Water resources development around the world has taken many different forms and directions since the dawn of civilization. Water shortage in arid and semiarid regions has encouraged the search for additional sources currently not exploited intensively. Hence, knowledge of the infiltration process is a requirement for understanding water management. The main aim here is to solve the one-dimensional nonlinear time-dependent Richard's equation for water flow in an unsaturated uniform soil. The main theory of soil infiltration is introduced using a mathematical-physical approach to describe water movement in unsaturated soils. This gives rise to Richard's flow equation; which is presented for both unsaturated and also saturated soil. Methods for solving Richard's equation by both analytical and numerical techniques are then introduced. This gives rise to a discussion of the similarity methods first used by Philip to determine analytical solutions of Richard's equation in an unsaturated soil. This is then generalised to determine a broader class of solutions using the Lie (classical) symmetry approach. The non-classical symmetries of Bluman and Cole are also determined. Although these group methods provide the most widely applicable technique to find solutions of ordinary and partial differential equations, a large number of tedious calculations are involved. With the help of computer algebra it is shown that the determining equations for the non-classical case lead to four new highly non-linear equations which are solved in five particular cases. Each case of classical and non-classical solutions is then reduced to an ordinary differential equation and explicit solutions are produced when possible. The potential classical and non-classical method, first suggested by Bluman, Reid and Kumei, is also discussed and presented. The potential non-classical method produced new results, which the potential classical method did not. The solution is useful as a tool by which to judge the quality of numerical methods. A practical solution of classical (Lie/ potential) and non-classical symmetry of Richard's equation is presented. Finally, conclusions and suggestions for further work are discussed.

Includes bibliographical references (p. 202-209).

published_or_final_version / Civil Engineering / Master / Master of Philosophy

Thesis (Ph.D.)--Hong Kong University of Science and Technology, 2009. / Includes bibliographical references (p. 278-291).

Thesis (Ph. D.) -- Lincoln University, 2009. / Also available via the World Wide Web.

Thesis (MScAgric)--Stellenbosch University, 2013. / ENGLISH ABSTRACT: A new orange oil based soil ameliorant is available on the market. Apart from the orange oil, the other main constituents of the product are a nonionic surfactant and an anionic surfactant. Surfactants are used in the agricultural sector, amongst others, as a countermeasure for soil with poor infiltrability or with hydrophobic characteristics. Farmers who applied the orange oil based soil ameliorant to the soil observed a positive growth response by the crop. However, the main concern about surfactants is that it can cause the soil to disperse and thereby decrease the infiltration and saturated hydraulic conductivity thereof. The aim of this study was therefore to determine the effect which this product might have on the following selected soil physical properties: bulk density, aggregate stability, soil strength and unsaturated hydraulic conductivity. The product was applied on four farms on soils with different textures: Dublin Farm (22% clay), Wansbek (20% clay), Toitskraal (7% clay) and Two Rivers (3% clay). Field studies were repeated at Dublin Farm and Toitskraal to study the longevity effect of the product. Differences in bulk density were not attributed to the effect of the product, but to spatial variation. The aggregate stability at the 50 mm depth tended to decrease after application of the product at Dublin Farm trial 1, Toitskraal trial 1 and at Wansbek. At Dublin Farm trial 2 and Toitskraal trial 2 the application of the product tended to increase the aggregate stability. For Dublin Farm trial 2 and Wansbek the shear strength at the 50 mm depth tended to increase with increased application rates. The opposite was observed at Toitskraal and Two Rivers. The unsaturated hydraulic conductivity tended to be higher at the 0 mm depth for the treated soils at all of the trials except Toitskraal trial 2. From the aggregate stability results it is clear that the initial effect of the product was detrimental which can be attributed to the anionic surfactant. The long term effect can be attributed to the effect of the nonionic surfactant. The differences in shear strength can be attributed to aggregate stability (for Dublin Farm trial 2) and bulk density (for Two Rivers). There is however no explanation for the results found at Toitskraal and Wansbek. From the linear regression of bulk density against unsaturated hydraulic conductivity for Wansbek and Two Rivers it is clear that the application of the product definitely had an influence on the unsaturated hydraulic conductivity. For both farms, the correlation between bulk density and unsaturated hydraulic conductivity was better for the control than for the treated soils. To conclude with, the application of the product according to the recommended application rate, resulted in a slightly detrimental effect to the soil on the short term, but on the long term it tended to have a slightly positive effect on the soils. / AFRIKAANSE OPSOMMING: ‘n Nuwe grondverbeteringsproduk met lemoenolie as ‘n basis en ‘n nie-ioniese en ‘n anioniese benattingsmiddel as hoof bestandele, is op die mark. In die landbou sektor word benattingsmiddels onder andere gebruik as ‘n teenvoeter vir gronde met swak infiltrasie of hidrofobiese eienskappe. Die grootste voorbehoud omtrent die gebruik van benattingsmiddels is die moontlike afname in infiltrasie en versadigde hidroulieses geleivermoë as gevolg van klei dispergering. Positiewe reaksies van die gewasse is waargeneem deur boere wat van die produk gebruik maak. Die doel van die studie was dus om die moontlike effek van die bogenoemde grondverbeterings produk op die volgende geselekteerde grondfisiese eienskappe te bepaal: bulkdigtheid, aggregaatstabiliteit, grondsterkte en onversadigde hidrouliese geleivermoë. Die produk is toegedien op vier plase met verskillende grondteksture: Dublin Farm (22% klei), Toitskraal (7% klei), Wansbek (20% klei) and Two Rivers (3% klei). ‘n Ondersoek na die lewensduur van die produk is gedoen deur ‘n opvolg studie te doen by Dublin Farm en Toitskraal. Vir die bulkdigtheid resultate kon geen van die verskille toegeskryf word aan die effek van die produk nie. Die aggregaate stabiliteit by die 50 mm diepte van Dublin Farm proef 1, Toitskraal proef 1 en Wansbek, het geneig om laer te wees vir die behandelde gronde. Die aggregaatstabiliteit by die 50 mm diepte van Dublin Farm proef 2 en Toitskraal proef 2 het geneig om hoër te wees vir die behandelde gronde. Die skuifsterkte by die 50 mm diepte by Dublin Farm proef 2 en Wansbek, het geneig om toe te neem met ‘n toename in toedienings hoeveelheid, terwyl die teenoorgestelde tendens by Toitskraal en Two Rivers waargeneem is waar minder klei teenwoordig is in die grond. Die onversadigde hidroliese geleivermoë het geneig om hoër te wees by die 0 mm diepte van al die plase met die uitsondering van Toitskraal proef 2. Dit is duidelik vanaf die aggregaatstabiliteit resultate dat die aanvanklike effek van die produk nadelig is en dit kan toegeskryf word aan die effek van die anioniese benattingsmiddel. Die langtermyn effek kan toegeskryf word aan die nie-ioniese benatingsmiddel wat aggregaatstabiliteit kan verbeter. Die verskille in skuifsterkte kan toegeskryf word aan die verskille in aggregaatstabiliteit (vir Dublin Farm proef 2) en bulkdigtheid (vir Two Rivers). Daar is egter geen verklaring vir die verskille in skuifsterkte by Toitskraal en Wansbek nie. Die liniêre regressie van bulkdigtheid teenoor onversadigde hidroliese geleivermoë van Wansbek en Two Rivers dui aan dat die produk ‘n invloed het op die onversadigde hidroliese geleivermoë. Vir albei plase het die kontrole die beste liniêre verband tussen die twee grondeienskappe gehad, met ‘n swakker korrelasie vir gronde waar die lemoenolieproduk toegedien is. Dus kan die afleiding gemaak word dat op die korttermyn het die produk ‘n geringe negatiewe effek op die grond, maar op die langtermyn neig dit om ‘n positiewe effek te hê.

Orientador: Maria da Consolação Fonseca de Albuquerque / Resumo: Inúmeros problemas sociais e ambientais são causados pela impermeabilização dos solos em decorrência da urbanização descontrolada e sem planejamento. O pavimento em concreto permeável aparece como uma forma de mitigação de enchentes, devido à sua característica de permitir a infiltração total ou parcial de água proveniente de precipitações. O objetivo deste trabalho foi estudar um traço eficiente e empregá-lo de maneira efetiva em uma calçada, para promover a captação total de eventos pluviométricos ocorridos no local e observar, com o decorrer do tempo, a eficiência de manutenção periódica na superfície do pavimento permeável quanto à colmatação. Foram experimentadas três proporções de misturas: 1:3,5; 1:5 e 1:6,5, sendo que em nenhuma foi utilizado agregado miúdo. Também foi observado o comportamento das misturas com duas granulometrias de agregados graúdos de 9,5/25,0 e 4,75/12,5. Ensaios destrutivos e não destrutivos foram realizados, entre eles: resistência à compressão axial, tração por compressão diametral, tração na flexão e taxa de infiltração. A mistura mais eficiente e escolhida para a construção da calçada foi a de teor 1:5, com a utilização do agregado de faixa granulométrica 4,75/12,5. Testes estatísticos ―t Student” foram utilizados para comparar os resultados obtidos na presente pesquisa com trabalhos semelhantes. A calçada foi dimensionada para ter eficiência de caráter pluviométrico, de acordo com incidência pluviométrica regional e mecânico através de análi... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: Uncounted social and environmental problems are caused by the waterproofing of soils as a result of uncontrolled and unplanned urbanization. The pervious concrete pavement appears as a form of flood mitigation due to its characteristic of allowing total or partial infiltration of water from rainfall. The aim of this work was to study an efficient mixture and to use it effectively on a sidewalk, to promote the total retention of rainfall events occurring locally and to observe the efficiency of periodic maintenance on the pervious pavement surface, regarding clogging over time. Three proportions of mixtures were tested: 1:3.5; 1:5 and 1:6.5, in which none fine aggregates was used. Furthermore, the behavior in the mixtures of two coarse aggregates gradations of 9.5/25.0 and 4.75/12.5 was observed. Destructive and non-destructive tests were performed, such as: compressive strength, splitting tensile strength, flexural strength and infiltration rate. The most efficient and chosen mixture for the construction of the sidewalk was 1:5, with the use of the aggregate size 4.75/12.5. ―Student’s t‖ statistical tests were used to compare the results obtained in the present research with similar works. The sidewalk was dimensioned to have rainfall efficiency, according to regional rainfall incidence, and mechanical efficiency, through analysis in the EverFE computational program, followed by calculation of fatigue life. The permeability rate of the pavement was monitored weekly over time,... (Complete abstract click electronic access below) / Mestre

A infiltração é o processo pelo qual a água atravessa a superfície do solo, com grande importância para a hidrologia, irrigação e agricultura. À medida que a água infiltra, as camadas superiores do solo vão se umedecendo, alterando gradativamente o perfil de umidade. Sob condições de campo, a água que infiltra pode fluir tanto na vertical, como na horizontal, dependendo do tipo de solo e declividade do terreno. A taxa de infiltração da água no solo é afetada, principalmente, pelas características do solo que afetam a geometria de seu sistema poroso, como textura e estrutura, e pode ser determinada tanto no campo como em laboratório, por diferentes métodos. Com a intenção de otimizar a previsão da infiltração da água no solo, diversos modelos foram desenvolvidos, podendo ser classificados em três grupos: empíricos, semi-empíricos e com base física. O objetivo deste trabalho foi avaliar a infiltração de água em solos com diferentes texturas e comparar a qualidade do ajuste de diferentes modelos usualmente empregados. As curvas da taxa de infiltração e da infiltração acumulada foram determinadas em laboratório utilizando amostras de solo homogeneamente acondicionadas em colunas e comparadas pelos seguintes modelos: Kostiakov, Horton, Green & Ampt, e Philip. Dentre os solos estudados, o solo 3 (textura franco arenosa) foi o que apresentou a maior taxa de infiltração e a maior VIB, provavelmente devido a menor proporção de argila e maior presença de macroporos, facilitando a infiltração da água no solo. Dos modelos analisados, o de Kostiakov, seguido pelo de Philip, foram os que apresentaram em média os melhores valores estimados da taxa de infiltração quando comparados com os valores medidos em laboratório. O gráfico do avanço da frente de molhamento com a raiz quadrada do tempo de infiltração (horizontal) ajustou-se perfeitamente ao modelo de Philip. No que respeita a infiltração vertical tal gráfico foi semelhante ao da horizontal (linha reta), mas com maior inclinação. / Infiltration is the process in which the water passes through the soil surface, being of great importance for hydrology, irrigation and agriculture. As the water infiltrates, the soil water content profile will changing and the infiltrated water can flow vertically or horizontally, depending on the soil type and land slope. The soil water infiltration rate is mainly affected by soil properties that affect its porous geometry, such as texture and structure, and can be determined in the field and in the laboratory, using different methods. In order to optimize the prediction of the soil water infiltration, many different models have been developed and may be classified into three groups: empirical, semi-empirical and physically based. The objective of this study was to evaluate the water infiltration in soils with different textures and compare the quality of fit of the different used models. The infiltration rate curves and the cumulative infiltration curves were determined in the laboratory using soil samples homogeneously packed in column and compared by the following models: Kostiakov, Horton, Green & Ampt and Philip. Among the studied soils, the soil 3 (sandy loam texture) presented the highest infiltration rate and the highest basic infiltration rate, probably due to lower clay content and larger quantity of macropores, facilitating the water infiltration into the soil. Among the tested models, Kostiakov, followed by Philip, presented, on average, the best estimated values of the infiltration rate compared to the values measured in the laboratory. The front of the advancing wetting graph of the square root of the infiltration time (horizontal) well set to Philip model. With respect to this vertical graph infiltration was similar to the horizontal (straight line) but more inclined.

A infiltração é o processo pelo qual a água atravessa a superfície do solo, com grande importância para a hidrologia, irrigação e agricultura. À medida que a água infiltra, as camadas superiores do solo vão se umedecendo, alterando gradativamente o perfil de umidade. Sob condições de campo, a água que infiltra pode fluir tanto na vertical, como na horizontal, dependendo do tipo de solo e declividade do terreno. A taxa de infiltração da água no solo é afetada, principalmente, pelas características do solo que afetam a geometria de seu sistema poroso, como textura e estrutura, e pode ser determinada tanto no campo como em laboratório, por diferentes métodos. Com a intenção de otimizar a previsão da infiltração da água no solo, diversos modelos foram desenvolvidos, podendo ser classificados em três grupos: empíricos, semi-empíricos e com base física. O objetivo deste trabalho foi avaliar a infiltração de água em solos com diferentes texturas e comparar a qualidade do ajuste de diferentes modelos usualmente empregados. As curvas da taxa de infiltração e da infiltração acumulada foram determinadas em laboratório utilizando amostras de solo homogeneamente acondicionadas em colunas e comparadas pelos seguintes modelos: Kostiakov, Horton, Green & Ampt, e Philip. Dentre os solos estudados, o solo 3 (textura franco arenosa) foi o que apresentou a maior taxa de infiltração e a maior VIB, provavelmente devido a menor proporção de argila e maior presença de macroporos, facilitando a infiltração da água no solo. Dos modelos analisados, o de Kostiakov, seguido pelo de Philip, foram os que apresentaram em média os melhores valores estimados da taxa de infiltração quando comparados com os valores medidos em laboratório. O gráfico do avanço da frente de molhamento com a raiz quadrada do tempo de infiltração (horizontal) ajustou-se perfeitamente ao modelo de Philip. No que respeita a infiltração vertical tal gráfico foi semelhante ao da horizontal (linha reta), mas com maior inclinação. / Infiltration is the process in which the water passes through the soil surface, being of great importance for hydrology, irrigation and agriculture. As the water infiltrates, the soil water content profile will changing and the infiltrated water can flow vertically or horizontally, depending on the soil type and land slope. The soil water infiltration rate is mainly affected by soil properties that affect its porous geometry, such as texture and structure, and can be determined in the field and in the laboratory, using different methods. In order to optimize the prediction of the soil water infiltration, many different models have been developed and may be classified into three groups: empirical, semi-empirical and physically based. The objective of this study was to evaluate the water infiltration in soils with different textures and compare the quality of fit of the different used models. The infiltration rate curves and the cumulative infiltration curves were determined in the laboratory using soil samples homogeneously packed in column and compared by the following models: Kostiakov, Horton, Green & Ampt and Philip. Among the studied soils, the soil 3 (sandy loam texture) presented the highest infiltration rate and the highest basic infiltration rate, probably due to lower clay content and larger quantity of macropores, facilitating the water infiltration into the soil. Among the tested models, Kostiakov, followed by Philip, presented, on average, the best estimated values of the infiltration rate compared to the values measured in the laboratory. The front of the advancing wetting graph of the square root of the infiltration time (horizontal) well set to Philip model. With respect to this vertical graph infiltration was similar to the horizontal (straight line) but more inclined.

Modern urban stormwater infrastructure includes vegetated bioretention facilities (BRFs) that are designed to detain water and pollutants. Phosphorus (P) is a pollutant in stormwater which can be retained in BRF soils in mineral, plant, and microbial pools. We explored soil properties and phosphorus forms in the soils of 16 operational BRFs in Portland, OR. Since soil hydrology can significantly impact P retention, we selected BRFs along an infiltration rate (IR) gradient. We conducted sequential fractionation and tests of P pools and measured P release in a subset of soils after drying and flooding samples for ten days. We hypothesized that mineral or organic soil P forms would be correlated with IR, and that vulnerability to P release would depend on the interaction of drying and flooding treatments with P forms and pools. IR did not significantly explain differences in P forms. Soil TP was elevated across all sites, compared with TP in agriculturally-impacted wetlands and was substantially composed of soil organic matter (OM)-associated P. Phosphorus sorbed to mineral Fe and Al oxides- was variable but positively correlated with water-extractable P. The concentration gradient of water-extractable P was primarily controlled by overall P pools. Experimentally induced P releases were seen in 5 of 6 soils exposed to drying conditions, presumably released through microbial mineralization of OM. Only one site showed significant P release following the flooding treatment. Our measurements supported the idea that Fe and Al oxides provide P sorption capacity in these BRF soils. Variable inputs of P to BRFs through stormwater and litterfall may contribute to variability in P profiles and P release vulnerability across sites. Design specifications and management decisions relating to bioretention soils (e.g. establishment of acceptable soil test P levels, focusing on P forms known to influence vulnerability of P release) may benefit from detailed biogeochemical investigations.