The effect of expansion ratio on the critical Reynolds number in single fracture flow with sudden expansion

Flow in a single fracture (SF) is an important research subject in groundwater hydrology, hydraulic engineering, radioactive nuclear waste repository and geotechnical engineering. An abruptly changing aperture is a unique type of SF. This study discusses the relation between the values of the critical Reynolds number (Re_c) for the onset of symmetry breaking of flow and the expansion ratio (E) of SF, which is defined as the ratio between the outlet (D) and inlet (d) apertures. This study also investigates the effect of inlet aperture d on Re_c for flow in an SF with abruptly changing apertures (SF‐ACA) using the finite volume method. Earlier numerical and experimental results showed that flow is symmetric in respect to the central plane of the SF‐ACA at small Reynolds number (Re) but becomes asymmetric when Re is sufficiently large. Our simulations show that the value of Re_c decreases with the increasing E, and the relationship between the logarithm of Re_c and E can be described accurately using either a quadratic polynomial function or a logarithmic function. However, the relationship of Re_c and d for a given E value is vague, and Re_c becomes even less sensitive to d when E increases. This study also reveals that the hydraulic gradient (J) and flow velocity (v) follow a super‐linear relationship that can be fitted almost perfectly by the Forchheimer equation. The inertial component (J_i) of J increases monotonically with Re, whereas the viscous component (J_v) of J decreases monotonically with Re. The Re value corresponding to equal inertial and viscous components of J (named as the transitional point Re) decreases when E increases, and such a transitional point Re should be closely related to the critical Reynolds number Re_c, although a rigorous theoretical proof is not yet available. Copyright © 2015 John Wiley & Sons, Ltd.     

Lateral extrusion along the Altyn Tagh Fault,Qilian Shan (NE Tibet): insight from a 3D crustal budget

The lithospheric strike‐slip Altyn Tagh Fault has accommodated hundreds of kilometres of displacement between the Qaidam and Tarim blocks since its Eocene reactivation. However, the way the deformation is accommodated in the Qilian Shan and further east remains uncertain. Based on 360 km of north‐eastward migration of the relatively rigid Qaidam block along the Altyn Tagh Fault and 3D isovolumetric balancing of the crustal deformation within the Altyn Tagh Fault–Qilian Shan system, we demonstrate that 250 ± 28 km (43.8–49.4%) of N20E directed crustal shortening and an additional ~250–370 km of eastward motion of the Qilian Shan crust must be accounted for by strike‐slip faulting in the Qilian Shan and crustal thickening in the Qinling area, as well as by extension in the adjoining North China block graben systems.     

New graphical methods for estimating aquifer hydraulic parameters using pumping tests with exponentially decreasing rates

Actual pumping tests may involve continuously decreasing rates over a certain period of time, and the hydraulic conductivity (K) and specific storage (S_s) of the tested confined aquifer cannot be interpreted from the classical constant‐rate test model. In this study, we revisit the aquifer drawdown characteristics of a pumping test with an exponentially decreasing rate using the dimensionless analytical solution for such a variable‐rate model. The drawdown may decrease with time for a short period of time at intermediate pumping times for such pumping tests. A larger ratio of initial to final pumping rate and a smaller radial distance of the observation well will enhance the decreasing feature. A larger decay constant results in an earlier decrease, but it weakens the extent of such a decrease. Based on the proposed dimensionless transformation, we have proposed two graphical methods for estimating K and S_s of the tested aquifer. The first is a new type curve method that does not employ the well function as commonly done in standard type curve analysis. Another is a new analytic method that takes advantage of the decreasing features of aquifer drawdown during the intermediate pumping stage. We have demonstrated the applicability and robustness of the two new graphical methods for aquifer characterization through a synthetic pumping test.     

Size and spatial distribution of loess slides on the Chinese Loess Plateau

ABSTRACT

The size and spatial distribution of loess slides are important for estimating the yield of eroded materials and determining the landslide risk. While previous studies have investigated landslide size distributions, the spatial distribution pattern of landslides at different spatial scales is poorly understood. The results indicate that the loess slide distribution exhibits a power-law scaling across a range of the size distribution. The mean landslide size and size distribution in the different geomorphic types are different. The double Pareto and inverse gamma functions can coincide well with the empirical probability distribution of the loess slide areas and can quantitatively reveal the rollover location, maximum probability, and scaling exponents. The frequency of loess slides increases with mean monthly precipitation. Moreover, point distance analysis showed that > 80% of landslides are located < 3 km from other loess slides. We found that the loess slides at the two study sites (Zhidan and Luochuan County) in northern Shaanxi Province, China show a significant clustered distribution. Furthermore, analysis results of the correlated fractal dimension show that the landslides exhibit a dispersed distribution at smaller spatial scales and a clustered distribution at larger spatial scales.     

Parallelized combined finite-discrete element (FDEM) procedure using multi-GPU with CUDA

This paper focuses on the efficiency of finite discrete element method (FDEM) algorithmic procedures in massive computers and analyzes the time-consuming part of contact detection and interaction computations in the numerical solution. A detailed operable GPU parallel procedure was designed for the element node force calculation, contact detection, and contact interaction with thread allocation and data access based on the CUDA computing. The emphasis is on the parallel optimization of time-consuming contact detection based on load balance and GPU architecture. A CUDA FDEM parallel program was developed with the overall speedup ratio over 53 times after the fracture from the efficiency and fidelity performance test of models of in situ stress, UCS, and BD simulations in Intel i7-7700K CPU and the NVIDIA TITAN Z GPU. The CUDA FDEM parallel computing improves the computational efficiency significantly compared with the CPU-based ones with the same reliability, providing conditions for achieving larger-scale simulations of fracture.     

Temporal variation of soil erosion resistance on sloping farmland during the growth stages of maize (Zea mays L.)

Maize growth has great effects on soil properties and thus likely induces the changes in soil erosion resistance on sloping farmland. However, temporal variation of soil erosion resistance during the growth stages of maize is still unclear in the mountainous yellow soil area where maize is the dominant crop. In this study, four maize plots (MP) and four bare land plots (CK) were conducted to investigate soil erosion resistance, and multiple indicators of soil erosion resistance were measured including the total soil anti-scourability (TAS), mean weight diameter (MWD), soil erodibility K factor and soil shear strength (SH). A comprehensive soil erosion resistance index (CSERI) was employed to quantify the temporal variation of soil erosion resistance during the growth stages of maize (seedling stage, SS; jointing stage, JS; tasselling stage, TS; maturing stage, MS). The results showed that TAS, MWD, SH increased significantly with maize growth and SH decreased when at MS. But K factor decreased significantly over time. CSERI increased significantly during the growth stages of maize and the CSERI of JS, TS, MS increased on average by 74.72, 180.68 and 234.57% than that of SS. Compared to CK, CSERI of MP increased by 49.90, 66.82, 55.60 and 38.61% during the growth stages of maize. The temporal variation of soil erosion resistance was closely related to the changes in maize cover, maize roots and soil organic carbon. The findings demonstrated that it is necessary to consider the temporal variation of soil erosion resistance in the mountainous yellow soil area.