Modeling Soil Water Retention Curve with a Fractal Method

Many empirical models have been developed to describe the soil water retention curve (SWRC). In this study, a fractal model for SWRC was derived with a specially constructed Menger sponge to describe the fractal scaling behavior of soil; relationships were established among the fractal dimension of SWRC, the fractal dimension of soil mass, and soil texture; and the model was used to estimate SWRC with the estimated results being compared to experimental data for verification. The derived fractal model was in a power-law form, similar to the Brooks-Corey and Campbell empirical functions. Experimental data of particle size distribution (PSD), texture, and soil water retention for 10 soils collected at different places in China were used to estimate the fractal dimension of SWRC and the mass fractal dimension. The fractal dimension of SWRC and the mass fractal dimension were linearly related. Also, both of the fractal dimensions were dependent on soil texture, i.e., clay and sand contents. Expressions were proposed to quantify the relationships. Based on the relationships, four methods were used to determine the fractal dimension of SWRC and the model was applied to estimate soil water content at a wide range of tension values. The estimated results compared well with the measured data having relative errors less than 10% for over 60% of the measurements. Thus, this model, estimating the fractal dimension using soil textural data, offered an alternative for predicting SWRC.

Determining the soil-water retention curve using mercury intrusion porosimetry test in consideration of soil volume change

It is well-known that a close link exists between soil-water retention curve(SWRC)and pore size distribution(PSD).Theoretically,mercury intrusion porosimetry(MIP)test simulates a soil drying path and the test results can be used to deduce the SWRC(termed SWRCMIP).However,SWRCMIP does not include the effect of volume change,compared with the conventional SWRC that is directly determined by suction measurement or suction control techniques.For deformable soils,there is a significant difference between conventional SWRC and SWRCMIP.In this study,drying test was carried out on a reconstituted silty soil,and the volume change,suction,and PSD were measured on samples with different water contents.The change in the deduced SWRCMIP and its relationship with the conventional SWRC were analyzed.The results showed that the volume change of soil is the main reason accounting for the difference between conventional SWRC and SWRCMIP.Based on the test results,a transformation model was then proposed for conventional SWRC and SWRCMIP,for which the soil state with no volume change is taken as a reference.Comparison between the experimental and predicted SWRCs showed that the proposed model can well consider the influence of soil volume change on its water retention property.

Water Retention Curve and Particle Breakage of Aggregates Recycled from Demolition Waste

CDW （construction and demolition wastes） present a high amount of aggregate chips covered with mortar. This results in high absorption of water with a direct impact in particle breakage or disaggregation. It is supposed that intra particle suction plays an important role in this phenomenon. However, WRCs （water retention curves） of CDW are not well understood. In this work, the WRCs of dynamically compacted specimens of aggregates recycled from the demolition of the National Stadium in Brasilia are studied. The objective of this study is to obtain WRCs of the recycled materials by using the pressure plate and filter paper methods. The breaking effect during compaction is quantified from the grain size distribution curves. The particle breakage during compaction increases when the energy is augmented. The results from the WRCs were incorporated into a pore size capillary model to predict pore size distribution.

Influence of Dry Density on Soil-Water Retention Curve of Unsaturated Soils and Its Mechanism Based on Mercury Intrusion Porosimetry

The soil-water retention curve(SWRC)can be used to evaluate the ability of unsaturated soils to attract water at various water contents and suctions. In this study, drying SWRCs for a kind of sandy soil were obtained in the laboratory by using self-modified SWRC apparatus. In addition, the porosity and the pore size distribution of the samples were investigated by a mercury porosimetry test in order to analyze the effect of dry density. Results showed that the soil-water retention of the soil specimens was strongly dependent on the dry density. Under zero suction, soil specimens with a higher dry density exhibited lower initial volumetric water content. The higher the dry density of soil, the more slowly the volumetric water content decreased with the increase of suction. There was a general and consistent trend for a soil specimen to possess a larger air-entry value and residual suction, while smaller slope of SWRC when it had a higher density. This was probably attributed to the presence of smaller interconnected pores in the soil specimen with a higher dry density. The proportion of large diameter pores decreased in comparison to pores with small diameters in the soil tested. The measured total pore volume of the soil specimen, which had a larger dry density, was lower than that of the relatively loose specimens.

Estimation of Soil Water Retention Curve: An Asymmetrical Pore-Solid Fractal Model

The soil water retention curve is an important hydraulic function for the study of flow transport processes in unsaturated soils. The objective of this study was to develop a soil water retention function using a generalized fractal approach. The model exhibits asymmetry between the solid phase and pore phase, which is in marked contrast to the symmetry between phases present in a conventional fractal model. The retention function includes 4 parameters： the saturated water content θs, the air entry value ha, the fractal dimension Df, and an empirical parameter β, characterizing the complicated soil pore structures. Sixty one data sets, covering a wide range of soil structure and textural properties, were used to evaluate the applicability of the proposed soil water retention function. The retention function is shown to be a general model, which incorporates several existing retention models. The values of β/θs and （θs-θr ）/β were used as indexes to quantify the relationships between the proposed retention function and the existing retention models. The proposed function fits all the data very well, whereas other tested models only match about 16%-48% of the soil retention data.

Determination of strain-dependent soil water retention characteristics from gradation curve

The importance of soil water retention characteristics in modelling the hydro-mechanical response of unsaturated soils has been well recognised by many investigators in recent years.Determination of strain-dependent soil water retention curve(SWRC)is likely to be extraordinarily difficult.The first two authors have recently shown that SWRC can be computed from the gradation curve and the calculation result is consistent with the experimental results obtained from pressure plate tests.In this paper,based on a hypothesis related to change in the pore size distribution(POSD)due to volumetric strain of soil skeleton,a method to compute strain-dependent SWRC is presented.It is found that at initial degrees of saturation higher than 0.8,the influence of volumetric strain may be marginal whilst at initial degrees of saturation lower than 0.8,its influence is likely to be substantial.In all cases,the gradation curve of the soil affects the SWRC.

A thermodynamics-based three-scale constitutive model for partially saturated granular materials

A three-scale constitutive model for unsaturated granular materials based on thermodynamic theory is presented.The three-scale yield locus,derived from the explicit yield criterion for solid matrix,is developed from a series of discrete interparticle contact planes.The three-scale yield locus is sensitive to porosity changes;therefore,it is reinterpreted as a corresponding constitutive model without phenomenological parameters.Furthermore,a water retention curve is proposed based on special pore morphology and experimental observations.The features of the partially saturated granular materials are well captured by the model.Under wetting and isotropic compression,volumetric compaction occurs,and the degree of saturation increases.Moreover,the higher the matric suction,the greater the strength,and the smaller the volumetric compaction.Compared with the phenomenological Barcelona basic model,the proposed three-scale constitutive model has fewer parameters;virtually all parameters have clear physical meanings.

Effect of vegetation on soil water retention and storage in a semi-arid alpine forest catchment

The runoff generated from mountainous regions is recognized as the main water source for inland river basins in arid environments. Thus, the mechanisms by which catchments retain water in soils are to be understood. The water storage capacity of soil depends on its depth and capacity to retain water under gravita- tional drainage and evapotranspiration. The latter can be studied through soil water retention curve （SWRC）, which is closely related to soil properties such as texture, bulk density, porosity, soil organic carbon conteMt, and so on. The present study represented SWRCs using HYDRUS-1D. In the present study, we measured pl^ysical and hydraulic properties of soil samples collected from Sabina przewalskii forest （south-facing slope with highest solar radiation）, shrubs （west-facing slope with medium radiation）, and Picea crassifolia forest （north-facing slope with lowest radiation）, and analyzed the differences in soil water storage capacity of these soil samples. Soil water content of those three vegetation covers were also measured to validate the soil water storage capacity and to analyze the relationship between soil organic matter content and soil water content. Statistical analysis showed that different vegetation covers could lead to different soil bulk densities and differences in soil water retention on the three slope aspects. Sand content, porosity, and organic carbon content of the P. crassifolia forest were rela- tively greater compared with those of the S. przewalskii forest and shrubs. However, silt content and soil bulk density were relatively smaller than those in the S. przewalskii forest and shrubs. In addition, there was a sig- nificant linear positive relationship between averaged soil water content and soil organic matter content （P〈0.0001）. However, this relationship is not significant in the P. crassifolia forest. As depicted in the SWRCs, the water storage capacity of the soil was 39.14% and 37.38% higher in the P. crassifolia forest than in the S. przewalskii forest and shrubs, respectively, at a similar soil depth.

Estimation of the van Genuchten Soil Water Retention Properties from Soil Textural Data

The van Genuchten (vG) function is often used to describe the soil water retention curve (SWRC) of unsaturated soils and fractured rock. The objective of this study was to develop a method to determine the vG model parameter m from the fractal dimension. We compared two approaches previously proposed by van Genuchten and Lenhard et al. for estimating m from the pore size distribution index of the Brooks and Corey (BC) model. In both approaches we used a relationship between the pore size distribution index of the BC model and the fractal dimension of the SWRC. A dataset containing 75 samples from the UNSODA unsaturated soil hydraulic database was used to evaluate the two approaches. The statistical parameters showed that the approach by Lenhard et al. provided better estimates of the parameter m. Another dataset containing 72 samples from the literature was used to validate Lenhard's approach in which the SWRC fractal dimension was estimated from the clay content. The estimated SWRC of the second dataset was compared with those obtained with the Rosetta model using sand, silt, and clay contents. Root mean square error values of the proposed fractal approach and Rosetta were 0.081 and 0.136, respectively, indicating that the proposed fractal approach performed better than the Rosetta model.

Assessment of Super Absorbent Polymer (SAP) on Plant Available Water (PAW) in Dry Lands

One of the ways of overcoming the cost of irrigation is through in-situ water harvesting at the plant roots. Super absorbent polymer (SAP) can facilitate water harvesting at the plant roots. This study attempted to assess the effect of SAP on plant available water (PAW) of different soils. In this study, SAP was sequentially added at the rate of 0.2%, 0.3% and 0.5% of the soil weight and its impact assessed in clay, sandy clay and sandy loam soils. The moisture retention characteristics of the original and SAP treated soils were studied using soil water retention curves (SWRC) and results modelled using Gardner model. PAW was estimated from SWRC as the difference between moisture content at 1.5 and 3 bar in all soils. The difference in PAW between original and treated soils was assessed at 5% level of significance. The WRC of all the samples was adequately found to be described by the Gardner model (Coefficient of determination R2 ≥ 98% and residual standard error (RSE) ≤ 0.04). SWRC changed with increase in SAP percentage in clay, sandy clay and sandy loam soils. Clay had a higher change in water retention then sandy clay and lastly sandy loam. Plant available water content (PAW) in all soils increased. In clay soil it increased with increase in SAP from 0.3291 at zero SAP to 0.6223 at 0.5% SAP. Sandy clay soil increased in PAW from 0.2721 at zero SAP to 0.5335 at 0.5% SAP and Sandy loam soils from 0.1691 at zero SAP to 0.3461 at 0.5% SAP. Hence, from the study SAP can be used to conserve irrigation water in the plant roots and therefore reducing the cost since PAW has been increased.

Topographic differentiations of biological soil crusts and hydraulic properties in fixed sand dunes, Tengger Desert

Biological soil crusts （BSCs） play an important role in surface soil hydrology. Soils dominated with moss BSCs may have higher infiltration rates than those dominated with cyanobacteria or algal BSCs. However, it is unnown whether improved infiltration in moss BSCs is accompanied by an increase in soil hydraulic conductivity or water retention capacity. We investigated this question in the Tengger Desert, where a 43-year-old revegetation program has promoted the formation of two distinct types of BSCs along topographic positions, i.e. the moss-dominated BSCs on the interdune land and windward slopes of the fixed sand dunes, and the al- gal-dominated BSCs on the crest and leeward slopes. Soil water retention capacity and hydraulic conductivity were measured using an indoor evaporation method and a field infiltration method. And the results were fitted to the van Genuchten-Mualem model. Unsaturated hydraulic conductivities under greater water pressure （〈-0.01 MPa） and water retention capacities in the entire pressure head range were higher for both crust types than for bare sand. However, saturated and unsaturated hydraulic conductivities in the near-saturation range （〉-0.01 MPa） showed decreasing trends from bare sand to moss crusts and to algal crusts. Our data suggested that topographic differentiation of BSCs significantly affected not only soil water retention and hydraulic conductivities, but also the overall hydrology of the fixed sand dunes at a landscape scale, as seen in the reduction and spatial variability in deep soil water storage.

Incorporation of a nanotechnology-based additive in cementitious products for clay stabilisation

The mechanical performances and water retention characteristics of clays,stabilised by partial substitution of cement with by-products and inclusion of a nanotechnology-based additive called RoadCem(RC),are studied in this research.The unconfined compression tests and one-dimensional oedometer swelling were performed after 7 d of curing to understand the influence of addition of 1%of RC material in the stabilised soils with the cement partially replaced by 49%,59%and 69%of ground granulated blast furnace slag(GBBS)or pulverised fuel ash(PFA).The moisture retention capacity of the stabilised clays was also explored using the soil-water retention curve(SWRC)from the measured suctions.Results confirmed an obvious effect of the use of RC with the obtained strength and swell properties of the stabilised clays suitable for road application at 50%replacement of cement.This outcome is associated with the in-depth and penetrating hydration of the cementitious materials by the RC and water which results in the production of needle-like matrix with interlocking filaments e a phenomenon referred to as the‘wrapping’effect.On the other hand,the SWRC used to describe the water holding capacity and corresponding swell mechanism of clays stabilised by a proportion of RC showed a satisfactory response.The moisture retention of the RC-modified clays was initially higher but reduced subsequently as the saturation level increased with decreasing suction.This phenomenon confirmed that clays stabilised by including the RC are water-proof in nature,thus ensuring reduced porosity and suction even at reduced water content.Overall,the stabilised clays with the combination of cement,GGBS and RC showed a better performance compared to those with the PFA included.

Shear strength of an unsaturated weakly expansive soil

To study the weakly expansive clay obtained from a slope along Wuhan—Shiyan expressway in Hubei Province,soil-water property tests and some unsaturated triaxial tests with suction control were conducted,and the soil-water retention curve（SWRC） and unsaturated shear strength of this soil were obtained.Results show that the air-entry suction and the residual degree of saturation of the tested soil are 106 kPa and 8%,respectively.The boundary effect zone and the transition zone can be identified on the desorption curve,but the residual zone is not so obvious.The unsaturated shear strength increases as suction increases within the range of controlled suction in the test,and friction angle,b,in the triaxial shear test is 17.6°.Based on the results,constitutive models for predicting the unsaturated shear strength using the SWRC were evaluated,and comparisons between prediction and measurement were made.It is concluded that for engineering purpose,the constitutive model should be carefully selected based on soil properties when predicting the unsaturated shear strength using the SWRC.

Soil-water characteristics of Gaomiaozi bentonite by vapour equilibrium technique

Soil-water characteristics of Gaomiaozi(GMZ)Ca-bentonite at high suctions(3–287MPa)are measured by vapour equilibrium technique.The soil-water retention curve(SWRC)of samples with the same initial compaction states is obtained in drying and wetting process.At high suctions,the hysteresis behaviour is not obvious in relationship between water content and suction,while the opposite holds between degree of saturation and suction.The suction variation can change its water retention behaviour and void ratio.Moreover,changes of void ratio can bring about changes in degree of saturation.Therefore,the total change in degree of saturation includes changes caused by suction and that by void ratio.In the space of degree of saturation and suction,the SWRC at constant void ratio shifts to the direction of higher suctions with decreasing void ratio.However,the relationship between water content and suction is less affected by changes of void ratio.The degree of saturation decreases approximately linearly with increasing void ratio at a constant suction.Moreover,the slope of the line decreases with increasing suction and they show an approximately linear relationship in semi-logarithmical scale.From this linear relationship,the variation of degree of saturation caused by the change in void ratio can be obtained.Correspondingly,SWRC at a constant void ratio can be determined from SWRC at different void ratios.

Hydro-mechanical behaviours of highly compacted sand-bentonite mixture

： This paper presents the results of laboratory testing on a heavily compacted sand-bentonite mixture. To measure the soil-water retention curve （SWRC） of the mixture over a large range of suction, a pressure plate apparatus and filter papers were used. The obtained SWRC shows that the measurements via the two methods consistently agree with each other. By using a suction-controlled oedometer for unsaturated soils, a series of one-dimensional compression tests were performed on the unsaturated compacted sand-bentonite mixture at different constant suctions. The testing results indicate that the yield stress increases and compression index decreases with the increase of imposed suction. The results also demonstrate that the mixture wetted to saturation and subsequently dried to a certain suction level has a lower yield stress than that wetted directly to the same suction.

Variation of soil organic carbon and bulk density during afforestation regulates soil hydraulic properties

Grain to Green program on arable land has been conducted for decades in semi-arid regions of North China.However,it remains uncertain how afforestation practices affect soil hydraulic properties(SHP).Two afforestation types,i.e.shrubland(SL)and woodland(WL),and the adjacent cropland(CL)were investigated to determine afforestation effects on SHP in this area.Disturbed and undisturbed soil cores were collected in three experimental sites.Soil field capacity(FC),wilting point(WP),and available water capacity(AWC)increased in SL compared to the CL.Soil saturated water content,however,decreased significantly in both SL and WL.Correlation and redundancy analysis identified that bulk density(BD)and soil organic carbon(SOC)were the main factors regulating SHP across different land uses.Lower saturated water contents in afforestation sites were likely driven by the higher BD,compared to the adjacent cropland.FC,WP,and AWC were positively correlated to SOC content.While afforestation may not increase the saturated water content of a landscape,our results indicate that it can improve soil water retention and could be an effective practice for soil and water conservation.

Matrix Suction of Unsaturated Colluvium Slope Influenced by Rainfall and Plant Condition:A Case of Taiwan Huafan University

This study investigates the variation of matrix suction, water content and ground water level before and after the rainfall for the unsaturated colluvium slope in the campus of Fuafan University. The measuring devices including electrical matrix suction, water content and ground water level were set up in different surface of planting condition for each depth in real-time. It is observed that the matrix suction in the time from July to September is higher; however, when heavy rains caused by typhoon happened, matrix suction will drop rapidly. This variation is obvious in short grass zone and less clear in the broadleaftree zone. The maximum value in short grass zone, long grass zone and broadieaf tree zone at 2 m depth are 90.3, 68.2, 18.5 kPa, respectively. These results are expected to serve as a reference for the study of slope stability mechanisms.

On the thermo-mechanical properties of unsaturated soils

The establishment of energy balance equation is necessary to study the thermo-mechanical properties of unsaturated soils.To solve this equation,the determination of two fundamental parameters as volumetric specific parameter and thermal conductivity coefficient is essential.In this paper,the effective thermal conductivity coefficient of dry soil grain is analyzed for soils with different compositions,and the thermo-mechanical properties of porous media with water and gas are studied by considering the soil water retention curve（SWRC）.Different methods,i.e.volumetric average method,self-consistent method,Hashin-Strikman method,are employed to calculate thermal conductivity coefficients,and a new method is proposed to determine the thermo-mechanical parameters.Comparison of the results obtained by different methods shows that the proposed method is in a good agreement with the experimental results and is suitable for describing the main properties of the thermo-mechanical behaviors of soils.The relationship between the SWRC and the seepage curve is further studied by the natural proportional rule.The characteristics of the SWRC,its differential coefficient and the seepage curve,are investigated by considering the physico-mechanical mechanism;the limit scopes of the indices of the SWRC and the seepage curve are also given.

Pedotransfer Functions for Estimating Soil Hydraulic Properties： A Review

Characterization of soil hydraulic properties is important to environment management; however, it is well recognized that it is laborious, time-consuming and expensive to directly measure soil hydraulic properties. This paper reviews the development of pedotransfer functions （PTFs） used as an alternative tool to estimate soil hydraulic properties during the last two decades. Modern soil survey techniques like satellite imagery/remote sensing has been used in developing PTFs. Compared to mechanistic approaches, empirical relationships between physical properties and hydraulic properties have received wide preference for predicting soil hydraulic properties. Many PTFs based on different parametric functions can be found in the literature. A number of researchers have pursued a universal function that can describe water retention characteristics of all types of soils, but no single function can be termed generic though van Cenuchten （VG） function has been the most widely adopted. Most of the reported parametric PTFs focus on estimation of VG parameters to obtain water retention curve （WRC）. A number of physical, morphological and chemical properties have been used as predictor variables in PTFs. Conventionally, regression algorithms/techniques （statistical/neurM regression） have been used for calibrating PTFs. However, there are reports of utilizing data mining techniques, e.g., pattern recognition and genetic algorithm. It is inferred that it is critical to refine the data used for calibration to improve the accuracy and reliability of the PTFs. Many statistical indices, including root mean square error （RMSE）, index of agreement （d）, maximum absolute error （ME）, mean absolute error （MAE）, coefficient of determination （r2） and correlation coefficient （r）, have been used by different researchers to evaluate and validate PTFs. It is argued that being location specific, research interest in PTFs will continue till generic PTFs are developed and validated. In future studies, improved methods will be required to extract information from the existing database.

Influence of Organic Matter Content on Hydro-Structural Properties of Constructed Technosols

Constructed Technosols may be an alternative for creating urban green spaces. However, the hydro-structural properties emer- ging from the assembly of artefacts have never been documented. The soil shrinkage curve （SSC） could provide relevant structural information about constructed Technosols, such as the water holding capacity of each pore system （macropores and micropores）. The objectives of this study were （i） to evaluate the SSC and water retention curve （WRC） to describe the structure of constructed Tech- nosols and （ii） to understand the influence of organic matter content on soil hydro-structural properties. In this study, Technosols were obtained by mixing green waste compost （GWC） with the material excavated from deep horizons of soil （EDH）. The CWC was mixed with EDH in six different volumetric percentages from 0% to 50% （GWC/total）. The GWC and EDH exhibited highly divergent hydro-structural properties： the SSC was hyperbolic for GWC and sigmoid for EDH. All six mixture treatments （0%, 10%, 20%, 30%, 40% and 50% GWC） exhibited the classical sigmoid shape, revealing two embedded levels of pore systems. The 20% GWC treatment was hydro-structurally similar to the 30% and 40% GWC treatments; so, a large quantity of expansive GWC is unnecessary. The relation with the GWC percentage was a second-degree equation for volumetric available water in micropores, but was linear for volumetric available water in macropores and total volumetric available water. Total volumetric available water in the 50% GWC treatment was twice as high as that in the 0% GWC treatment. By combining SSCs and WRCs, increasing the GWC percentage increased water holding capacity by decreasing the maximum equivalent size of water-saturated micropores at the shrinkage limit and increasing the maximum equivalent size of water-saturated macropores, resulting in an increased range of pore diameter able to retain available water.