通量的定量数据和变化特征,采用参数化方法分析有效扩散系数与其主要影响参数之间的依赖关系。实验结果表明,在实验参数变化范围内,受上覆水平均流速、床面粗糙度和底床渗透率的共同作用,有效扩散系数从水力光滑区、过渡粗糙区至完全粗糙区呈现较为明显的分段变化特征,采用渗透率雷诺数可将有效扩散系数与其主要影响参数的依赖关系进行较为一致的描述。基于双参数(粗糙雷诺数和渗透率雷诺数)分析,确定了不同流动区域的相应阈值以合理表征床面粗糙度和底床渗透率对界面物质交换特性的综合影响。     

床面粗糙度和底床渗透率对泥-水界面物质交换特性的影响

泥-水界面物质交换过程对自然水体中污染物的迁移转化起重要作用,粗糙底床界面物质交换过程涉及到床面粗糙度和底床渗透率的影响。通过实验室环形水槽实验测量得到水力粗糙砂质底床条件下界面物质交换通量的定量数据和变化特征,采用参数化方法分析有效扩散系数与其主要影响参数之间的依赖关系。实验结果表明,在实验参数变化范围内,受上覆水平均流速、床面粗糙度和底床渗透率的共同作用,有效扩散系数从水力光滑区、过渡粗糙区至完全粗糙区呈现较为明显的分段变化特征,采用渗透率雷诺数可将有效扩散系数与其主要影响参数的依赖关系进行较为一致的描述。基于双参数(粗糙雷诺数和渗透率雷诺数)分析,确定了不同流动区域的相应阈值以合理表征床面粗糙度和底床渗透率对界面物质交换特性的综合影响。     

Direct numerical simulation of a turbulent stably stratified air flow above a wavy water surface

The influence of the roughness of the underlaying water surface on turbulence is studied in a stably stratified boundary layer (SSBL). Direct numerical simulation (DNS) is conducted at various Reynolds (Re) and Richardson (Ri) numbers and the wave steepness ka. It is shown that, at constant Re, the stationary turbulent regime is set in at Ri below the threshold value Ri_c depending on Re. At Ri > Ri_c, in the absence of turbulent fluctuations near the wave water surface, three-dimensional quasiperiodical structures are identified and their threshold of origin depends on the steepness of the surface wave on the water surface. This regime is called a wave pumping regime. The formation of three-dimensional structures is explained by the development of parametric instability of the disturbances induced by the surface water in the air flow. The DNS results are quite consistent with prediction of the theoretical model of the SSBL flow, in which solutions for the disturbances of the fields of velocity and temperature in the wave pumping regime are found to be a solution of a two-dimensional linearized system with the heterogeneous boundary condition, which is caused by the presence of the surface wave. In addition to the turbulent fluctuations, the three-dimensional structures in the wave pumping regime provide for the transfer of impulse and heat, i.e., the increase in the roughness of the water–air boundary caused by the presence of waves intensifies the exchange in the SSBL.     

Palaeohydraulics of a tabular,cross-stratified sand in the Brampton Esker,Ontario

Several hydraulic techniques were used to estimate the flow depth (0.3 m) associated with the deposition of a tabular set (micro-delta) of cross-stratified sand in the Brampton esker. The competency of the flow, deduced from both the grain size and structural characteristics of the set, gave a value of approximately 0.65 m/sec for the palaeo-velocity of the flow. Estimates of palaeo-depth and velocity facilitated calculation of the Froude and Reynolds numbers, about 0.38 and 1.24 · 10⁵, respectively. Extrapolation of other parameters included bed shear stress τ₀ (4.50 N/m²), shear velocity U_* (0.067 m/sec), dimensionless Chezy coefficient C/√g (9.7), slope of the energy gradient S(0.00153), Darcy-Weisbach friction factor f(0.085), Manning roughness coefficient n(0.027) and discharge of bed-material load (19 metric tons/day/m). The figures cited are reasonable estimates only. The occurrence of regressive ripples in the bottomset of the micro-delta aided in the hydraulic interpretation. These flow characteristics are only representative of the final stages of deposition at one location on the flank of the esker. The core of the esker was probably deposited under different hydraulic conditions.     

Fine particle deposition to initially starved,stationary, planar beds

Reported here are results from new flume experiments examining deposition and entrainment of inert, silt‐sized particles (with spherical diameters in the range from 20 to 60 μm) to and from planar, impermeable and initially starved beds underlying channel flows. Bed surfaces comprised smooth or fixed sand‐size granular roughness and provided hydraulically smooth to transitionally rough boundaries. Results of these experiments were analysed with a simple model that describes the evolution of vertically averaged concentration of suspended sediment and accommodates the simultaneous delivery to and entrainment of grains from the bed. The rate of particle arrival to a bed diminishes linearly, and the rate of particle entrainment increases by the 5/2 power, as the value of the dimensionless Saffman parameter S = u_*³/g’ν approaches a threshold value of order unity, where u is the conventional friction velocity of the turbulent channel flow, g’ is the acceleration due to gravity adjusted for the submerged buoyancy of individual particles and ν is the kinematic viscosity of the transporting fluid. This transport behaviour is consistent with the notion that non‐cohesive, silt‐sized particles can neither reach nor remain on an impermeable bed under flow conditions where mean lift imposed on stationary particles in the viscous sublayer equals or exceeds the submerged weight of individual particles. Within the size range of particles used in these experiments, particle size and the characteristic size of granular roughness, up to that of medium sand, did not affect rates of dimensionless arrival or entrainment to a significant degree. Instead, a new but consistent picture of fine‐particle transport is emerging. Silt‐sized material, at least, is subject to potentially significant interaction with the bed during intermittent suspension transport at intermediate flow speeds greater than the value required for initiation of transport (ca 20 cm sec^?1) but less than the value (ca 50 cm sec^?1) required by the Saffman criterion ensuring transport in fully passive suspension or, equivalently, ‘wash‐load’.     

Differences in the quality of polishing between sound and weathered granites

Aesthetic characteristics are important when rocks are used as construction materials. Among all the surface finishes available, the polished finish is the one which best enhances the rock attractiveness. Colour (C), roughness (R) and gloss (G) are surface properties usually used to assess the rock polishing. In this research, the CRG properties were assessed in polished samples of three ornamental granites with different textures and physical–mechanical properties, one weathered and two sound. C was evaluated in CIE-L ^* a ^* b ^* and CIE-L ^* C ^* _ab h _ab systems, R with R _a and R _z parameters and G using the 20°, 60° and 85° geometries. The weathered granite presents a noticeable colour variation, especially in the b ^* parameter, while the sound ones have a more homogeneous colour. Sound and more textural homogeneous granites have a low surface roughness and high gloss, which are uniformly distributed. The weathered granite shows a higher surface roughness and lower gloss, with scattered distribution. The mineral contacts are the main cause of the surface irregularities. The results show the interdependence between the CRG properties and stress the importance of the polishing process for enhancing the aesthetic characteristics of the granites. CRG properties could be used for quality control in granite processing plants, thus avoiding noticeable differences in the facades of buildings, particularly when weathered granites are used.     

Method for Quantification of Wear of Sheared Joint Walls Based on Surface Morphology

Roughness and wear evolution of three different joint wall surfaces were characterized using surface roughness and surface wear parameters. Parameters were defined by considering the two components of morphology: waviness (“primary” roughness) and surface roughness (“secondary” roughness). Two surface roughness parameters are proposed: joint interface (or single wall) specific surface roughness coefficient SR _s (0 ≤ SR _s  ≤ 1) for quantifying the amount of “pure” roughness (or specific roughness), and degree of joint interface (or single wall) relative surface roughness DR _r (0 ≤ DR _r  ≤ 0.5). Two further parameters are also proposed in order to quantify the wear of wall surface: joint interface (or single wall) surface wear coefficient Λ_interface, and the degree of joint interface (or single wall) surface wear D _w(interface). The three test specimens were: man-made granite joints with hammered surfaces, man-made mortar joints with corrugated surfaces, and mortar joints prepared from natural rough and undulated schist joint replicas. Shearing under monotonic and cyclic shearing was performed using a computer-controlled bidirectional and biaxial shear apparatus. Joint surface data were measured using a noncontact laser sensor profilometer prior to and after each shear test. Calculation of specific surface roughness coefficient SR _s , and degree of surface wear D _w , indicated that the hammered joint interface with predominant interlocking wears much more (>90%) than the corrugated (27%) and the rough and undulated (23%) joint interfaces having localized interlocking points. The proposed method was also successfully linked to the classical wear theory.     

Changes in velocity profiles at roughness transitions in coarse grained channels

Heterogeneous coarse grained channels are often characterized by local transitions in bed surface roughness. Distinct spatial zones in terms of grain size have been reported, for example sand ribbons and bedload sheets. The transition from areas of finer to coarser grained surface sediment is often abrupt. However, the effects of these transitions on the shape of the velocity profile and associated shear velocity and roughness length estimates have not been investigated in detail in coarse grained channels. This paper therefore examines the combined effects of a sudden change in surface roughness and of superimposed scales of resistancé on the structure of the turbulent boundary layer. Measurements along roughness transitions from smooth to rough beds were conducted in a flume using artificial roughness features and in a natural gravel bed river. Immediately at the transition from a zone of close packed roughness to a rougher section dominated by obstacles superimposed on the more or less uniform roughness surface, boundary shear stress and roughness length increase considerably. Downstream from this transition, velocity profiles become concave upwards. Downstream and upstream sections show significant differences in terms of near bed velocities (deceleration downstream of the transition), velocity gradient and turbulence intensity of the streamwise velocity component. Comparing the mean velocity profiles corresponding to these two different roughness surfaces gives some indication of the proportion of total shear velocity (or shear stress) associated with the pressure drag produced by large and isolated obstacles.     

Modified governing equation and numerical simulation of seepage flow in a single fracture with three-dimensional roughness

Roughness and tortuosity influence groundwater flow through a fracture. Steady flow through a single fracture can be described primitively by the well-known Cubic Law and Reynolds equation with the assumption that the fracture is made of smooth parallel plates. However, ignoring the roughness and tortuosity of the fracture will lead to inaccurate estimations of the flow rate. To obtain a more accurate flow rate through a rough fracture, this paper has derived a modified governing equation, taking into account the three-dimensional effect of the roughness. The equation modifies the Reynolds equation by adding correction coefficients to the terms of the flow rates, which are relative to the roughness angles in both the longitudinal and transverse directions. Experiments of steady seepage flow through sawtooth fractures were conducted. The accuracy of the modified equation has been verified by comparing the experimental data and the theoretical computational data. Furthermore, three-dimensional numerical models were established to simulate the steady flow in rough fractures with the triangular, sinusoidal surfaces and the typical joint roughness coefficient (JRC) profiles. The simulation results were compared with the calculation results of the modified equation and the current equations. The comparison indicates that the flow rate calculated by the modified equation is the closest to the numerical result.     

Bearing capacity computation for a ring foundation using the stress characteristics method

The stress characteristics method (SCM) has been used to compute the bearing capacity of smooth and rough ring foundations. Two different failure mechanisms for a smooth footing, and four different mechanisms for a rough footing have been considered. For a rough base, a curvilinear non-plastic wedge has been employed below the footing. The analysis incorporates the stress singularities at the inner as well as outer edges of the ring footing. Bearing capacity factors, N_c, N_q and N_γ are presented as a function of soil internal friction angle (ϕ) and the ratio (r_i/r_o) of inner to outer radii of the footing.     

过渡区动床明渠流的流速分布

利用激光流速仪测量了随水流强度加大松散床面,从定床到具有一定输沙强度的动床流动,试验水流条件均处于过渡区。试验资料分析表明,动床过渡区明渠流的卡门常数小于通常所采用的0.4;水流强度逐渐增大,随着推移质运动量增加,阻力系数有减小再增大的趋势;雷诺应力分布和紊动强度分布规律同光滑明渠流类似。     

Diagnostics for accretion disks around UX Ori stars based on Balmer, Paschen, and Brackett Lines

We have modeled the H_α, H_β, and H_γ (Balmer series), P₁₄ (Paschen series), and Br_γ (Brackett series) hydrogen lines formed in the inner regions of the accretion disk around the Herbig Ae star UX Ori. Our calculations are based on spectra obtained with the Nordic Optical Telescope (NOT) and the IRTF. We computed a grid of non-LTE models for a radiating area in the accretion disk and determined the basic parameters of the lines using the method of Sobolev. Analyzing the theoretical and observed line profiles, equivalent widths, and luminosities, we have estimated the accretion rate and electron-temperature distribution in the inner parts of the accretion disk. The accretion rate of UX Ori is about $\dot M_a = (3 - 10) \times 10^{ - 9} M_ \odot /yr$ , and the temperature distribution is consistent with the power law T(r)=T(r _*)(r/r _*)^?1/n , where the electron temperature near the stellar surface T(r _*) is 15000–20000 K and the power-law index n≈2–3 is about two to three. The resulting value for $\dot M_a $ eliminates problems connected with the application of magnetospheric accretion models to Herbig Ae/Be stars. Another important conclusion is that, at the estimated accretion rate, the energy release is substantially (about two orders of magnitude) lower than the stellar luminosity. Therefore, the optical radiation of UX Ori accretion disks cannot appreciably contribute to the observed variability of these stars, which must be determined mainly by variability in the circumstellar extinction.     

Bearing capacity of foundations on slopes

By applying the lower bound finite element limit analysis in conjunction with non-linear optimisation, the bearing capacity factors, N_c, N_q and N_γ, due to the components of cohesion, surcharge and unit weight, respectively, have been estimated for a horizontal strip footing placed along a sloping ground surface. The variation of N_c, N_q and N_γ with changes in slope angle (β) for different soil friction angle (φ) have been computed for smooth as well as rough strip footings. The analysis reveals that along a sloping ground surface, in addition to N_γ, the factors N_c and N_q also vary considerably with changes in footing roughness. Compared to the smooth footing, the extent of the plastic zone around the footing becomes greater for the rough footing. The results obtained from the analysis are found to compare well with those previously reported in literature.     

Phase-field study of grain boundary tracking behavior in crack-seal microstructures

In order to address the growth of crystals in veins, a multiphase-field model is used to capture the dynamics of crystals precipitating from a super-saturated solution. To gain a detailed understanding of the polycrystal growth phenomena in veins, we investigate the influence of various boundary conditions on crystal growth. In particular, we analyze the formation of vein microstructures resulting from the free growth of crystals as well as crack-sealing processes. We define the crystal symmetry by considering the anisotropy in surface energy to simulate crystals with flat facets and sharp corners. The resulting growth competition of crystals with different orientations is studied to deduce a consistent orientation selection rule in the free-growth regime. Using crack-sealing simulations, we correlate the grain boundary tracking behavior depending on the relative rate of crack opening, opening trajectory, initial grain size, and wall roughness. Further, we illustrate how these parameters induce the microstructural transition between blocky (crystals growing anisotropically) to fibrous morphology (isotropic) and formation of grain boundaries. The phase-field simulations of crystals in the free-growth regime (in 2D and 3D) indicate that the growth or consumption of a crystal is dependent on the orientation difference with neighboring crystals. The crack-sealing simulation results (in 2D and 3D) reveal that crystals grow isotropically and grain boundaries track the opening trajectory if the wall roughness is high, opening increments are small, and crystals touch the wall before the next crack increment starts. Further, we find that within the complete crack-seal regime, anisotropy in surface energy results in the formation of curved/oscillating grain boundaries (instead of straight) when the crack-opening velocity is increased and wall roughness is not sufficiently high. Additionally, the overall capability of phase-field method to simulate large-scale polycrystal growth in veins (in 3D) is demonstrated enumerating the main advantages of adopting the novel approach.     

Threshold for particle entrainment into suspension

ABSTRACT Laboratory observations regarding the limit conditions for particle entrainment into suspension are presented. A high‐speed video system was used to investigate conditions for the entrainment of sediment particles and glass beads lying over a smooth boundary as well as over a rough bed. The results extend experimental conditions of previous studies towards finer particle sizes. A criterion for the limit of entrainment into suspension is proposed which is a function of the ratio between the flow shear velocity and particle settling velocity. Observations indicate that particles totally immersed within the viscous sublayer can be entrained into suspension by the flow, which contradicts the conclusions of previous researchers. A theoretical analysis of the entrainment process within the viscous sublayer, based on force–balance considerations, is used to show that this phenomenon is related to turbulent flow events of high instantaneous values of the Reynolds stress, in agreement with previous observations. In the case of experiments with a rough bed, a hiding effect was observed, which tends to preclude the entrainment of particles finer than the roughness elements. This implies that, as the ratio between particle and roughness element sizes becomes smaller, progressively higher bed shear stresses are required to entrain particles into suspension. On the other hand, an overexposure effect was also observed, which indicates that a particle moving on a smooth bed is more prone to be entrained than the same particle moving on a bed formed by identical particles.     

Scour holes and ripples occur below the hydraulic smooth to rough transition of movable beds

Scour holes often form in shallow flows over sand on the beach and in morphodynamic scale experiments of river reaches, deltas and estuarine landscapes. The scour holes are on average 2 cm deep and 5 cm long, regardless of the flow depth and appear to occur under similar conditions as current ripples: at low boundary Reynolds numbers, in fine sand and under relatively low sediment mobility. In landscape experiments, where the flow is only about 1 cm deep, such scours may be unrealistically large and have unnatural effects on channel formation, bar pattern and stratigraphy. This study tests the hypotheses that both scours and ripples occur in the same conditions and that the roughness added by sediment saltation explains the difference between the ripple–dune transition and the clear‐water hydraulic smooth to rough transition. About 500 experiments are presented with a range of sediment types, sediment mobility and obstructions to provoke scour holes, or removal thereof to assess scour hole persistence. Most experiments confirm that ripples and scour holes both form in the ripple stability field in two different bedform stability diagrams. The experiments also show that scours can be provoked by perturbations even below generalized sediment motion. Moreover, the hydraulic smooth to rough transition modified with saltation roughness depending on sediment mobility was similar in magnitude and in slope to ripple–dune transitions. Given uncertainties in saltation relations, the smooth to rough transitions modified for movable beds are empirically equivalent to the ripple–dune transitions. These results are in agreement with the hypothesis that scours form by turbulence caused by localized flow separation under low boundary Reynolds numbers, and do not form under generalized flow separation over coarser particles and intense sediment saltation. Furthermore, this suggests that ripples are a superposition of two independent forms: periodic bedforms occurring in smooth and rough conditions plus aperiodic scours occurring only in hydraulic smooth conditions.