abstract: The infrastructure is built in Unsaturated Soils. However, the geotechnical practitioners insist in designing the structures based on Saturated Soil Mechanics. The design of structures based on unsaturated soil mechanics is desirable because it reduces cost and it is by far a more sustainable approach. The research community has identified the Soil-Water Characteristic Curve as the most important soil property when dealing with unsaturated conditions. This soil property is unpopular among practitioners because the laboratory testing takes an appreciable amount of time. Several authors have attempted predicting the Soil-Water Characteristic Curve; however, most of the published predictions are based on a very limited soil database. The National Resources Conservation Service has a vast database of engineering soil properties with more than 36,000 soils, which includes water content measurements at different levels of suctions. This database was used in this study to validate two existing models that based the Soil-Water Characteristic Curve prediction on statistical analysis. It was found that although the predictions are acceptable for some ranges of suctions; they did not performed that well for others. It was found that the first model validated was accurate for fine-grained soils, while the second model was best for granular soils. For these reasons, two models to estimate the Soil-Water Characteristic Curve are proposed. The first model estimates the fitting parameters of the Fredlund and Xing (1994) function separately and then, the predicted parameters are fitted to the Fredlund and Xing function for an overall estimate of the degree of saturation. Results show an overall improvement on the predicted values when compared to existing models. The second model is based on the relationship between the Soil-Water Characteristic Curve and the Pore-Size Distribution of the soils. The process allows for the prediction of the entire Soil-Water Characteristic Curve function and proved to be a better approximation than that used in the first attempt. Both models constitute important tools in the implementation of unsaturated soil mechanics into engineering practice due to the link of the prediction with simple and well known engineering soil properties. / Dissertation/Thesis / M.S. Civil and Environmental Engineering 2011

The aim of this thesis is to compare the results of water infiltration from field tests, from laboratories and from numerical modeling at two selected locations. The first objective is the search procedure and the description of both sites and its adjacent areas. Further work continues with infiltration field tests using ring infiltrometer, at first theoretically for each method, and then practically with own personal measurements in the field. Further from the collected soil samples the measurements are performed in the laboratory, first in the permeameter, and followed by the grain size distribution test, from which the hydraulic conductivity is derived by using empirical formulas. At last the numerical modeling is used and all the results are compared. In the final phase of thesis the recommendations are given for infiltration at various locations and comparsion of the infiltration methods.

This licentiate thesis reports analytical results for the electrostatic response to a test charge moving through dusty plasma. Two particular cases for a slowly moving test charge, namely, grain size distribution and grain charging dynamics are considered. Analytical results for the delayed shielding of a test charge due to dynamical grain charging in dusty plasma are also reported. In the first case, a dusty plasma in thermal equilibrium and with a distribution of grain sizes is considered. A size distribution is assumed which decreases exponentially with the grain mass for large sizes and gives a simple smooth reduction for small sizes. The electrostatic response to a slowly moving test charge, using a second order approximation is found and the effects of collisions are also investigated. It turns out that for this particular size distribution, there is a remarkably simple result that the resulting effective distribution for the electrostatic response is a kappa (generalized Lorentzian) distribution. In the second case, we present an analytical model for the shielding of a slowly moving test charge in a dusty plasma with dynamical grain charging for cases both with and without the collision effects. The response potential is treated as a power series in test charge velocity. Analytical expressions for the response potential are found up to second order in test charge velocity. The first-order dynamical charging term is shown to be the consequence of the delay in the shielding due to the dynamics of the charging process. It is concluded that the dynamical charging of the grains in a dusty plasma enhances the shielding of a test charge. To clarify the physics, a separate study is made where the charging is approximated by using a time delay. The resulting potential shows the delayed shielding effect explicitly. The terms in the potential that depend on the charging dynamics involve a spatial shift given by the test charge velocity and the charging time. This kind of work has relevance both in space and astrophysical plasmas. / QC 20101220

The efficiency of multicrystalline (mc) silicon solar cells depends strongly on the fraction of recombination active crystal defects. This work focuses on a systematic analysis of how the area fraction of recombination active crystal defects and thus the solar cell efficiency is af-fected by the grain structure of mc-silicon wafers, i.e. grain size, grain orientation and type of the grain boundaries between adjacent grains. For that purpose a new characterization method was developed which allows the measurement of the grain orientation and grain boundary type of full 156x156 mm² mc-silicon wafers. The results of the grain structure analysis were correlated with the etch pit density, the recombination active area fraction measured by photo-luminescence imaging, and the solar cell efficiency in order to quantify the most important features of the grain structure, which were relevant to obtain high quality mc-silicon wafer material. For the determination of the grain orientation and grain boundary type two metrology sys-tems were combined. The so-called grain detector determines the geometrical data of each grain (size and form) by a reflectivity measurement. Afterwards the wafer with the geomet-rical information of all grains is transferred into the so-called Laue Scanner. This system irra-diates each grain larger 3 mm² with white x-rays and creates a backscatter diffraction pattern (Laue pattern) for each grain. From this Laue pattern the grain orientation and the grain boundary type of neighboured grains is calculated and statistically analysed in combination with the geometrical data of the grain detector. In this work the grain structure of twelve industrially grown mc-silicon bricks, which were produced by different manufacturers, and two laboratory grown bricks were investigated. Seven of these bricks show a fine grain structure. This material named class F is considered to be typical for so-called High Performance Multi (HPM) silicon. The other bricks show a coarse-grained structure. This grain structure was called class G and corresponds to the con-ventional mc-silicon material. The results show that the grain structures of the start of the crystallization process differ sig-nificantly between class F and class G. The class F mc-silicon wafers have a uniform initial grain size (characterized by coefficient of variation CV¬KG < 2.5) and grain orientation (charac-terized by coefficient of variation CVKO < 1.5) distribution with a small mean grain size (< 4 mm²) and a high length fraction of random grain boundaries (> 60 %) in comparison to the class G wafers. Despite the totally different initial grain structure for the class F and class G bricks, the grain structure of the wafers which represent the end of the crystallization process is more or less comparable. It can be concluded that the development of the grain structure along the crystal height of the class F bricks is driven by an energy minimization due to the surface energy and the grain boundary energy, that means that the share of (111) oriented grains having the lowest surface energy and the share of ∑3 grain boundaries having the lowest interface energy increase from the start of crystallization to the end. This phenomenon could not be observed for the class G bricks, which show a decreasing ∑3 length fraction and a decreasing area fraction of {111} oriented grains. This energetically unfavourable grain structure development is not clear so far but it means another kind of energy minimization effect must exist within class G. This could be for instance the formation of dislocations. The grain structure investigations show clearly that especially the initially fine-grained struc-ture of the class F bricks, i.e. at the start of crystallization, influences beneficially the area fraction of recombination active defects and the solar cell efficiency subsequently. This ob-servation can be explained as follows. Reduced dislocation cluster formation: • The small grain sizes in combination with the low length fraction of ∑3 grain bounda-ries capture the dislocations within a grain. Dislocations are not able to move across the grain boundaries which have not the ∑3-type within moderate stress and tempera-ture fields. This prohibits the formation and expansion of large dislocation cluster. • The previously described energetically driven grain selection and the continuously in-creasing grain size from bottom to top leads to an overgrowth of grains. This means that also dislocated grains will disappear which also prohibits the formation of large dislocation cluster. Reduced possibility of dislocation formation: • Compared to the class G bricks the area fraction of {111} oriented grains is reduced. Therefore, the possibility of the formation of dislocations is reduced, because they would be activated first in {111} oriented grains taking the Schmidt factor in account which is lowest for {111} oriented grains. After the dislocation generation within a {111} oriented grain, the dislocation can move forward on 3 of 4 possible {111} slip planes which have an angle of 19.5° with regard to the growth direction. No other ori-entation has more slip planes for the dislocation movement which have an angle smaller 20° with regard to the growth direction. These arguments in combination with the high reproducibility of the characteristic initial class F structure can explain the observed low recombination active area fraction from start to end of crystallization which was smaller 5 % and especially the low variation of 2 % of the electrical active wafer area in between the class F bricks. One can also easily explain the higher recombination active area fraction up to 14 % and the large variation of 10 % between the class G bricks due to the obtained grain structure data. These differences in the recombination active area fractions are reflected in the solar cell efficiency which is 0.4 % higher for the class F bricks compared to the class G bricks. In consideration of the above mentioned reasons it is not beneficial for the industrial ingot production technology to increase the ingot height further, due to the fact that the advanta-geous initial grain structure properties of class F bricks disappear with increasing crystal height.

Fosforutsläpp kan leda till övergödning i vattenrecipienten om kritiska nivåer överskrids. De enskilda avloppen står idag för en relativt stor andel av Sveriges fosforutsläpp jämfört med de kommunala avloppen. Detta kan sättas i bakgrund av att staten, alltsedan 1970-talet, har lagt ner stora resurser på att reducera utsläppen hos kommunala avlopp, medan en motsvarande satsning på de enskilda avloppen uteblivit. Merparten av dagens enskilda avlopp utgörs av markbaserade reningssystem, det vill säga avloppslösningar där avloppsvattnet får passera genom markmaterial för att renas. Fosforreningen i markbaserade reningssystem har forskningshistoriskt sett inte varit en prioriterad fråga, vilket har lett till kunskapsbrist inom området. Naturvårdsverket har i och med miljöbalkens införande skärpt sina krav på fosforreningen hos enskilda avlopp. Trots att Naturvårdsverket nu har satt upp exakta kravgränser på fosforutsläpp, exempelvis att en normal skyddsnivå motsvarar en rening på 70 %, saknas dock råd för hur gemene man, inför byggandet av ett markbaserat reningssystem, ska kunna uppskatta fosforreningsförmågan i markmaterialet. Emellertid rekommenderar Naturvårdsverket att man inför byggandet ska uppskatta markmaterialets hydrauliska konduktivitet, en uppskattning som ofta utförs genom att mäta markmaterialets kornstorleksfördelning. Det finns även forskning som tyder på att kornstorleksfördelningen skulle kunna ha samband med fosforreningen. Syftet med detta examensarbete var framförallt att utvärdera om kornstorleks- fördelningen kan användas som ett mått på fosforreningen. Som ett sidospår till detta utvärderades även om den hydrauliska konduktiviteten kan bestämmas ur kornstorleks- fördelningen. Empiriska formler har vid tidigare studier etablerats för detta, men frågan är om dylika empiriska formler gäller för de undersökta markbaserade reningssystemen. Undersökningens resultat tydde på ett samband mellan kornstorlek och hydraulisk konduktivitet medan det inte kunde påvisas något samband mellan kornstorleks- fördelning och fosforrening. Det är därmed önskvärt att finna ett annat mått på fosforreningen i markbaserade reningssystem. Kan vi inte uppskatta hur mycket de markbaserade reningssystemen bidrar till övergödningen kan vi inte heller väga denna negativa miljöpåverkan mot de markbaserade systemens fördelar, såsom relativt låg energiförbrukning och relativt små utsläpp av växthusgaser. / Release of phosphorus is one of the contributing factors of eutrophication in aquatic recipients. In Sweden, on-site wastewater treatment represents large emissions of phosphorous per person in comparison to municipal wastewater treatment. This can be put in the context of the Government’s large investments for reducing phosphorus in municipal wastewater treatment plants, while no corresponding investment has yet been made in the field of on-site wastewater treatment. In Sweden, the on-site wastewater treatment systems of today mainly consist of WSAS (Wastewater soil absorption systems), i.e. systems where wastewater is cleaned by passing though soil material. During the history of research about WSAS issues of phosphorous removal have not been first priority, which has led to a considerable lack of knowledge regarding these issues. Since 1999, when the Swedish regulations of environmental law were established, the SEPA (Swedish Environmental Protection Agency) has tightened up their demands of phosphorus removal in on-site wastewater treatment systems, for instance by stating that a phosphorous removal of 70% shall be reached to accomplish a “normal level of protection”. Despite this fact, there are no recommendations of how to estimate phosphorus removal in the soil material. However, the SEPA recommends estimation of hydraulic conductivity before building WSAS. This estimation is usually made by measuring grain size distribution in the soil material. One interesting fact is that there, according to some scientists, might be a connection between grain size distribution and phosphorus removal. The aim of this thesis was mainly to investigate if measure of grain size distribution can be used in order to estimate phosphorus removal. The aim was also to evaluate if grain size distribution is a good indicator of hydraulic conductivity in the investigated WSAS. It was concluded that grain size distribution is a suitable indicator of hydraulic conductivity, but not a suitable indicator of phosphorus removal. Thus, we still need to find an easy way to estimate the phosphorus removal in WSAS. If we do not know the extent of impact on eutrophication by WSAS, we cannot weigh this negative impact against the positive aspects of relatively low energy usage and low release of green house gases compared to other on-site wastewater treatment systems.

Cemented carbides are composite materials consisting of a hard carbide and a ductile binder. They are powdermetallurgically manufactured, where liquid-phase sintering is one of the main steps. The most common cemented carbide consists of WC and Co and it is widely used for cutting tools. Two of the most important factors controlling the mechanical properties are the WC grain size and the grain size distribution and thus it is of great interest to understand the grain growth behavior. In this thesis the grain growth during sintering at 1430 °C is studied both experimentally and through computer simulations. The grain growth behavior in cemented carbides cannot be explained from the classical LSW-theory. The WC grains have a faceted shape necessitating growth by 2-D nucleation of new atomic layers or surface defects. A new model based on 2-D nucleation, long-range diffusion and interface friction is formulated. Three powders having different average sizes are studied and both experiments and simulations show that a fine-grained powder may grow past a coarse-grained powder, indicating that abnormal grain growth has taken place in the fine-grained powder. Fine-grained powders with various fractions of large grains are also studied and it is seen that a faster growth is obtained with increasing fraction of large grains and that an initially slightly bimodal powder can approach the logaritmic normal distribution after long sintering times. The grain size measurements are performed on 2-D sections using image analysis on SEM images or EBSD analysis. Since the growth model is based on 3-D size distributions the 2-D size distributions have to be transformed to 3-D, and a new method, Inverse Saltykov, is proposed. The 2-D size distribution is first represented with kernel estimators and the 3-D size distribution is optimized in an iterative manner. In this way both negative values in the 3-D size distribution and modifications of the raw data are avoided. / QC 20110426

ABSTRACT Comparative study of established test methods for aggregate strength and durabilityof Archean rocks from Botswana In the current situation, river sand is used for building of roads and as raw material forconcrete in Botswana. River sand is a finite resource and important to preserve as itacts as natural water purification, groundwater aquifer and protection against soil erosion.Mining of bedrock may be a good alternative to replace the river sand with crushed rock(aggregates) in concrete and as road materials.The main purpose of this thesis was to determine if the rock grain size can be usedas a parameter to indicate durability and rock strength. It was also of interest to find outif the grain size correlates with established technical analysis and strength test methods.This knowledge can be used as a prospecting tool when searching for new quarry sites inthe future.In this master’s thesis, rock samples from the Gaborone granite complex have beenanalysed to examine how established test methods and the mineral grain size correspondswith the rock strength. By comparing technical properties (Los Angeles (LA) value ,aggregate crushing value (ACV), aggregate impact value (AIV) and 10 percent fines aggregatecrushing test (10 % FACT)) with quantitative analysis (mineral grain size andmineral grain size distribution), it is possible to determine the mineral grain size correspondenceto rock strength. Generally the result show that more fine-grained granitesshow better technical properties than more coarse-grained granites. The calculated meangrain size show weak negative correlation to ACV value, and a positive correlation to LA-, AIV- and 10 % FACT values. Best correlation can be seen between mean grain size andLA values (R2= 0.61) and AIV values (R2= 0.58). Low mean grain size tend to give bettertechnical properties in form of lower LA- and AIV values. The cumulative distributioncurve show that a high concentration of very fine material or fine material tend to contributeto a lower LA value. The results indicate that equigranular rocks with low meangrain size contributes to good technical properties, but when it comes to uneven grainedrock more factors must be taken into account to estimate technical properties.

This doctoral thesis reports analytical and numerical results for the electrostatic response of a dusty plasma to a moving test charge. Two important physical aspects of dusty plasmas, namely grain size distribution and grain charging dynamics were taken into account. In the first case, a dusty plasma in thermal equilibrium and with a distribution of grain sizes is considered. A size distribution is assumed which decreases exponentially with the grain mass for large sizes and gives a simple smooth reduction for small sizes. The electrostatic response to a slowly moving test charge, using a second order approximation is found and the effects of collisions are also investigated. It turns out that for this particular size distribution, there is a remarkably simple result that the resulting effective distribution for the electrostatic response is a kappa (generalized Lorentzian) distribution. In the second case, we present an analytical model for the shielding of a slowly moving test charge in a dusty plasma with dynamical grain charging for cases both with and without the collision effects. The response potential is treated as a power series in test charge velocity. Analytical expressions for the response potential are found up to second order in test charge velocity. The first-order dynamical charging term is shown to be the consequence of the delay in the shielding due to the dynamics of the charging process. It is concluded that the dynamical charging of the grains in a dusty plasma enhances the shielding of a test charge. To clarify the physics, a separate study is made where the charging is approximated by using a time delay. The resulting potential shows the delayed shielding effect explicitly. The terms in the potential that depend on the charging dynamics involve a spatial shift given by the test charge velocity and the charging time. The wake potential of a fast moving test charge in the case of grain charging dynamics was also found. It was observed that the grain charging dynamics leads to a spatial damping and a phase shift in the potential response. Finally, combining these two physical aspects, generalized results for the electrostatic potential were found incorporating the terms from both grain size distribution and grain charging dynamics. The generalized results contain the previous work where these two effects were studied separately and which can now be found as special limiting cases. This kind of work has relevance both in space and astrophysical plasmas. / QC 20100920

The sediment movement system in a river basin consists of sediment production process in the mountainous region, sediment supply process to the torrents and sediment deposition process in the lower reach and coastal area. There are human impacts as well as natural impacts in the system. These impacts affect the topographical feature and ecosystem in the basin including the coastal area. Bed variation model is one of the tools for assessing the topographical feature of river. In previous riverbed variation calculations, engineers or researchers conventionally assumed that the porosity in riverbed material is a constant, regardless of whether the grain sizes of the riverbed material was uniform. Since there is no doubt that the porosity depends on the grain sizes distribution, fixing the porosity at a constant value is inadequate for simulating practical sediment movements, such as the removal of fine materials out of the riverbed material or the deposition of fine material into voids between the coarse material. Voids in a riverbed themselves are also important as habitat for aquatic biota. Not only natural sediment transport phenomena, such as floods and debris flows induced by heavy rainstorms, but also artificial impacts, such as the construction of dams or sediment flushing from reservoirs, seriously affect the voids in the riverbed. So far no bed variation model has been available for the analysis of the change in porosity. As the void of bed material plays an important role in fluvial geomorphology, infiltration system in riverbeds and river ecosystem, a structural change of the void with bed variation is one of the concerned issues in river management. Thus, a bed-porosity variation model is strongly required and it is expected that the model contributes the analysis of those problems as a tool for integrated sediment management. The objectives of this work are: 1) to point out recent problems in a volcanic river basin, as well as the impacts on riverbed variation and ecosystem; the problems in Merapi volcano area and Progo River, Indonesia were chosen as case studies; 2) to develop a method for identifying the type of grain size distribution and two methods for obtaining the porosity for the different type of grain size distribution; 3) to develop a framework and a bed variation model available for the analysis of the change in porosity of bed material as well as the bed variation. The report consists of four subjects and organized into six chapters as shown in the diagram below (Figure 1). The following diagram shows the framework of proposed bed-porosity variation model and the correspondence of each chapter of this report. In Chapter 2, the sediment-related problems in volcanic area, particularly in Mt. Merapi and Progo River, Indonesia and the impacts on bed variation and ecosystem were pointed out. The sediment-related problems persist in the upper reach, middle reach, also in lower reach. Some problems are triggered by natural activities such as volcanic activity of Mt. Merapi and heavy rainfall, and many others are occurred due to the human interfere such as deforestation, construction of sabo dam and sand mining. Uncontrolled sand mining is the serious problem in this area. Those problems are increasing the susceptibility in the downstream and deteriorating the watershed. A flume experiment was conducted to realize the impact of mining pit on bed variation. Countermeasures of sediment problems, which have been done in Mt. Merapi area and Progo River, were also presented. Finally, the necessity of a tool for integrated sediment management in consideration of the ecosystem in river was indicated. In Chapter 3, the method for classifying and geometrically identifying the type of grain size distribution was presented. First, grain size distribution was classified into some typical types and those characteristic parameters were found out. Then a method for geometrically identifying the type of grain size distribution by using geometric indices .. and .. was presented. Based on the geometrical analysis of typical grain size distributions, a diagram on classification of grain size distribution type was indicated. The presented identification method was then applied to the natural grain size distribution data and the validity of the method was verified. In Chapter 4, two methods for estimating the porosity of sediment mixtures were presented. One was based on a particle packing simulation model and the other was based on a measurement method. The porosity of particle mixtures depends on not only the grain size distribution but also the compaction degree. However, the compaction degree could not be intentionally controlled in the model. Both of the methods were applied to estimate the porosity of three typical grain size distributions, namely lognormal distribution, modified-Talbot distribution and bimodal distribution. Particularly in the measurement, it was very difficult to mix the sediment evenly. Consequently, the coarser particle lies at higher position than the finer particle. This grading process made the porosity larger, while in the simulation the particles were mixed evenly. Thus, the particles packing in the simulation might be denser than the packing of particles in the measurement. The results showed that the relationship between grain size distribution and porosity could be determined by using the characteristic parameters of typical grain size distribution. This relation could be introduced into the bed variation model. In Chapter 5, a one dimensional bed-porosity variation model was developed for simulating the changes in porosity of bed material as well as the bed variation. Analytical model for binary mixtures with much different grain sizes and the relationship between the characteristic parameters of grain size distribution and porosity presented in Chapter 4 were introduced into the bed variation model. Two numerical methods were employed to solve the governing equations, i.e., standard successive approximation and MacCormack scheme. A flume experiment was conducted to realize the transformation processes of void structure for two conditions; one was the only fine sediment was removed from a sediment mixture and another was the fine sediment deposited into a coarser bed material. After the validity of the presented model was verified using a data set provided by the experiment, the model was applied to the bed and porosity variation process for bed material with binary mixtures and continuous grain size distribution. Its performance was examined in detail for two conditions; (1) no sediment supply condition and (2) sediment supply condition. The simulation results showed the model could produce a reasonable distribution of porosity of the riverbed material in the longitudinal and vertical directions for both conditions. A one-dimensional bed-porosity variation model proposed in this study is different from the previous model from a viewpoint of considering the porosity of bed material. Hence, the proposed model is available for the analysis of the change in porosity of bed material as well as the bed variation. The model contributes in two aspects; from the hydraulics point of view, the model provides an improvement of the accuracy in the riverbed variation calculation and from ecological point of view, the model provides the changes in porosity with the bed variation. In the case of binary mixtures, the validity of the model has been verified using a data set provided by the experiment and the simulation result showed that the model produced a reasonable result on the change in porosity as well as the bed variation. In the case of sediment mixtures with continuous grain size distribution, although the validity of the model has not been verified yet, the simulation result showed the model available for analysis of bed and porosity variation. / Kyoto University (京都大学) / 0048 / 新制・課程博士 / 博士(工学) / 甲第13795号 / 工博第2899号 / 新制||工||1428(附属図書館) / 26011 / UT51-2008-C711 / 京都大学大学院工学研究科社会基盤工学専攻 / (主査)教授 藤田 正治, 教授 中川 一, 教授 戸田 圭一 / 学位規則第4条第1項該当

Les modèles d'érosion et de transport couramment utilisés sont construits à partir de données empiriques obtenues avec des sédiments de granulométries quasi uniformes. Or, il y a beaucoup de situations pour lesquelles la granulométrie des sédiments n’est pas uniforme. Les expériences réalisées en laboratoire et dans les rivières montrent que l’érosion et le transport des sédiments dépendent de la dispersion du diamètre des grains. Cette observation est à l’origine de cette thèse qui a pour objectif l’étude de l’influence de la distribution du diamètre des grains sur le transport de sédiments. Cette influence est envisagée à partir du développement d’un modèle numérique. La prédiction de l’érosion et du transport de sédiments tient de la résolution de deux problèmes : le premier est lié à l’écoulement au dessus du lit, le second à la mise en mouvement du sédiment. Le modèle développé détermine explicitement le mouvement des grains dans le lit de sédiments lorsque sa face supérieure est soumise à un écoulement. Pour cela, il mobilise la Méthode des Eléments Discrets (DEM), développée par Cundall et Strack (1979). Afin de reproduire l’effet de la topographie du lit sur le champ de vitesse du fluide, le modèle DEM est couplé avec le modèle d’écoulement FLOWSTAR. Le modèle FLOWSTAR est proposé par Carruthers et al. (2004) pour déterminer l’écoulement moyen dans une couche limite turbulente atmosphérique au-dessus des collines de faible pente. Le modèle numérique développé est appliqué à différents types d’arrangements de grains. Il permet d’estimer l’évolution du débit de sédiments au cours du temps pour différentes vitesses de frottement. Les seuils d’érosion des lits et l’évolution des débits de sédiments en fonction de la vitesse de frottement sont conformes à l’expérience. L’utilisation de l’approche DEM permet par ailleurs de connaître le comportement des grains dans et à la surface du lit au cours du temps (profil vertical de la vitesse des grains à l’intérieur de l’arrangement par exemple) / The models for the erosion and transport of sediments that are currently used rely on empirical data obtained from experiments with sediments having a uniform or unimodal distribution. But there are many practical situations for which the size distribution is significantly different from this assumed distribution, and laboratory and field experiments have shown that the erosion threshold and the transport rate depend on the size distribution and the range of particle sizes. The aim of this study is therefore to investigate and explain the influence of size distribution on erosion and transport rates, using a numerical model that has been developed specifically to study this problem. The sediment bed is assumed to consist of individual, non-cohesive, spherical particles, and the physical interactions between the particles are modelled explicitly, using the Discrete Element Method developed by Cundall and Strack (1979). The flow above the bed is computed using the FLOWSTAR model (Carruthers et al 2000) which was originally developed to compute the flow in the atmospheric boundary layer above arbitrary topography. These two models are coupled, and the resulting numerical code has been used to investigate the temporal evolution of erosion and transport rates agree well with experimental measurements, and the DEM provides additional information concerning the temporal evolution of the particle size distribution within the bed.