DARCY'S COEFFICIENT OF PERMEABILITY AS SYMMETRIC TENSOR OF SECOND RANK

Synopsis

The dynamic equation of motion that governs the laminar flow of water through soils is the empirical equation of Darcy. According to Darcy's equation the velocity of the flowing water is proportional to the hydraulic gradient under which the water is flowing, with the constant of proportionality being the coefficient of permeability. The interesting question arising is whether or not the coefficient of permeability is a scalar quantity (having only a magnitude) or a vector (having both magnitude and direction). It is proved, in the present paper, that the permeability coefficient is neither a scalar nor a vector but a symmetric tensor of second rank. The fact that the permeability tensor is symmetric gives rise to great simplifications and permits a simple graphical construction of the tensor ellipsoid. Having the tensor ellipsoid, the determination of the direction at which the water will flow under a known imposed hydraulic gradient can be found graphically. In case of isotropic soils (the permeability coefficient has the same value along any direction) the ellipsoid reduces to a sphere and the tensor becomes a scalar. In the general case of anisotropic soils the permeability tensor is an entity with nine elements, six of which are independent representing pure extension or contraction along the three principal coordinate axes, thus transforming the permeability sphere into an ellipsoid and vice versa. It should be noted that in anisotropic soils the only directions along which the flow takes place in the direction of the hydraulic gradient are those of the principal axes of the tensor ellipsoid.

Permeability tests were conducted on anisotropic sandstone samples taken at different directions with respect to rectangular coordinates. The permeability coefficient values plotted on a two-dimensional polar coordinate graph paper give rise to an ellipse substantiating therefore the tensor concept of the permeability coefficient. The graphical construction of the tensor ellipse and the use of it in order to obtain the direction of flow by knowing the direction of the hydraulic gradient is also shown.     

The sediment delivery ratio in a small catchment in the black soil region of Northeast China

The black soil region of northeast China,which covers the Provinces of Heilongjiang,Jilin and the Inner Mongolia autonomous region with black soil,chernozem and meadow soil,has experienced soil erosion since intense agricultural reclamation began approximately 100 years ago.However,the sediment delivery ratio,defined as the fraction of gross erosion that is transported from a given area in a given time interval,is still unclear.In this study,we calculated the delivery ratio and analysed changes in erosive processes within Hebei catchment from 1977 to 2007 based on an analysis of sediments of the Liudui reservoir.The original vegetation layer clearly identified the bottom of the reservoir when it was constructed in 1977;thus,the reservoir sediments could be precisely dated.The delivery ratio,calculated by comparing the sediment deposition in the reservoir with the total soil erosion in the upstream catchment,was found to be exponentially correlated（r² = 0.95,P < 0.01） with decreasing grain size,except for the fraction <0.002 mm.The delivery ratio for the clays（<0.002 mm） was low,averaging 0.10 during the study period, which indicated partial removal of clays from the reservoir.The changes in the reservoir deposition rate reflected the temporal changes in the erosion processes.The exceptionally high rainfall in 1998 was confirmed by the distributions of ¹³⁷Cs,²¹⁰Pb,and the grain-size of the sediments.Beginning from the position of the original grass layer,we defined three periods from 1977 to 2007 based on deposition rates:2.40 cm year^-1 from 1977 to 1997,5.60 cm year^-1 in 1998 due to unusually high rainfall,and 1.55 cm year^-1 from 1999 to 2007.The overall average deposition rate for the entire period was 2.26 cm year^-1.Precipitation was found to be the main factor affecting the soil erosion of the study area.     

Tectonic and climatic controls on late Quaternary bajada sedimentation along Narmada-Son Fault(NSF),Gujarat,Western India

An alluvial bajada has been recognized along a part of the active Narmada-Son Fault(NSF) and confined by the Karjan River on the eastern side and by the Madhumati River on western side.The bajada sequence exposed along the incised cliffs of various north flowing parallel streams has been studied in their proximal,medial and distal part. The sediments are characterized on the basis of grain size,fabric,sedimentary structures,bed geometry and sorting, and lithologs prepared from the mapped cliff sections.Detailed study of sedimentary characteristics,lithofacies analysis and facies associations indicate that sediments are mainly of three types-sediments that were deposited by debris flows and sediment gravity flows,and as extensive bar deposits.Three major aggredational sequences are recognized.Each sequence is composed of coarsening-upward sequence of proximal facies overlain by fining-upward sequence of distal facies.Coarsening upward sequence record periods of tectonic activity related to uplift along the NSF and fan progradation,whereas fining-upward sequence results from tectonic quiescence periods.The presence of rhizocretions,calcium carbonate nodules and calcite sheets within the basal debris flow and sediment gravity flow indicate semi-arid climate,whereas the formation of pedoginized paleosol indicate relatively wetter climate prevailing in the study area.Tectonic activity along the NSF has played dominant role by controlling the geometry and volume of bajada sediments.Climate is found to be responsible for compositional and temporal distribution of bajada sediments.OSL dating suggests that the bajada sediments were deposited during the later part of late Pleistocene.The incision of the sediments is attributed to uplift due to inversion of the lower Narmada basin during the early Holocene.     

3D inversion of gravity data by separation of sources and the method of local corrections: Kolarovo gravity high case study

We present a novel methodology for 3D gravity/magnetic data inversion. It combines two algorithms for preliminary separation of sources and an original approach to 3D inverse problem solution. The first algorithm is designed to separate sources in depth and to remove the shallow ones. It is based on subsequent upward and downward data continuation. For separation in the lateral sense, we approximate the given observed data by the field of several 3D line segments. For potential field data inversion we apply a new method of local corrections. The method is efficient and does not require trial-and-error forward modeling. It allows retrieving unknown 3D geometry of anomalous objects in terms of restricted bodies of arbitrary shape and contact surfaces. For restricted objects, we apply new integral equations of gravity and magnetic inverse problems. All steps of our methodology are demonstrated on the Kolarovo gravity anomaly in the Danube Basin of Slovakia.     

Structure,diversity and stability of two oligochaete communities according to sedimentary inputs in Lake Geneva (Switzerland)

Two oligochaete communities were sampled monthly during one year in two 35 m deep locations of Lake Geneva (Switzerland). Organic sedimentation was lower and less variable in station 1 than in station 2 (157 versus 214 g C m⁻²yr⁻¹). The oligochaete community in station 1 was more diverse and more stable (persistent over time) than in station 2, as long as the organic sedimentation was low. Diversity and stability decreased in station 1 when the organic sedimentation increased, and during anOscillatoria bloom. The less diverse community in station 2 was more resistent to these changes. Diversity was associated with environmental stability, but resistance to perturbation was greater in the simpler community which is adapted to changing environmental conditions. The value of oligochaete communities as an indicator of the level of eutrophication was reassessed according to our present data. Changes in the structure of oligochaete communities were related to changes in sedimentation processes.