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.

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.

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.

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.

Characteristics of soil water retention curve at macro-scale

Scale adaptable hydrological models have attracted more and more attentions in the hydrological modeling research community, and the constitutive relationship at the macro-scale is one of the most important issues, upon which there are not enough research activities yet. Taking the constitutive relationships of soil water movement--soil water retention curve (SWRC) as an example, this study extends the definition of SWRC at the micro-scale to that at the macro-scale, and aided by Monte Carlo method we demonstrate that soil property and the spatial distribution of soil moisture will affect the features of SWRC greatly. Furthermore, we assume that the spatial distribution of soil moisture is the result of self-organization of climate, soil, ground water and soil water movement under the specific boundary conditions, and we also carry out numerical experiments of soil water movement at the vertical direction in order to explore the relationship between SWRC at the macro-scale and the combinations of climate, soil, and groundwater. The results show that SWRCs at the macro-scale and micro-scale presents totally different features, e.g., the essential hysteresis phenomenon which is exaggerated with increasing aridity index and rising groundwater table. Soil property plays an important role in the shape of SWRC which will even lead to a rectangular shape under drier conditions, and power function form of SWRC widely adopted in hydrological model might be revised for most situations at the macro-scale.

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.

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.

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.

物理化学效应对膨胀土收缩特性的影响机制

膨胀土由于其骨架带有较多的固定负电荷,层间存在与负电荷平衡的可交换阳离子,使得土体呈现较强的胀缩性。研究结果表明,膨胀土的胀缩性会受到孔隙溶液化学成分的影响。选用广西地区的强膨胀土作为研究对象,开展了不同浓度的NaCl溶液对膨胀土土-水特征曲线和收缩曲线影响的试验研究,引入了粒间应力的概念对收缩曲线进行描述,该粒间应力考虑了渗透、毛细和吸附的影响。结果表明:孔隙盐溶液是通过渗透吸力对土-水特征曲线产生影响,对基质吸力的影响较小。土样在脱湿过程中的收缩变形是由粒间应力来控制的,类似于加压固结现象。大部分的收缩都发生在毛细阶段,为弹塑性变形;吸附阶段的收缩较少,为弹性变形。通过识别压缩曲线上的弹塑性分界点可以得出毛细和吸附作用的分界点,该分界点与独立测量的不同密实度下的持水曲线结果一致。结果表明,粒间应力能够更好地描述膨胀土的化学-力学行为,特别是在低含水率条件下。

全吸力范围非饱和持水函数和渗透性函数的预测模型

非饱和土的持水函数和渗透性函数是刻画其持水能力和水分运移的基本参数。由于物理机制不同,持水函数及渗透性函数在毛细阶段和吸附阶段的特征有显著差异。多数传统的持水和渗透性函数仅考虑了毛细阶段内,毛细水的持水和渗透特性,不能表征吸附阶段内吸附水的特征。为使传统函数模型在吸附阶段也适用,以传统VG持水函数和VG-M渗透性函数为基础,用修正参数C(ψ)修正VG持水函数,并以此确定非饱和土的残余值ψr,区分毛细水的毛细流动和吸附水的薄膜流动。基于薄膜流动的特点,提出参数Γ(ψ),改进了传统VG-M渗透性函数在吸附阶段内低估非饱和渗透系数这一问题,从而建立了全吸力范围的渗透性函数模型。最后用3组持水及渗透性试验结果验证修正模型的合理性,结果表明修正持水函数模型和渗透性函数模型的预测结果在吸附阶段较传统模型更符合实测结果。

Unraveling the hydraulic properties of loess for landslide prediction:A study on variations in loess landslides in Lanzhou,Dingxi,and Tianshui,China

Loess has distinctive characteristics,leading to frequent landslide disasters and posing serious threats to the lives and properties of local re sidents.The involvement of water repre sents a critical factor in inducing loess landslides.This study focuses on three neighboring cities sequentially situated on the Loess Plateau along the direction of aeolian deposition of loess,namely Lanzhou,Dingxi,and Tianshui,which are densely populated and prone to landslide disasters.The variations in hydraulic properties,including water retention capacity and permeability,are investigated through Soil Water Characteristic Curve(SWCC)test and hydraulic conductivity test.The experimental findings revealed that Tianshui loess exhibited the highest water retention capacity,followed by Dingxi loess,while Lanzhou loess demonstrated the lowest water retention capacity.Contrastingly,the results for the saturated permeability coefficient were found to be the opposite:Tianshui loess showed the lowest permeability,whereas Lanzhou loess displayed the highest permeability.These results are supported and analyzed by scanning electron microscopy(SEM)observation.In addition,the water retention capacity is mathematically expressed using the van Genuchten model and extended to predict unsaturated hydraulic properties of loess.The experimental results exhibit a strong accordance with one another and align with the regional distribution patterns of disasters.

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.

基于孔径分布函数的单/双峰持水曲线模型

非饱和土持水曲线是研究非饱和土强度、渗透性以及本构理论的基础.目前大多数非饱和持水曲线模型主要针对单峰持水曲线,而对于双峰持水曲线的模型研究相对较少.本文通过分析单/双峰孔隙结构土体的孔径分布特征,利用Young-Laplace方程建立土体吸力和孔径之间的关系,再采用对数正态分布函数来描述土体单/双峰孔径分布特征.在此基础上进一步提出了一个适用于模拟单/双峰持水曲线的模型,模型中各参数均具有明确物理意义.最后选取文献中不同类型土的持水实验数据对本模型进行验证,结果表明,新模型能较好地模拟不同类型土的单/双峰持水曲线.

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.

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.

基于NMR技术及分形理论预测SWRC

土-水特征曲线（SWRC）是非饱和土力学中的基础本构关系,在研究非饱和土强度、体变及渗透系数等方面具有重要作用。通过试验直接测量SWRC,耗时较长,且通常得到的只是离散数据点,缺乏连续性,不能完全满足非饱和土研究的需要,因此,通过间接方法快速预测SWRC的完整数学表达式具有实际意义。以无损伤的核磁共振（nuclear magnetic resonance）技术为基础,结合Young-Laplace理论,建立基质吸力ψ与T2值的关系式;利用分形理论,推导出质量含水率w与T2值的关系式,最终建立了预测SWRC的数学模型,研究结果表明其预测结果与实测值吻合较好。

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.

双孔隙结构重塑非饱和膨胀土的抗剪强度特性

针对具有双孔隙结构(即集聚体间和集聚体内孔隙)及双峰持水曲线的内乡膨胀土压实样,进行了一系列宽广吸力范围内非饱和土三轴剪切试验及峰值强度演化规律的研究。试验结果表明:在净应力相同的条件下,中低吸力下的应力应变关系为应变硬化,伴随明显的剪缩变形;高吸力下为峰值后软化,在经历了1%~3%的体积收缩变形之后开始出现剪胀。试样的脆性随吸力的增加而增长,在中低吸力下呈桶形或中心鼓形的延性破坏模式,在高吸力下发生应变局部化现象,伴随着明显的剪切带出现。此外,脆性增加了峰后软化的幅度,表现为峰值偏应力与残余破坏状态之间的差值增大。基于区分毛细和吸附作用的双峰持水曲线(SWRC)模型,针对内乡膨胀土与其它具有双孔隙结构及双峰SWRC的土体在毛细吸应力空间进行了峰值强度分析,将吸力从孔隙应力尺度乘以毛细饱和度变为骨架应力尺度时,其呈现的强度包络线为双折线特征。理论分析表明,低吸力范围内,双孔隙结构非饱和土的抗剪强度由饱和强度与毛细吸应力贡献;高吸力范围内,抗剪强度应由饱和强度、毛细吸应力与胶结作用提供。