Soil-water Characteristic Curve Research Articles

Structural, soil-water, and dynamic characteristics of clay with different moisture and temperature histories

Variations in the hydro-mechanical properties of pavement subgrade soils are complex under long-term, repeated, and interlaced moisture and temperature (M-T) effects, such as wetting-drying (WD) and freeze-thaw (FT) processes. This study compares the soil structure, soil-water characteristic curves, and accumulated plastic strain (ɛ p) of compacted Heilongjiang clay with three different M-T histories. Experimental results demonstrated that (i) after M-T actions, structural pores develop while textural pores shrink, leading to a reduction in the water retention capacity and an increase in the desaturation rate. Following the stabilization of the M-T effects, the soil structure and soil-water characteristics of specimens with different M-T histories become similar; (ii) at high moisture content (w), ɛ p is more sensitive to moisture changes (including w and suction, s). Following the FT cycles, ε p and ε pa (the difference between the ε p at 5000th and 3000th cyclic loading) become more sensitive to moisture changes; (iii) after M-T effects, the ε pa-w relationship is nonlinear while the ε pa-logs relationship is linear. Different M-T histories generated differences in only the ε p at the beginning of the FT processes while such differences disappear after M-T effects have stabilized. The experimental data presented in this paper could prove valuable in understanding the behaviors of pavement soils under complex environmental conditions.

Water balance estimation for an ordinary solid waste sanitary landfill in Costa Rica

To assess the necessity of treatment systems for leachate generated by ordinary solid waste deposited in a sanitary fill, accurate estimation of the leachate and gas amount produced during biodegradation process is essential. Climatic conditions at the site significantly influence leachate generation; therefore, accurate estimation of rainfall, temperature, solar radiation, and infiltration into the fill is imperative. In this study, we analyzed the water balance of the Miramar landfill in Costa Rica, assessed the amount of leachate produced using various methodologies, and then compared these findings with the field data to identify the best methodology for specific environmental conditions. To comprehensively analyze landfill behavior, as well as the leachate and gases generated from waste decomposition, determining the hydraulic properties of the materials inside the cells is necessary. These properties must consider variables such as the types of materials present at the site, age of the ordinary waste, and their densities. The hydraulic properties of the materials were obtained from various laboratory tests, which included determining the soil–water characteristic curve necessary for assessing unsaturated conditions in the solid waste. These properties are compared with the results of studies conducted in other landfills to validate the current methodology and the obtained results, which can be used for conducting studies on leachate generation or slope stability analysis for sanitary landfill slopes. The amount of leachate generated was estimated using the methodology proposed by Delgado A. (2018). Additionally, the Hydrologic Evaluation of Landfill Performance model (HELP V 4.0) was employed, demonstrating superior estimation compared to recorded field data. The HELP V 4.0 model facilitated the incorporation of different material layers and thicknesses, weather information at the site, slopes, and drainage conditions.

Mitigation of soil frost heave with fungi

Frost heave and thaw weakening can impose engineering issues on cold region infrastructures, including pavements, slopes, pipes, foundations, and buildings. This study investigated the potential of fungi treatment to mitigate the frost susceptibility of soils. Fungi were grown with organic waste to develop fungal mycelium. Subsequently, it is introduced into the soil. A sensitivity study was conducted on the influence of fungi centration on soil behaviors. The volume change behaviors when subjected to freezing or thawing were monitored. The results indicated that both soil frost heave and thaw weakening were reduced significantly with fungi treatment. The mechanisms are investigated with the measurement of the soil water characteristic curves. The introduction of fungi treatment affected the SWCC and soil water affinity. These affect the moisture transport when soil is subjected to freezing/thawing. Subsequently, the volume changes were suppressed.

Assessment of Two SWCC models for predicting the curve fitting parameters of lateritic soil: bentonite mixtures

This study compares the capabilities of soil water characteristic curve (SWCC) models by Brooks-Corey (BC) and van Genuchten (vG) in estimating the curve fitting parameters for lateritic soil—bentonite mixtures. The SWCCs of soil treated with 0–10% bentonite and compacted with British standard light (BSL) energy at compaction states representing dry of optimum, optimum, and wet of optimum conditions were measured by sequential desorption using pressure plate extractor. The fitting parameters of the two equations were determined by a non-linear fitting program. The fitting capabilities of the models on the measured data were compared by statistical indices namely the root mean square error (RMSE), linearity (R2) and index of agreement (d). Results revealed that volumetric water content increased as bentonite content increased with specimens containing 10% bentonite recording the highest and therefore has greater capacity to retain water/contaminants, while the air entry value (AEV) for the various soil mixtures also increased with higher bentonite content. The study also found that the estimated volumetric water contents approximated the measured values at all suctions with a high degree of accuracy with RMSE values that ranged from 0.0035 to 0.0150 for vG model which are somewhat lower than the values for BC equation. Similarly, R2 for the vG equation (≥ 0.99) are, on average, slightly higher than those of the BC fits. However, the d values associated with the BC model which varied between 0.788 and 0.971 are higher than those of the vG (0.784–0.968). Overall, the study established that the vG model proved marginally superior in respect of goodness of fit.

A scaling-based model to describe temporal variability in soil hydraulic properties

Accurate knowledge of temporal variability in soil hydraulic properties (SHPs) can improve the prediction capability of flow and transport models. Lab and field measurements for determining SHPs at multiple timescales are expensive and time-consuming. Further, the existing Fokker-Plank equation (FPE) based numerical and analytical models for describing temporal variation in SHPs require parameterization. In this study, a scaling model is proposed to describe temporal variation in SHPs of four different soils. As field studies related to temporal variation in SHPs are limited, first synthetic temporally varying SHPs, soil water characteristic curves and hydraulic conductivity curves are generated using the analytical solution of FPE. Functional normalization approach is then used to develop reference curves and to obtain scale factors at different time-steps. The time-varying scale factors and the initial SHPs are related by two-step regression equations. The reference curves and the regression equations together can be used to estimate SHPs at any time given the initial SHPs. The developed model is validated using a 5-fold cross validation method and with experimental data at two study sites. The average percentage error in predicted van Genuchten parameters (θs,n and Ksat) except for α are mostly less than 10 %. The performance of the proposed model is comparable to that of FPE analytical model for experimental data. The proposed method holds promise for describing temporal variation in SHPs using only the initial SHPs.

Softening-based interface model and nonlinear load-settlement response analysis of piles in saturated and unsaturated multi-layered soils

This work presents a simplified method for the nonlinear analysis of the load–displacement response of piles in multi-layered soils. As a starting step, a new interface model based on the disturbed state concept (DSC) is put forth to simulate the interface shear stress-displacement relationship by considering the nonlinear hardening–softening behaviour. In the new model, input parameters can be conveniently calibrated using conventional interface shear tests or on-site tests. The good agreement between predictions and experimental data from interface direct shear tests validated the performance of the proposed DSC model. The DSC model performed better in terms of predictions when compared to the hyperbolic one. Next, the soil-structure interface model and bearing capacity theory are coupled to provide a theoretical framework for the analysis of pile load-transfer in saturated and unsaturated multi-layered soils, where the DSC model is employed to represent base resistance as well as skin friction. This work also discusses the profile of steady-state in-situ matric suction, soil–water characteristic curve, and pore-water pressure of unsaturated soils. The proposed method has the advantage of being used in practice as it is simple to obtain input parameters from laboratory tests, as well as Standard Penetration or Cone Penetration Tests. The proposed framework is finally applied to the analysis of five well-documentedcase studies. The proposed approach and the static load test results from the field measurements are found to be in satisfactory agreement, indicating that the proposed method performs well. The proposed method is suggested to be utilised for preliminary analysis, planning a suitable programme of loading tests, as well as optimizing the pile design by back analysis ofthe load test results.

Evaluation of Soil Water Characteristic Curves of Boron added Sand-bentonite Mixtures using the Evaporation Technique

Compacted bentonite or sand-bentonite mixtures are considered buffer/backfill materials in the engineering barriers of deep geological repositories for high-level nuclear waste (HLW) disposal in many countries. The design and long-term functionality of nuclear repositories have critical importance for environmental safety and public health. The initially unsaturated buffer material could become re-saturated long after following the sealing of the repository. Although the saturation degree of the buffer might decrease due to high temperatures and evaporation, it tends to increase with groundwater intrusion. Therefore, the soil water characteristic curves (SWCCs) for these unsaturated soils are a key factor in geotechnical engineering. Yet, the determination of SWCCs can be time-consuming and prone to inaccuracies. The HYPROP (Hydraulic Property Analyzer) evaporation technique is a preferred method for accurately determining water retention curves of soils. This reliable method was applied to estimate the water retention curves for sand-bentonite mixtures in the presence of boron minerals. Known for their minimal thermal expansion and commonly used in various industries, boron minerals may improve the thermal stability of sand-bentonite mixtures. The findings revealed that the boron addition increased the water retention capacity of the 10% bentonite mixtures but had a negligible impact on the 20% bentonite mixtures.

NMR-based pore water distribution characteristics of silty clay during the soil compaction, saturation, and drying processes

The pore water distribution (PWD) of soil provides key information about soil shear strength, hydraulic conductivity, and water-retention ability. The PWD characteristics of the soil depend on the specimen preparation conditions (i.e., the variations in initial water content or compaction degree) and drying-wetting processes, which were investigated by using the nuclear magnetic resonance (NMR) technique. The NMR T2 spectrum is mathematically transformed into the PWD curve to more accurately quantify the variations in pore water content stored with pores of different radii. The pore water in silty clay can be categorized into strongly bound water, intra-aggregate pore water, and inter-aggregate pore water, which are identified by the pore radius of <0.05 μm, 0.05-1.0 μm and >1.0 μm, respectively. The effects of compaction degree and initial water content on the PWD of the soil exhibit distinctions. For unsaturated compacted specimens, the PWDs remain unaffected by changes in compaction degree, while an increase in initial water content promotes the formation of clay aggregates, thereby increasing the maximum water-holding pore radius and the intra-aggregate pore water content. For saturated compacted specimens, the inter-aggregate and intra-aggregate pore water content increases with a decrease in the compaction degree, while the changes in the PWD shape from unimodal to bimodal with an increase in the initial water content. During the soil drying process, inter-aggregate pore water is rapidly drained, the intra-aggregate dominant pore water content increases first and then decreases, and the strongly bound water content remains constant. The relationship between the cumulative pore water distribution curve and the soil-water characteristic curve (SWCC) can be established through the Young-Laplace theory. The SWCC can be well predicted by using the envelope of the cumulative pore water distribution curves during soil drying.

Investigating the source of hysteresis in the soil–water characteristic curve using the multiphase lattice Boltzmann method

Investigating the source of hysteresis in the soil–water characteristic curve using the multiphase lattice Boltzmann method

Development of Wetting-Drying Curves from Elastic Wave Velocities Using a Novel Triaxial Test Apparatus

Abstract The relationship between the soil water characteristic curve (SWCC) and the mechanical behavior of unsaturated soil is imperative and has been well investigated. However, the correlation between elastic wave velocity along the wetting and drying paths of SWCC is largely unknown due to the nonavailability of a standard experimental setup for such a purpose. An ordinary triaxial apparatus has been modified for laboratory assessment of SWCCs under different Ko stresses, along with the measurement of shear and compression wave velocities in due course. The main aim of the study is to draw SWCC, wave velocity characteristic curve (WVCC), and a Poisson’s ratio characteristic curve (PRCC) and to establish the phenomenon that these curves possess hysteresis. The Poisson’s ratio was obtained indirectly by measuring Vp and Vs. Three soil samples with relative densities of 85%, 56%, and 39% were prepared and placed in a modified triaxial test apparatus under wetting and drying cycles. The test results showed that the newly developed apparatus is accurately capable of measuring SWCC. Owing to the similarity in the shape of wave velocity and Poisson’s ratio, response to SWCC, WVCC, and PRCC are drawn. The phenomenon of stress history and the effective stress of the soil affected the behavior during wetting and drying paths.

Analysis of Soil–Water Characteristic Curve and Microstructure of Undisturbed Loess

Long-term irrigation promotes the infiltration of water in the thick, stratified loess layer, significantly raising the groundwater table and triggering a series of landslides in loess platform areas. The soil–water characteristic curve (SWCC) of loess buried at different depths affects the unsaturated infiltration process and is intricately connected to the soil’s microstructure. The SWCCs, scanning electron microscope (SEMs), and pore size distributions (PSDs) for five sets of undisturbed loess samples at depths ranging from 3.4 to 51.9 m are shown in this paper. The results indicate that the fitting parameter air entry value (AEV) of the SWCC rises from 13.67 kPa to 40.19 kPa as the depth increases from 3.4 to 51.9 m. And the saturated volumetric water content drops by 10.9%, with a notable SWCC shape difference between the transition and residual zones observed. Additionally, the total porosity of undisturbed loess falls by 12% when the depth increases from 3.4 to 51.9 m, while the macropores and mesopores reduce by 3.6% and 12.1%, respectively. These findings highlight the control of the pore structure on the SWCC and emphasize the correspondence between the SWCC and PSD. The conclusions also illustrate that the compaction effect changes the microstructure characteristics of loess, thereby affecting the soil’s water retention behavior.

Research on the Coupled Dynamic Response of Vibratory Roller-Unsaturated Subgrade under Different Compaction and Moisture Content States

The dynamic response between the vibratory roller and subgrade under vibratory compaction is essential to improve the compaction quality and optimize the construction technology. Considering the nonlinear hysteresis characteristics of the subgrade in vibratory compaction, a two-degree-of-freedom viscoelastic-plastic, vibratory roller-unsaturated subgrade coupling model, is established to evaluate the effect of compaction stage and moisture content on the vibratory roller-unsaturated subgrade coupling dynamic response. The dynamic resilient modulus semi-empirical model is established based on the dynamic resilient modulus experiment by considering the matrix suction of the unsaturated subgrade and it is the basis of the vibratory roller-unsaturated subgrade coupling model to consider the moisture content influence of compaction. In addition, a plasticity index was proposed to divide the selection of coupling models to consider the influence of compaction stages. The results show that the semi-empirical model takes into account the effect of moisture content by soil–water characteristic curve and it performs well in responding to the experiment results and other experimental data in the published literature. Based on this, the vibratory roller-unsaturated subgrade coupling dynamic response varied for different compaction stages and the moisture content of the unsaturated subgrade. The compaction quality gradually improved as the increase of compaction passes and the decrease of the moisture content. However, the compaction quality of the unsaturated subgrade is weakened by over compaction and excessive moisture content and should balance the compaction operation and quality assurance of the unsaturated subgrade. The results of the research will indicate the compaction mechanism of unsaturated subgrade and provide a theoretical basis for the development of intelligent compaction technology.

The Difference in Shear Behavior and Strength between Loess and Paleosol and Their Prediction of Unsaturated Strength

In recent decades, loess landslide events have attracted increasing attention in the South Jingyang tableland. To elucidate the mechanical mechanism of landslide initiation in the region, this work collected undisturbed loess and paleosol samples taking from the Q2 strata in the South Jingyang tableland. A range of direct shear tests were carried out to explore the strength evolution law of shear zone soil subjected to a varying initial moisture content. In addition, soil water characteristic curves (SWCCs) were also charted and used for predicting the unsaturated shear strength. The findings show that the basic physical properties of the paleosol are different from those of loess due to their different pedogenic environments. The normal stress level and initial moisture content jointly determine whether the shear behavior is strain hardening or strain softening. The shear strength and strength parameters evidently diminish with an increasing initial moisture content, and cohesion contributes to the vast majority of strength attenuation. Paleosol samples possess higher values in shear strength and strength parameters than loess samples due to their stronger inter-particle cementation. The predictive formulas of unsaturated shear strength for undisturbed loess and paleosol are proposed, respectively, based on the Vanapalli model, and the calculated values of the strength prediction model are in perfect agreement with the experimental values.

Variation and correlation between water retention capacity and gas permeability of compacted loess overburden during wetting-drying cycles

Landfill gases can have numerous detrimental effects on the global climate and urban ecological environment. The protective efficacy of the final cover layer against landfill gases, following exposure to periodic natural meteorological changes during long-term service, remains unclear. This study conducted centrifuge tests and gas permeability tests on compacted loess. The experiments examined the impact and relationship of wetting-drying cycles and dry density on the soil water characteristic curve (SWCC) and gas permeability of compacted loess. Research findings reveal that during the dehumidification process of compacted loess, the gas permeability increases non-linearly, varying the gas permeability of soil with different densities to different extents under wetting-drying cycles. Two models were introduced to describe the impact of wetting-drying cycles on gas permeability of loess with various dry densities, where fitting parameters increased with the number of wetting-drying cycles. Sensitivity analysis of the parameters in the Parker-Van Genuchten-Mualem (P-VG-M) model suggests that parameter γ′s accuracy should be ensured in practical applications. Finally, from a microstructural perspective, wetting-drying cycles cause dispersed clay and other binding materials coalesce to fill minuscule pores, leading to an increase in the effective pores responsible for the gas permeability of the soil. These research results offer valuable guidance for designing water retention and gas permeability in compacted loess cover layers under wetting-drying cycles.

Saturated permeability and water retention capacity in biochar-methanotrophs-clay for new landfill cover system

A new landfill cover system, biochar-methanotrophs-clay (BMC) cover is recommended for reducing methane emissions at landfills. It also contributes to decreasing soil permeability and improving soil water retention in a long time, due to highly porous structure of biochar and the growth metabolism of methanotrophs. To determine the effects of biochar content, oxidation aging times and methane-filled days on hydraulic properties, a total of 60 groups of experiments were conducted. The saturated hydraulic conductivity (ksat) was obtained by flexible wall permeameter with controllable hydraulic head pressure. The results showed that the ksat of BMC increased with increasing biochar content and oxidation aging times, while decreased with adding methane-filled days. The soil-water characteristic curves (SWCCs) were obtained with soil suction measured by the filter paper method. The results indicated the water retention capacity of MBC reduced with increasing oxidation aging times but increased with adding methane-filled days. Detected by mercury intrusion porosimetry (MIP), fourier transform infrared spectroscopy (FTIR) and scanning electron microscope (SEM), the differences displayed the changes of pore structures and extracellular polymeric substances (EPS). The oxidation aging of biochar increased the volume of pores, resulting in the increased ksat and the decreased water retention capacity. However, the growing of methanotrophs decreased the volume of pores, resulting in the ksat decreased and the water retention capacity increased due to EPS. No matter how many times the oxidation aging process was experienced, the BMC with longer methane-filled days exhibited relatively lower ksat and better water retention capacity. This implied a more stable barrier capacity to reduce water infiltration in the long term. By combing a series of macro and micro experiments, this paper provides theoretical guidance for the application of biochar-methanotroph-clay mixture to landfill covers.

Biocrusts affect preferential flow and water holding capacity by regulating soil properties in Ultisols from subtropical China

Biological soil crusts (BSCs) play an important role in regulating the process of soil infiltration, and thus changing soil hydrological processes. However, little attention was paid to the effects of BSCs on soil infiltration and water holding capacity in the humid region. Therefore, the objective of this study was to quantitatively characterize the flow pathways of BSCs on soils developed over Quaternary clay and muddy shale from subtropical China by using dye tracer experiments. To determine the effects of BSCs on soil water holding capacity, the soil water characteristic curve (SWCC) was also measured. Results showed that BSCs significantly reduced the soil water infiltration compared with the bare soil. The dyeing coverage (DC) of BSCs on Quaternary clay and muddy shale decreased by 8.4% and 1.8%, respectively. SWCC results showed that the water content of BSCs was 3.5%–42.8% higher than that of bare soil under the same matrix potential, indicating that BSCs increased the water holding capacity. BSCs affected preferential infiltration by regulating surface soil properties, such as increased soil organic matter content (SOM), silt and clay content, and decreased bulk density (BD) and sand content. Furthermore, PLS-PM results revealed that BSCs and its induced increase of silt and clay content played important roles in inhibiting preferential infiltration. The results could help us to better understand the effects of BSCs on soil hydrological processes in Ultisols from subtropical China.

Hydraulic conductivity over a wide suction range of loess with different dry densities

Experimental research into the hydraulic conductivity curve (HCC) of unsaturated soil is limited due to the inherent challenge associated with labor, cost, and time. Typically, the HCC is estimated using the soil water characteristic curve (SWCC) based models and saturated hydraulic conductivity (SHC). However, the efficiency of the SWCC-based model is rarely assessed, and the influence of soil density and pore structure on HCC remains incomplete due to limited experimental data. To address this gap, this study employs an innovative filter-paper-based column method, which can measure the HCC over a wide suction range (e.g. 0−105 kPa), to capture the HCCs of both intact and compacted specimens with varying dry densities. The efficiency of two typical SWCC-based models is assessed using the measured data. Meanwhile, the mercury intrusion porosity (MIP) technique is employed to obtain the pore characteristic (i.e. pore size distribution (PSD)) and a method of predicting the HCC using the PSD data is proposed, emphasizing the dominant role of the pore structure in shaping the HCC. The results reveal that the dry density's influence on the HCC is primarily observed within the low suction range, corresponding to variations in the dominant and large pores. In the high suction range, the HCCs align along a linear trajectory when plotted in a log-log format. A notable finding is the overestimation of the HCC obtained from the SWCC-based models using the measured SHC. When the SHC is regarded as a fitting parameter, good agreement is achieved. The adjusted SHC value is typically 0-1 order of magnitude lower than the measured value, and this discrepancy diminishes as dry density increases. On the other hand, the proposed PSD-based model performs well with the measured SHC data. Caution is exercised when using the SHC to estimate the HCC for modeling water movement in partially saturated soil.

A Novel Three-Segment Model to Describe the Entire Soil–Water Characteristic Curve

This study aims to accurately describe the soil–water characteristic curve (SWCC) across the full range from saturation to oven dryness. We propose a smooth, continuous three-segmented SWCC model that divides the saturation range into wet, air-dried, and oven-dried segments. The two model junction points are anchored at matric suctions of 104.5 and 106.5 cm, respectively. The soil water content at 104.5 cm represents the maximum soil hygroscopy, reflecting the maximum water content in air-dried soil, while the soil water content at 106.5 cm characterizes the minimum soil water content. This imbues the junction points with specific physical significance regarding soil moisture content and matric potential. The model was tested with the water retention data of nine soils across the SWCC and compared with three existing SWCC models based on the adjusted coefficient of determination (adjR2) and root mean square error (RMSE). The results indicated that the proposed model accurately described the entire SWCC. The three-segmented model yielded an adjR2 of &gt;0.99 and an RMSE of ≤0.022 cm3 cm−3, outperforming other models. We also introduce a new method for predicting soil water data in air-dried and oven-dried segments. The results showed that the predicted soil water content values were accurate.

Prediction of the hydraulic conductivity function for unsaturated soils over the entire suction range

The hydraulic conductivity function (HCF) refers to in this paper is the variation of hydraulic conductivity over the entire suction range from 0 to 106 kPa. Most of the available HCF models in the literature are derived based on capillary theory and have limitations in the explanation of HCF in the high suction range. Recently, several models have been proposed for accounting for the thin film flow dominated by the adsorbed water in the high suction range. However, these models require measured HCF data for describing the thin film flow, which is time-consuming. In this study, a mathematically continuous and simple model is proposed for predicting the HCF. The model has physically meaningful parameters for predicting the HCF. In this model, the residual suction estimated from the soil–water characteristic curve (SWCC) is used to distinguish the capillary and adsorption-dominated regions, and a correction operator that considers the thin film flow is introduced. The performance of the model was validated using the measured and published experimental data for various soils. In addition, the proposed model is successfully applied in a numerical investigation of the hydraulic behavior of a capillary barrier system, highlighting the role of the thin film flow.

Research on hydro-thermal coupling model of canal foundation soil based on particle grading curve predicting soil-water characteristic curve

Hydro-thermal coupling is the essence of the freeze-thaw process, and theoretical studies of this coupled process have been hot topics in the field of frozen soil. Darcy's law of unsaturated soil water flow, heat conduction theory, and relative saturation and solid-liquid ratio are based on this paper. According to the principle that the cumulative curve of particle gradation of canal foundation soil is similar to soil-water properties. A soil-water characteristic curve is derived using the cumulative particle gradation curve. VG model is then used to fit soil-water characteristic curves to obtain the canal foundation soil's hydraulic characteristic parameters, and the established hydro-thermal coupling model is modified to reflect canal foundation soil hydro-thermal evolution more objectively. A closed system one-way freezing test method is used to verify the feasibility of the proposed method in this part. The results show that the optimal parameters of the VG model of the subsoil are a = 0.06, n = 1.2, and m = 0.17, and the temperature and water fields obtained from the simulation are in good agreement with the measured data, showing the utility of the hydro-thermal coupling model in predicting hydraulic parameters. Analysis of the multi-field interaction mechanism and dynamic coupling process of the canal foundation soil during freezing and thawing. This has great importance for preventing freezing damage in canals and protecting agricultural safety.