A complementary approach to quantify the basic GSI chart considering scale effect on rock structure

Geological strength index(GSI)has been widely used as an input parameter in predicting the strength and deformation properties of rock masses.This study derived a series of equations to satisfy the original GSI lines on the basic GSI chart.Two axes ranging from 0 to 100 were employed for surface conditions of the discontinuities and the structure of rock mass,which are independent of the input parameters.The derived equations can analyze GSI values ranging from 0 to 100 within±5%error.The engineering dimensions(EDs)such as the slope height,tunnel width,and foundation width were used together with representative elementary volume(REV)in jointed rock mass to define scale factor(sf)from 0.2 to 1 in evaluating the rock mass structure including joint pattern.The transformation of GSI into a scaledependent parameter based on engineering scale addresses a crucial requirement in various engineering applications.The improvements proposed in this study were applied to a real slope which was close to the time of failure.The results of stability assessments show that the new proposals have sufficient capability to define rock mass quality considering EDs.

Similarity Criterion and Scale Effect for Ship Distortion Model Under Combined Loads

For the ultimate strength model test evaluation of large ship structures, the distortion model with non-uniform ratio between the main size and the plate thickness size is usually adopted. It is the key to carry out scale model test to establish a distortion model similar to the real ship structure under combined load. A similarity criterion for ship distortion model under the combined action of bending moment and surface pressure was proposed, and the scale effect for the criterion was verified by a se ries of numerical analysis and model tests. The results show that the similarity criterion for ship distor tion model under combined loads has a certain scale effect. For the model tests of ship cabin struc tures, it is suggested that the scale range between the plate thickness scale and the main dimension scale should be controlled within 2:1, which can be used as a reference for distortion model design and ultimate strength test of large-scale ship structures.

Size-dependent vibration and buckling of porous functionally graded microplates based on modified couple stress theory in thermal environments by considering a dual power-law distribution of scale effects

In this study,the thermodynamic behaviors of the intrinsic frequency and buckling temperature of rectangular plates of functionally graded materials(FGMs)are explored based on the modified couple stress theory(MCST)and the novel dual powerlaw scale distribution theory.The effects of linear,homogeneous,and non-homogeneous temperature fields on the frequency and buckling temperature of FGM microplates are evaluated in detail.The results show that the porosity greatly affects the mechanical properties of FGM plates,reducing their frequency and flexural temperature compared with non-porous plates.Different temperature profiles alter plate frequencies and buckling temperatures.The presence and pattern of scale effect parameters are also shown to be crucial for the mechanical response of FGM plates.The present research aims to provide precise guidelines for the micro-electro-mechanical system(MEMS)fabrication by elucidating the complex interplay between thermal,material,and structural factors that affect the performance of FGM plates in advanced applications.

Scale dependence of forest fragmentation and its climate sensitivity in a semi-arid mountain:Comparing Landsat,Sentinel and Google Earth data

Landscape fragmentation is generally viewed as an indicator of environmental stresses or risks,but the fragmentation intensity assessment also depends on the scale of data and the definition of spatial unit.This study aimed to explore the scale-dependence of forest fragmentation intensity along a moisture gradient in Yinshan Mountain of North China,and to estimate environmental sensitivity of forest fragmentation in this semi-arid landscape.We developed an automatic classification algorithm using simple linear iterative clustering(SLIC)and Gaussian mixture model(GMM),and extracted tree canopy patches from Google Earth images(GEI),with an accuracy of 89.2%in the study area.Then we convert the tree canopy patches to forest category according to definition of forest that tree density greater than 10%,and compared it with forest categories from global land use datasets,FROM-GLC10 and GlobeLand30,with spatial resolutions of 10 m and 30 m,respectively.We found that the FROM-GLC10 and GlobeLand30 datasets underestimated the forest area in Yinshan Mountain by 16.88%and 21.06%,respectively;and the ratio of open forest(OF,10%<tree coverage<40%)to closed forest(CF,tree coverage>40%)areas in the underestimated part was 2:1.The underestimations concentrated in warmer and drier areas occupied mostly by large coverage of OFs with severely fragmented canopies.Fragmentation intensity of canopies positively correlated with spring temperature while negatively correlated with summer precipitation and terrain slope.When summer precipitation was less than 300 mm or spring temperature higher than 4℃,canopy fragmentation intensity rose drastically,while the forest area percentage kept stable.Our study suggested that the spatial configuration,e.g.,sparseness,is more sensitive to drought stress than area percentage.This highlights the importance of data resolution and proper fragmentation measurements for forest patterns and environmental interpretation,which is the base of reliable ecosystem predictions with regard to the future climate scenarios.

Impact of climate extremes on agricultural water scarcity and the spatial scale effect

Amid the escalating frequency of climate extremes,it is crucial to determine their impact on agricultural water scarcity to preserve agricultural development.Current research does not often examine how different spatial scales and compound climate extremes influence agricultural water scarcity.Using an agricultural water scarcity index(Awsl),this study examined the effects of precipitation and temperature extremes on AwSl across secondary and tertiary river basins in China from 1971 to 2010.The results indicated a marked increase in Awsl during dry years and elevated temperatures.The analysis underscores that precipitation had a greater impact on Awsl than temperature variation.In secondary basins,AwsI was about 26%higher than the long-term average during dry years,increasing to nearly 49%in exceptionally dry conditions.By comparison,in tertiary basins,the increases were 28%and 55%,respectively.In hot years,AwSl rose by about 6.8%(7.3%for tertiary basins)above the average,surging to about 19.1%(15.5%for tertiary basins)during extremely hot periods.These results show that AwSl assessment at the tertiary basin level better captured the influence of climate extremes on Awsl than assessments at the secondary basin level,which highlights the critical importance of a finer spatial scale for a more precise assessment and forecast of water scarcity within basin scales.Also,this study has highlighted the paramount urgency of implementing strategies to tackle water scarcity issues under compound extreme dry and hot conditions.Overall,this study offers an in-depth evaluation of the influence of both precipitation and temperature variation,and research scale on water scarcity,which will help formulate better water resource management strategies.

Scale effect removal and range migration correction for hypersonic target coherent detection

The detection of hypersonic targets usually confronts range migration(RM)issue before coherent integration(CI).The traditional methods aiming at correcting RM to obtain CI mainly considers the narrow-band radar condition.However,with the increasing requirement of far-range detection,the time bandwidth product,which is corresponding to radar’s mean power,should be promoted in actual application.Thus,the echo signal generates the scale effect(SE)at large time bandwidth product situation,influencing the intra and inter pulse integration performance.To eliminate SE and correct RM,this paper proposes an effective algorithm,i.e.,scaled location rotation transform(ScLRT).The ScLRT can remove SE to obtain the matching pulse compression(PC)as well as correct RM to complete CI via the location rotation transform,being implemented by seeking the actual rotation angle.Compared to the traditional coherent detection algorithms,Sc LRT can address the SE problem to achieve better detection/estimation capabilities.At last,this paper gives several simulations to assess the viability of ScLRT.

Scale effect mechanism on micro rod upsetting deformation analyzed by crystal plasticity model

To analyze the effect of single grain deformation behaviors on microforming process, a crystal plasticity model was developed considering grains at free surface layer as single grains. Based on the rate-dependent crystal plasticity theory, the analysis of the scale effect mechanism on upsetting deformation of micro rods was performed with respect to specimen dimension, original grain orientation and its distribution. The results show that flow stress decreases significantly with the scaling down of the specimen. The distribution of the grain orientation has an evident effect on flow stress of the micro specimen, and the effect becomes smaller with the progress of plastic deformation. For the anisotropy of single grains, inhomogeneous deformation occurs at the surface layer, which leads to the increase of surface roughness, especially for small specimens. The effect of grain anisotropy on the surface topography can be decreased by the transition grains. The simulation results are validated by upsetting deformation experiments. This indicates that the developed model is suitable for the analysis of microforming processes with characteristics, such as scale dependency, scatter of flow stress and inhomogeneous deformation.

Scale effects on non-cavitation hydrodynamics and noise of highly-skewed propeller in wake flow

Regarding the scale effects on propeller＇s noncavitation hydrodynamics and hydroacoustics, three similar 7bladed highly-skewed propellers in the wake flow are addressed with diameters of 250, 500 and 1 000 mm, respectively. The discrete line-spectrum noise and its standardized spectrum level scaling law, together with the total sound pressure level are analyzed. The non-cavitation noise predictions are completed by both the frequency domain method and the time domain method. As a fluctuated noise source, the time-dependent fluctuated pressure and normal velocity distribution on propeller blades are obtained by the unsteady Reynolds-averaged Navier-Stokes （ URANS ） simulation. Results show that the pressure coefficient distribution of three propellers on the 0.7R section is nearly superposed under the same advance ratio. The periodic thrust fluctuation of three propellers can exactly reflect the tonal components of the axial passing frequency （APF） and the blade passing frequency （BPF）, and the fluctuation enhancement from the small to the middle propeller at the BPF is greater than that from the middle to the big one. By the two noise prediction methods, the increment of the total sound pressure level from the small to the big propeller differs by 2.49 dB. Following the standardized scaling law, the spectrum curves of the middle and big propellers are nearly the same while significantly differing from the small one. The increment of both the line-spectrum level and the total sound pressure increases with the increase in diameter. It is suggested that the model scale of the propeller should be as large as possible in engineering to reduce the prediction error of the empirical scalin~ law and weaken the scale effects.

Hazard degree identification of goafs based on scale effect of structure by RS-TOPSIS method

In order to precisely predict the hazard degree of goaf(HDG), the RS-TOPSIS model was built based on the results of expert investigation. To evaluate the HDG in the underground mine, five structure size factors, i.e. goaf span, exposed area, goaf height, goaf depth, and pillar width, were selected as the evaluation indexes. And based on rough dependability in rough set(RS)theory, the weights of evaluation indexes were identified by calculating rough dependability between evaluation indexes and evaluation results. Fourty goafs in some mines of western China, whose indexes parameters were measured by cavity monitoring system(CMS), were taken as evaluation objects. In addition, the characteristic parameters of five grades' typical goafs were built according to the interval limits value of single index evaluation. Then, using the technique for order preference by similarity to ideal solution(TOPSIS), five-category classification of HDG was realized based on closeness degree, and the HDG was also identified.Results show that the five-category identification of mine goafs could be realized by RS-TOPSIS method, based on the structure-scale-effect. The classification results are consistent with those of numerical simulation based on stress and displacement,while the coincidence rate is up to 92.5%. Furthermore, the results are more conservative to safety evaluation than numerical simulation, thus demonstrating that the proposed method is more easier, reasonable and more definite for HDG identification.

Evaluation of Spectral Scale Effects in Estimation of Vegetation Leaf Area Index Using Spectral Indices Methods

Spectral index methodology has been widely used in Leaf Area Index(LAI) retrieval at different spatial scales. There are differences in the spectral response of different remote sensors and thus spectral scale effect generated during the use of spectral indices to retrieve LAI. In this study, PROSPECT, leaf optical properties model and Scattering by Arbitrarily Inclined Layers(SAIL) model, were used to simulate canopy spectral reflectance with a bandwidth of 5 nm and a Gaussian spectral response function was employed to simulate the spectral data at six bandwidths ranging from 10 to 35 nm. Additionally, for bandwidths from 5 to 35 nm, the correlation between the spectral index and LAI, and the sensitivities of the spectral index to changes in LAI and bandwidth were analyzed. Finally, the reflectance data at six bandwidths ranging from 40 to 65 nm were used to verify the spectral scale effect generated during the use of the spectral index to retrieve LAI. Results indicate that Vegetation Index of the Universal Pattern Decomposition(VIUPD) had the highest accuracy during LAI retrieval. Followed by Normalized Difference Vegetation Index(NDVI), Modified Simple Ratio Indices(MSRI) and Triangle Vegetation Index(TVI), although the coefficient of determination R^2 was higher than 0.96, the retrieved LAI values were less than the actual value and thus lacked validity. Other spectral indices were significantly affected by the spectral scale effect with poor retrieval results. In this study, VIUPD, which exhibited a relatively good correlation and sensitivity to LAI, was less affected by the spectral scale effect and had a relatively good retrieval capability. This conclusion supports a purported feature independent of the sensor of this model and also confirms the great potential of VIUPD for retrieval of physicochemical parameters of vegetation using multi-source remote sensing data.

Physical modelling and scale effects of air-water flows on stepped spillways

During the last three decades, the introduction of new construction materials (e.g. RCC (Roller Compacted Concrete), strengthened gabions) has increased the interest for stepped channels and spillways. However stepped chute hydraulics is not simple, because of different flow regimes and importantly because of very-strong interactions between entrained air and turbu- lence. In this study, new air-water flow measurements were conducted in two large-size stepped chute facilities with two step heights in each facility to study experimental distortion caused by scale effects and the soundness of result extrapolation to pro- totypes. Experimental data included distributions of air concentration, air-water flow velocity, bubble frequency, bubble chord length and air-water flow turbulence intensity. For a Froude similitude, the results implied that scale effects were observed in both facilities, although the geometric scaling ratio was only Lr=2 in each case. The selection of the criterion for scale effects is a critical issue. For example, major differences (i.e. scale effects) were observed in terms of bubble chord sizes and turbulence levels al- though little scale effects were seen in terms of void fraction and velocity distributions. Overall the findings emphasize that physical modelling of stepped chutes based upon a Froude similitude is more sensitive to scale effects than classical smooth-invert chute studies, and this is consistent with basic dimensional analysis developed herein.

Scale Effects on Propeller Cavitating Hydrodynamic and Hydroacoustic Performances with Non-uniform Inflow

Considering the lack of theoretical models and ingredients necessary to explain the scaling of the results of propeller cavitation inception and cavitating hydroacoustics from model tests to full scale currently, and the insufficient reflection of the nuclei effects on cavitation in the numerical methods, the cavitating hydrodynamics and cavitation low frequency noise spectrum of three geometrically similar 7-bladed highly skewed propellers with non-uniform inflow are addressed. In this process, a numerical bridge from the multiphase viscous simulation of propeller cavitation hydrodynamics to its hydro-acoustics is built, and the scale effects on performances and the applicability of exist scaling law are analyzed. The effects of non-condensable gas（NCG） on cavitation inception are involved explicitly in the improved Sauer＇s cavitation model, and the cavity volume acceleration related to its characteristic length is used to produce the noise spectrum. Results show that, with the same cavitation number, the cavity extension on propeller blades increases with diameter associated with an earlier shift of the beginning point of thrust decline induced by cavitation, while the three decline slopes of thrust breakdown curves are found to be nearly the same. The power of the scaling law based on local Reynolds number around 0.9R section is determined as 0.11. As for the smallest propeller, the predominant tonal noise is located at blade passing frequency（BPF）, whereas 2BPF for the middle and both 2BPF and 3BPF for the largest, which shows the cavitating line spectrum is fully related to the interaction between non-uniform inflow and fluctuated cavity volume. The predicted spectrum level exceedance from the middle to the large propeller is 6.65 dB at BPF and 5.94 dB at 2BPF. Since it just differs less than 2 dB to the increment obtained by empirical scaling law, it is inferred that the scale effects on them are acceptable with a sufficient model scale, and so do the scaling law. The numerical implementation of cavitating hydrodynamics and hydro-acoustics prediction of propeller in big scale in wake has been completed.

Spatial Scale Effects of Water Erosion Dynamics:Complexities, Variabilities, and Uncertainties

Severe water erosion is notorious for its harmful effects on land-water resources as well as local societies. The scale effects of water erosion, however, greatly exacerbate the difficulties of accurate erosion evaluation and hazard control in the real world. Analyzing the related scale issues is thus urgent for a better understanding of erosion variations as well as reducing such erosion. In this review article, water erosion dynamics across three spatial scales including plot, watershed, and regional scales were selected and discussed. For the study purposes and objectives, the advantages and disadvantages of these scales all demonstrate clear spatial-scale dependence. Plot scale studies are primarily focused on abundant data collection and mechanism discrimination of erosion generation, while watershed scale studies provide valuable information for watershed management and hazard control as well as the development of quantitatively distributed models. Regional studies concentrate more on large-scale erosion assessment, and serve policymakers and stakeholders in achieving the basis for regulatory policy for comprehensive land uses. The results of this study show that the driving forces and mechanisms of water erosion variations among the scales are quite different. As a result, several major aspects contributing to variations in water erosion across the scales are stressed: differences in the methodologies across various scales, different sink-source roles on water erosion processes, and diverse climatic zones and morphological regions. This variability becomes more complex in the context of accelerated global change. The changing climatic factors and earth surface features are considered the fourth key reason responsible for the increased variability of water erosion across spatial scales.

Numerical Study on Scale Effect of Form Factor for DTMB5415, KCS,KVLCC2, and 4000TEU Container Ship

Four ships,a twin-propeller naval ship,two single-propeller container ships,and a single-propeller very large crude carrier(VLCC),were studied to investigate the scale effect of the form factor.The viscous flow fields of the ships at different scales were solved numerically via the Reynolds-averaged Navier–Stokes method combined with the shear stress transport k–ωturbulence model.The numerical method was validated through comparisons with experimental data,and numerical uncertainty analysis was carried out based on the ITTC recommended procedure.On this basis,scale effects of the form factor were analyzed using different friction lines,and scale effects of flow fields and the mean axial wake fractions were further analyzed in details.The results showed that the form factor exhibited scale effects when adopting the ITTC-1957 line,and it increased with the increase in the Reynolds number.The scale effect of the form factor reduces the prediction precision of the full-scale ship resistance.The friction line has a significant effect on the form factor.The form factor exhibits little dependence on the Reynolds number when using the numerical friction line or the Katsui line,which is useful for full-scale ship resistance predictions.With the increasing Reynolds number,the boundary layer thickness becomes thinner and the axial velocity contour contracts toward the center plane,and there is nearly a linear relationship between the reciprocal of mean axial wake fraction on propeller disc and Reynolds number in logarithmic scale for the three types of ship forms.

Investigation of acoustic scale effects and boundary effects for the similitude model of underwater complex shell-structure

In this paper, the acoustic scale effects and boundary effects for the similitude model of underwater complex shell-structure are investigated. The similitude conditions and relations between the similitude model and its prototype were studied in the references. This paper investigates the acoustic scale effects for the similitude model, which are influenced by loss factor, shear and rotatory inertia. At the same time, the boundary effects which are influenced by surface sound reflection are investigated in the experiment of similitude model. The results show that the acoustic scale effects may be controlled with model designing, the boundary effects can be controlled with experimental designing between the similitude model and its prototype.

Scale effects of eroded sediment transport in Wujiang River Basin, Guizhou Province, China

In recent years, research on spatial scale and scale transformation of eroded sediment transport has become a forefront field in current soil erosion research, but there are very few studies on the scale effect problem in Karst regions of China. Here we quantitatively extracted five main factors influencing soil erosion, namely rainfall erosivity, soil erodibility, vegetative cover and management, soil and water conservation, and slope length and steepness. Regression relations were built between these factors and also the sediment transport modulus and drainage area, so as to initially analyze and discuss scale effects on sediment transport in the Wujiang River Basin(WRB). The size and extent of soil erosion influencing factors in the WRB were gauged from: Advanced Spaceborne Thermal Emission and Reflection Radiometer Global Digital Elevation Model(ASTER GDEM), precipitation data, land use, soil type and Normalized Difference Vegetation Index(NDVI) data from Global Inventory Modeling and Mapping Studies(GIMMS) or Advanced Very High Resolution Radiometer(AVHRR), and observed data from hydrometric stations. We find that scaling effects exist between the sediment transport modulus and the drainage area. Scaling effects are expressed after logarithmic transformation by a quadratic function regression relationship where the sediment transport modulus increases before decreasing, alongside changes in the drainage area. Among the five factors influencing soil erosion, slope length and steepness increases first and then decreases, alongside changes in the drainage area, and are the main factors determining the relationship between sediment transport modulus and drainage area. To eliminate the influence of scale effects on our results, we mapped the sediment yield modulus of the entire WRB, adopting a 1 000 km^2 standard area with a smaller fitting error for all sub-basins, and using the common Kriging interpolation method.

Delineation and Scale Effect of Precision Agriculture Management Zones Using Yield Monitor Data Over Four Years

In this study, precision agriculture management zones were delineated using yield data over four years from the combine harvester equipped with yield monitor and DGPS receiver. Relative yields measured during each year were interpolated to 4 m2 grid size using ordinary kriging. The resultant interpolated yield maps were averaged across years to create a map of the mean relative yield, which was then used for cluster analysis. The mean yield map of post-classification was processed by applying majority filtering with window sizes that were equivalent to the grid sizes of 12, 20, 28, 36, 44, 52 and 60 m. The scale effect of management zones was evaluated using relative variance reduction, test of significant differences of the means of yield zones, spatial fragmentation, and spatial agreement. The results showed that the post-classification majority filtering （PCMF） eliminated lots of isolated cells or patches caused by random variation while preserving yield means, high variance reduction, general yield patterns, and high spatial agreement. The zoned result can be used as yield goal map for preplant or in-season fertilizer recommendation in precision agriculture.

Model of Polysilicon Electro-thermal Micro Actuator and Research of Micro Scale Effect

A type of crank beam electro-thermal micro actuator was prescribed. Mechanical model of the actuator was established, and the static characteristic was analyzed.Comparing the theoretical analysis with experimental data, it is found that the thermodynamic character of material in micro actuator has a different variable regularity contrasted to that used in macro scale machines. It is the micro scale effect that results in the deviation between the simulating result and experimental results. The thermodynamic expression of polysilicon, which was fitted by means of the experimental data concerned, was used to modify the mechanical model. The modified model, in which the micro scale thermodynamic characteristic was considered, was more reasonable and could make the optimal design and control strategies analyzing the straight-line micro actuator more feasible.

Investigation of scale efect for the computation of turbulent flow around a circular cylinder

In order to investigate the scale effect of turbulent flow around a circular cylinder, two similarity numbers （criteria） based on turbulent kinetic and dissipation rates associ- ated with the fluctuation characteristics of turbulence wake are deduced by analyzing the Reynolds averaged NavierStokes equations （RANS）. The RNG k-s models and finite volume method are used to solve the governing equations and the second-order implicit time and upwind space discretization algorithms are used to discrete the governing equations. A numerical computation of flow parameters around a two-dimensional circular cylinder with Reynolds numbers ranging from 102 to l07 is accomplished and the result indicates that the fluctuation of turbulence flow along the center line in the wake of circular cylinder can never be changed with increasing Reynolds numbers when Re ≥ 3 × 10^6. This conclusion is useful for controlling the scale of numerical calculations and for applying model test data to engineering practice.

Simulation study on fluctuant flow stress scale effect

Crystal plasticity theory was used to simulate upsetting tests of different dimensions and grain size micro copper cylinders in this study on the fluctuant flow stress scale effect. Results showed that with the decrease of billet grain quantity, flow stress fluctuation is not always increased, but there is a maximum. Through this study, the fluctuant flow stress scale effect can be understood deeper, and relevant necessary information was obtained for further prediction and control of this scale effect and to design the microforming process and die.