994 resultados para Sand Bed


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The particle size of the bed sediments in or on many natural streams, alluvial fans, laboratory flumes, irrigation canals and mine waste deltas varies exponentially with distance along the stream. A plot of the available worldwide exponential bed particle size diminution coefficient data against stream length is presented which shows that all the data lie within a single narrow band extending over virtually the whole range of stream lengths and bed sediment particle sizes found on Earth. This correlation applies to both natural and artificial flows with both sand and gravel beds, irrespective of either the solids concentration or whether normal or reverse sorting occurs. This strongly suggests that there are common mechanisms underlying the exponential diminution of bed particles in subaerial aqueous flows of all kinds. Thus existing models of sorting and abrasion applicable to some such flows may be applicable to others. A comparison of exponential laboratory abrasion and field diminution coefficients suggests that abrasion is unlikely to be significant in gravel and sand bed streams shorter than about 10 km to 100 km, and about 500 km, respectively. Copyright (C) 1999 John Wiley & Sons, Ltd.

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This paper presents the shaking table studies to investigate the factors that influence the liquefaction resistance of sand. A uniaxial shaking table with a perspex model container was used for the model tests, and saturated sand beds were prepared using wet pluviation method. The models were subjected to horizontal base shaking, and the variation of pore water pressure was measured. Three series of tests varying the acceleration and frequency of base shaking and density of the soil were carried out on sand beds simulating free field condition. Liquefaction was visualized in some model tests, which was also established through pore water pressure ratios. Effective stress was calculated at the point of pore water pressure measurement, and the number of cycles required to liquefy the sand bed were estimated and matched with visual observations. It was observed that there was a gradual variation in pore water pressure with change in base acceleration at a given frequency of shaking. The variation in pore water pressure is not significant for the range of frequency used in the tests. The frequency of base shaking at which the sand starts to liquefy when the sand bed is subjected to any specific base acceleration depends on the density of sand, and it was observed that the sand does not liquefy at any other frequency less than this. A substantial improvement in liquefaction resistance of the sand was observed with the increase in soil density, inferring that soil densification is a simple technique that can be applied to increase the liquefaction resistance.

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Based on similarity analyses, a series of experiments have been conducted with a newly established hydro-elastic facility to investigate the transverse vortex-induced vibrations (VIVs) of a submarine pipeline near an erodible sandy seabed under the influence of ocean currents. Typical characteristics of coupling processes between pipe vibration and soil scour in the currents have been summarized for Case 1: pipe is laid above seabed and Case 11: pipe is partially embedded in seabed on the basis of the experimental observations. Pipe vibration and the corresponding local scour are usually two coupled physical processes leading to an equilibrium state. The influence of initial gap-to-diameter ratio (e(0)/D) on the interaction between pipe vibration and local scour has been studied. Experimental results show that the critical values of V-r for the initiation of VIVs of the pipe near an erodible sand bed get bigger with decreasing initial gap-to-diameter ratio within the examined range of e(0)/D (-0.25 < e(0)/D < 0.75). The comparison of the pipe vibrations near an erodible soil with those near a rigid boundary and under wall-free conditions indicates that the vibration amplitudes of the pipe near an erodible sand bed are close to the curve fit under wall-free conditions; nevertheless, for the same stability parameter, the maximum amplitudes for the VIV coupled with local scour increase with the increase of initial gap-to-diameter ratio. (c) 2007 Elsevier Ltd. All rights reserved.

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Ordos Basin is a typical cratonic petroliferous basin with 40 oil-gas bearing bed sets. It is featured as stable multicycle sedimentation, gentle formation, and less structures. The reservoir beds in Upper Paleozoic and Mesozoicare are mainly low density, low permeability, strong lateral change, and strong vertical heterogeneous. The well-known Loess Plateau in the southern area and Maowusu Desert, Kubuqi Desert and Ordos Grasslands in the northern area cover the basin, so seismic data acquisition in this area is very difficult and the data often takes on inadequate precision, strong interference, low signal-noise ratio, and low resolution. Because of the complicated condition of the surface and the underground, it is very difficult to distinguish the thin beds and study the land facies high-resolution lithologic sequence stratigraphy according to routine seismic profile. Therefore, a method, which have clearly physical significance, based on advanced mathematical physics theory and algorithmic and can improve the precision of the detection on the thin sand-peat interbed configurations of land facies, is in demand to put forward.Generalized S Transform (GST) processing method provides a new method of phase space analysis for seismic data. Compared with wavelet transform, both of them have very good localization characteristics; however, directly related to the Fourier spectra, GST has clearer physical significance, moreover, GST adopts a technology to best approach seismic wavelets and transforms the seismic data into time-scale domain, and breaks through the limit of the fixed wavelet in S transform, so GST has extensive adaptability. Based on tracing the development of the ideas and theories from wavelet transform, S transform to GST, we studied how to improve the precision of the detection on the thin stratum by GST.Noise has strong influence on sequence detecting in GST, especially in the low signal-noise ratio data. We studied the distribution rule of colored noise in GST domain, and proposed a technology to distinguish the signal and noise in GST domain. We discussed two types of noises: white noise and red noise, in which noise satisfy statistical autoregression model. For these two model, the noise-signal detection technology based on GST all get good result. It proved that the GST domain noise-signal detection technology could be used to real seismic data, and could effectively avoid noise influence on seismic sequence detecting.On the seismic profile after GST processing, high amplitude energy intensive zone, schollen, strip and lentoid dead zone and disarray zone maybe represent specifically geologic meanings according to given geologic background. Using seismic sequence detection profile and combining other seismic interpretation technologies, we can elaborate depict the shape of palaeo-geomorphology, effectively estimate sand stretch, distinguish sedimentary facies, determine target area, and directly guide oil-gas exploration.In the lateral reservoir prediction in XF oilfield of Ordos Basin, it played very important role in the estimation of sand stretch that the study of palaeo-geomorphology of Triassic System and the partition of inner sequence of the stratum group. According to the high-resolution seismic profile after GST processing, we pointed out that the C8 Member of Yanchang Formation in DZ area and C8 Member in BM area are the same deposit. It provided the foundation for getting 430 million tons predicting reserves and unite building 3 million tons off-take potential.In tackling key problem study for SLG gas-field, according to the high-resolution seismic sequence profile, we determined that the deposit direction of H8 member is approximately N-S or NNE-SS W. Using the seismic sequence profile, combining with layer-level profile, we can interpret the shape of entrenched stream. The sunken lenticle indicates the high-energy stream channel, which has stronger hydropower. By this way we drew out three high-energy stream channels' outline, and determined the target areas for exploitation. Finding high-energy braided river by high-resolution sequence processing is the key technology in SLG area.In ZZ area, we studied the distribution of the main reservoir bed-S23, which is shallow delta thin sand bed, by GST processing. From the seismic sequence profile, we discovered that the schollen thick sand beds are only local distributed, and most of them are distributary channel sand and distributary bar deposit. Then we determined that the S23 sand deposit direction is NW-SE in west, N-S in central and NE-SW in east. The high detecting seismic sequence interpretation profiles have been tested by 14 wells, 2 wells mismatch and the coincidence rate is 85.7%. Based on the profiles we suggested 3 predicted wells, one well (Yu54) completed and the other two is still drilling. The completed on Is coincident with the forecastThe paper testified that GST is a effective technology to get high- resolution seismic sequence profile, compartmentalize deposit microfacies, confirm strike direction of sandstone and make sure of the distribution range of oil-gas bearing sandstone, and is the gordian technique for the exploration of lithologic gas-oil pool in complicated areas.

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Cette thèse examine les impacts sur la morphologie des tributaires du fleuve Saint-Laurent des changements dans leur débit et leur niveau de base engendrés par les changements climatiques prévus pour la période 2010–2099. Les tributaires sélectionnés (rivières Batiscan, Richelieu, Saint-Maurice, Saint-François et Yamachiche) ont été choisis en raison de leurs différences de taille, de débit et de contexte morphologique. Non seulement ces tributaires subissent-ils un régime hydrologique modifié en raison des changements climatiques, mais leur niveau de base (niveau d’eau du fleuve Saint-Laurent) sera aussi affecté. Le modèle morphodynamique en une dimension (1D) SEDROUT, à l’origine développé pour des rivières graveleuses en mode d’aggradation, a été adapté pour le contexte spécifique des tributaires des basses-terres du Saint-Laurent afin de simuler des rivières sablonneuses avec un débit quotidien variable et des fluctuations du niveau d’eau à l’aval. Un module pour simuler le partage des sédiments autour d’îles a aussi été ajouté au modèle. Le modèle ainsi amélioré (SEDROUT4-M), qui a été testé à l’aide de simulations à petite échelle et avec les conditions actuelles d’écoulement et de transport de sédiments dans quatre tributaires du fleuve Saint-Laurent, peut maintenant simuler une gamme de problèmes morphodynamiques de rivières. Les changements d’élévation du lit et d’apport en sédiments au fleuve Saint-Laurent pour la période 2010–2099 ont été simulés avec SEDROUT4-M pour les rivières Batiscan, Richelieu et Saint-François pour toutes les combinaisons de sept régimes hydrologiques (conditions actuelles et celles prédites par trois modèles de climat globaux (MCG) et deux scénarios de gaz à effet de serre) et de trois scénarios de changements du niveau de base du fleuve Saint-Laurent (aucun changement, baisse graduelle, baisse abrupte). Les impacts sur l’apport de sédiments et l’élévation du lit diffèrent entre les MCG et semblent reliés au statut des cours d’eau (selon qu’ils soient en état d’aggradation, de dégradation ou d’équilibre), ce qui illustre l’importance d’examiner plusieurs rivières avec différents modèles climatiques afin d’établir des tendances dans les effets des changements climatiques. Malgré le fait que le débit journalier moyen et le débit annuel moyen demeurent près de leur valeur actuelle dans les trois scénarios de MCG, des changements importants dans les taux de transport de sédiments simulés pour chaque tributaire sont observés. Ceci est dû à l’impact important de fortes crues plus fréquentes dans un climat futur de même qu’à l’arrivée plus hâtive de la crue printanière, ce qui résulte en une variabilité accrue dans les taux de transport en charge de fond. Certaines complications avec l’approche de modélisation en 1D pour représenter la géométrie complexe des rivières Saint-Maurice et Saint-François suggèrent qu’une approche bi-dimensionnelle (2D) devrait être sérieusement considérée afin de simuler de façon plus exacte la répartition des débits aux bifurcations autour des îles. La rivière Saint-François est utilisée comme étude de cas pour le modèle 2D H2D2, qui performe bien d’un point de vue hydraulique, mais qui requiert des ajustements pour être en mesure de pleinement simuler les ajustements morphologiques des cours d’eau.

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Ocean Drilling Program (ODP) Site 1119 is located at water depth 395 m near the subtropical front (STF; here represented by the Southland Front), just downslope from the shelf edge of eastern South Island, New Zealand. The upper 86.19 metres composite depth (mcd) of Site 1119 sediment was deposited at an average sedimentation rate of 34 cm/kyr during Marine Isotope Stages (MIS) 1-8 (0-252 ka), and is underlain across a ~25 kyr intra-MIS 8 unconformity by MIS 8.5-11 (277-367 ka) and older sediment deposited at ~14 cm/kyr. A time scale is assigned to Site 1119 using radiocarbon dates for the period back to ~39 ka, and, prior to then, by matching its climatic record with that of the Vostok ice core, which it closely resembles. Four palaeoceanographic proxy measures for surface water masses vary together with the sandy-muddy, glacial-interglacial (G/I) cyclicity at the site. Interglacial intervals are characterised by heavy delta13C, high colour reflectance (a proxy for carbonate content), low Q-ray (a proxy for clay content) and light delta18O; conversely, glacial intervals exhibit light delta13C, low reflectance, high Q-ray and heavy delta18O signatures. Early interglacial intervals are represented by silty clays with 10-105-cm-thick beds of sharp-based (Chondrites-burrowed), shelly, graded, fine sand. The sands are rich in foraminifera, and were deposited distant from the shoreline under the influence of longitudinal flow in relatively deep water. Glacial intervals comprise mostly micaceous silty clay, though with some thin (2-10 cm thick) sands present also at peak cold periods, and contain the cold-water scallop Zygochlamys delicatula. Interglacial sandy intervals are characterised by relatively low sedimentation rates of 5-32 cm/kyr; cold climate intervals MIS 10, 6 and 2 have successively higher sedimentation rates of 45, 69 and 140 cm/kyr. Counter-intuitively,and forced by the bathymetric control of a laterally-moving shoreline during G/I and I/G transitions, the 1119 core records a southeasterly (seaward) movement of the STF during early glacial periods, accompanied by the incursion of subtropical water (STW) above the site, and northwesterly (landward) movement during late glacial and interglacial times, resulting in a dominant influence then of subantarctic surface water (SAW). The history of passage of these different water masses at the site is clearly delineated by their characteristic delta13C values. The intervals of thin, graded sands-muds which occur within MIS 2-3, 6, 7.4 and 10 indicate the onset at times of peak cold of intermittent bottom currents caused by strengthened and expanded frontal flows along the STF, which at such times lay near Site 1119 in close proximity to seaward-encroaching subantarctic waters within the Bounty gyre. In common with other nearby Southern Hemisphere records, the cold period which represents the last glacial maximum lasted between ~23-18 ka at Site 1119, during which time the STF and Subantarctic Front (SAF) probably merged into a single intense frontal zone around the head of the adjacent Bounty Trough.

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El remonte extremo o remonte del 2% es un parámetro clave en la ingeniería costera dado que permite acometer actuaciones en las playas bajo criterios de sostenibilidad económico y socioambiental. Estas actuaciones van desde el diseño de estructuras en el trasdós de la playa a planes de actuación urbanística en la costa tal que se determine adecuadamente los límites de dominio público. El adecuado diseño de estas actuaciones adquiere más relevancia hoy en día debido a las nuevas amenazas que se ponen de relieve debido al cambio climático, y que en el caso concreto de la costa se materializa en inundaciones que provocan pérdidas económicas. Estudios precedentes han realizado ensayos in situ o en modelo físico para la determinación del remonte extremo en playas. Al comparar estas formulaciones la dispersión es alta lo que implica que la precisión en la obtención del remonte no sea suficiente. Esta dispersión se justifica debido al amplio espectro de playas existentes y la alta variabilidad del clima marítimo. Este problema cobra más relevancia debido a las actuaciones preventivas o correctivas a acometer frente al cambio climático bajo un criterio de sostenibilidad. Con el fin de realizar actuaciones sostenibles bajo el contexto actual del probable aumento de inundaciones costeras por cambio climático no deben obtenerse ni magnitudes sobredimensionadas con el consecuente consumo de recursos y afección a las actividades económicas, ni magnitudes subestimadas que pongan en riesgo la estabilidad y/o la funcionalidad de las actuaciones para un periodo de diseño. El principal objetivo de esta tesis es proponer una formulación de aplicación en la obtención del remonte extremo tal que se cumplan los criterios de seguridad para el servicio y funcionalidad de la obra y los criterios de sostenibilidad económico y socio-ambiental que se requieren hoy en día. Es decir, una fórmula que no sobredimensione el cálculo de este valor pero que pueda cubrir la casuística que acontece en las distintas tipologías de playas. Complementariamente a este objetivo se ejemplifica la aplicación de estas formulaciones en casos reales tal que se reduzca la incertidumbre y ambigüedad en la obtención de las variables independientes de las formulaciones. Para la consecución de estos objetivos se realiza un estado del arte en el que se estudia tanto los estudios estadísticos en la obtención de este parámetro como los modelos numéricos propuestos para ello, tal que se deduzca la mejor línea de investigación en la consecución del fin de esta tesis. Tras este estudio del arte se concluye que la mejor línea de investigación sigue la vía estadística y se diseña un modelo físico con fondo de arena en contraste con modelos físicos con fondo impermeable fijo. Los resultados de dicho modelo se han comparado con las formulaciones precedentes y se proponen las fórmulas de aplicación más convenientes para la obtención del remonte extremo. Complementariamente a la propuesta de formulaciones se desarrolla una metodología de aplicación de dichas formulaciones a casos de la costa española que ejemplifican convenientemente su uso para una adecuada predicción de este valor en las playas. The extreme runup is a key parameter in coastal management. This parameter allows to develop sustainability actions at the coast that meet economical and environmental criteria. At the coast the actions can be either design of structures at the shore or actions plans delimiting reclamation areas. The climate change has given more relevance to accomplish an appropriate design for the coastal management actions. At the coast the threaten are mainly focused on more frequent floods that cause economic losses. Previous studies have carried out field or physical model experiments to accomplish an equation for the extreme runup prediction. Although dispersion remains high when comparing the different proposals so the accuracy in the prediction might be risky. This scattering comes from the wide sort of beaches and the high variability of the maritime climate. The new actions that are needed to develop to counteract the effects of the climate change need a more efficient criteria. Hence formulations should not overestimate or underestimate the values of the extreme runup. The overestimation implies to consume resources that are not needed and the underestimation means in a structure risk to support safely the loads. The main goal of this thesis is to propose a formulation for the extreme runup prediction so the safety of the structure can be accomplished but at the same time the sustainability of the action is ensured under economical and environmental criteria that are demanded nowadays. So the formulation does not overestimate the extreme value but cover with enough confidence the different sort of beaches. The application of the formulation is also explained in order to reduce uncertainty when the input values are obtained. In order to accomplish the goal of this research firstly a literature review is done. Statistical and numerical models are studied. The statistical model is selected as the most convenient research guideline. In order to obtain runup results a physical model with sand bed is carried out. The bed differs from those that used impermeable slope in previous experiments. Once the results are obtained they are compared with the previous equations and a final formulation is proposed. Finally a methodology to apply the deduced formulation to the Spanish beaches is addressed.

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Equations for extreme runup worked out from several experimental studies are compared. Infragraviatory oscillations dominate the swash in a dissipative state but not in intermediate - reflective states. Therefore two kinds of equation depending on either significant wave height, H-0, or the Iribarren number, xi(0), should be used. Through a sand bed physical model with a uniform sand bed slope, equations are proposed for both beach states, and results are compared with precedent field and physical model experiments. Once the equations are chosen, the time-longshore variability in a medium - long term time scale of the foreshore slope is evaluated in two extreme cases relating to the Spanish coast. The Salinas beach on the North coast (Bay of Biscay) displayed a permanent dissipative beach state with small variations in the beach foreshore slope both along the shore and in time, so foreshore slope deviations in a medium-long term period were irrelevant and extreme runup is predicted with the wave height worked out from the design return period. Peniscola beach on the East coast (Mediterranean sea) displayed an intermediate state. If only time variations are analysed, variations in determining extreme runup are irrelevant. In contrast, significant differences were found when the longshore variations were studied in this Mediterranean beach.

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The stratigraphic distribution, assemblage content, paleoecology and age of foraminifera recovered in fourteen of sixteen samples from the 5.63 m thick CRP-2 (Lithostratigraphic Unit 2.2) are discussed. LSU 2.2 comprises four discrete lithologic beds. The upward sequence is informally referred to as the lower sand bed, diamicton bed, middle sand bed, and upper sand bed and it is surmised that these four units are closely related in time. The lower sand bed (~1.5m), which overlies lower Miocene sediments and from which it is separated by the Ross Sea Unconformity, contains traces of recycled Miocene diatoms but is otherwise barren of biogenic material. The diamicton bed (~2.42 m) contains 21 species of benthic foraminifera, with assemblages consistently dominated by Cassidulinoides porrectus, Ammoelphidiella antarctica, Rosalina cf. globularis, Cibicides refulgens, and Ehrenbergina glabra. The overlying middle sand bed (~1.9 m) contains 13 species. with C. porrectus and E. glabra dominant and A. antarctica less common than in the underlying diamicton bed. The upper sand bed (~0.46 m) contains four species and very few tests. The diamicton bed and middle sand bed assemblages are considered to be near in situ thanatocoenoses; and sediments interpreted as marine in origin but influenced by hyposaline waters and nearby ice. Planktic taxa are absent, perhaps indicating the presence of tidewater glaciers, sea ice and/or hyposaline surface waters. The small assemblage in the upper sand bed is more problematic and may be recycled. On the basis of foraminifera in the diamicton and middle sand beds. LSU 2.2 is assigned to the Pliocene. The overlying diamicton in LSU 2.1 contains abundant Quaternary foraminifera.

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In marine environments, sediments from different sources are stirred and dispersed, generating beds that are composed of mixed and layered sediments of differing grain sizes. Traditional engineering formulations used to predict erosion thresholds are however, generally for unimodal sediment distributions, and so may be inadequate for commonly occurring coastal sediments. We tested the transport behavior of deposited and mixed sediment beds consisting of a simplified two-grain fraction (silt (D50 = 55 µm) and sand (D50 = 300 µm)) in a laboratory-based annular flume with the objective of investigating the parameters controlling the stability of a sediment bed. To mimic recent deposition of particles following large storm events and the longer-term result of the incorporation of fines in coarse sediment, we designed two suites of experiments: (1) "the layering experiment": in which a sandy bed was covered by a thin layer of silt of varying thickness (0.2 - 3 mm; 0.5 - 3.7 wt %, dry weight in a layer 10 cm deep); and (2) "the mixing experiment" where the bed was composed of sand homogeneously mixed with small amounts of silt (0.07 - 0.7 wt %, dry weight). To initiate erosion and to detect a possible stabilizing effect in both settings, we increased the flow speeds in increments up to 0.30 m/s. Results showed that the sediment bed (or the underlying sand bed in the case of the layering experiment) stabilized with increasing silt composition. The increasing sediment stability was defined by a shift of the initial threshold conditions towards higher flow speeds, combined with, in the case of the mixed bed, decreasing erosion rates. Our results show that even extremely low concentrations of silt play a stabilizing role (1.4% silt (wt %) on a layered sediment bed of 10 cm thickness). In the case of a mixed sediment bed, 0.18% silt (wt %, in a sample of 10 cm depth) stabilized the bed. Both cases show that the depositional history of the sediment fractions can change the erosion characteristics of the seabed. These observations are summarized in a conceptual model that suggests that, in addition to the effect on surface roughness, silt stabilizes the sand bed by pore-space plugging and reducing the inflow in the bed, and hence increases the bed stability. Measurements of hydraulic conductivity on similar bed assemblages qualitatively supported this conclusion by showing that silt could decrease the permeability by up to 22% in the case of a layered bed and by up to 70% in the case of a mixed bed.

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In mixed sediment beds, erosion resistance can change relative to that of beds composed of a uniform sediment because of varying textural and/or other grain-size parameters, with effects on pore water flow that are difficult to quantify by means of analogue techniques. To overcome this difficulty, a three-dimensional numerical model was developed using a finite difference method (FDM) flow model coupled with a distinct element method (DEM) particle model. The main aim was to investigate, at a high spatial resolution, the physical processes occurring during the initiation of motion of single grains at the sediment-water interface and in the shallow subsurface of simplified sediment beds under different flow velocities. Increasing proportions of very fine sand (D50=0.08 mm) were mixed into a coarse sand matrix (D50=0.6 mm) to simulate mixed sediment beds, starting with a pure coarse sand bed in experiment 1 (0 wt% fines), and proceeding through experiment 2 (6.5 wt% fines), experiment 3 (10.5 wt% fines), and experiment 4 (28.7 wt% fines). All mixed beds were tested for their erosion behavior at predefined flow velocities varying in the range of U 1-5=10-30 cm/s. The experiments show that, with increasing fine content, the smaller particles increasingly fill the spaces between the larger particles. As a consequence, pore water inflow into the sediment is increasingly blocked, i.e., there is a decrease in pore water flow velocity and, hence, in the flow momentum available to entrain particles. These findings are portrayed in a new conceptual model of enhanced sediment bed stabilization.

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Soil porosity is the fraction of total volume occupied by pores or voids measured at matric potential 0. To measure soil porosity, soil samples were taken from each plot using sample rings with an internal diameter of 57 mm and height of 40.5 mm (inner volume of Vs=100 cm3). The samples were placed on a sand bed box with water level set to allow saturation of the samples with water. After 48 h the samples were weighed (ms), oven dried at 105 °C and weighed again to determine the dry weight (md). We calculated soil porosity (n [%]) using the density of water (?w=1 g cm?3), n=100 ? (mw-md) / (?w?Vs). To account for the spatial variation of soil properties, three replicates were taken per plot, approximately 2, 3 and 4 weeks after the flood that occurred at the field site during June 2013. Data are the average soil porosity values per plot. All data where measured in the main experiment plots of a large grassland biodiversity experiment (the Jena Experiment; see further details below). In the main experiment, 82 grassland plots of 20 x 20 m were established from a pool of 60 species belonging to four functional groups (grasses, legumes, tall and small herbs). In May 2002, varying numbers of plant species from this species pool were sown in the plots to create a gradient of plant species richness (1, 2, 4, 8, 16 and 60 species) and functional richness (1, 2, 3, or 4 functional groups). Plots were maintained by bi-annual weeding and mowing.