Bimodal Soil-water Characteristic Curve Research Articles

Effect of Initial Conditions on the Pore Structure and Bimodal Soil–Water Characteristic Curve of Compacted Granite Residual Soil

Granite residual soil typically forms complex pore structures and exhibits high water sensitivity due to physical and chemical weathering processes. Changes in initial compaction conditions significantly affect the mechanical and hydraulic properties of in situ granite residual soil subgrades, with these variations fundamentally related to changes in pore structure and soil–water characteristics. This study investigates the pore structure and bimodal soil–water characteristic curve (SWCC) of a compacted granite residual soil through laboratory tests and mercury intrusion porosimetry tests. Nine initial conditions were selected based on potential in situ compaction conditions of subgrades, and their effects on the pore size distribution (PSD) and SWCC were thoroughly analyzed. The results show strong correlations between bimodal pore structure and SWCC. The size and volume of inter-aggregate pores exhibit noticeable changes with initial conditions, affecting SWCC within the low and middle suction range. Conversely, the intra-aggregate pores, which constitute over 60% of the pore structures, remain nearly intact across different initial conditions, resulting in similar SWCCs within the high suction range. As the compaction energy increases, the inter-aggregate pores are compressed and lead to a higher water retention capacity. In addition, as the compaction water content increases, the SWCC becomes less sensitive to compaction energy after the aggregates in the pore structure are fully saturated. Additionally, a three-dimensional bimodal SWCC equation is proposed and validated using test data with an R2 value above 0.98. These findings offer valuable insights for the design and quality control of granite residual soil subgrades.

Determining the Bimodal Soil–Water Characteristic Curve of Fine-Grained Subgrade Soil Derived from the Compaction Condition by Incorporating Pore Size Distribution

The soil–water characteristic curve (SWCC) is a key constitutive relationship for unsaturated soil which can be unimodal or bimodal. For the fine-grained compacted subgrade soil with a bimodal pattern, the determination of SWCC is complicated and needs a wide-range suction measurement. In this paper, the bimodal SWCC of a subgrade soil derived from the compaction condition was measured and determined by incorporating pore size distribution. For this purpose, a series of laboratory tests were conducted, including the pressure plate method, filter paper method, and vapor equilibrium method, which were used to measure SWCC at the low, medium, and high suction range, respectively. The pore size distribution (PSD) data were obtained by mercury intrusion porosimetry (MIP) tests and used to predict SWCC. Based on the analysis of hydraulic paths and SWCC-PSD correlations, the SWCC of the subgrade soil should be determined to follow the actual hydraulic path. SWCC within a low suction range can be filled by PSD-based data to improve the fitting accuracy. Then, a graphical method is applied to predict the bimodal SWCC by combining the filter paper method, vapor equilibrium method, and PSD-based data. The prediction curves fit well with the test data for all selected compaction conditions. Furthermore, the prediction method can still provide good prediction performance in the absence of high suction section data, which is beneficial for the application of bimodal SWCC.

Bimodal SWCC and Bimodal PSD of Soils with Dual-Porosity Structure

The soil–water characteristic curve (SWCC) and pore-size distribution (PSD) are fundamental characteristics of soils that determine many physical and mechanical properties. Recent studies demonstrate that both SWCC and PSD sometimes exhibit a bimodal feature. In this paper, soils with bimodal SWCCs are mainly divided into three categories: gap-graded soils, compacted clayey soils, and natural dual-porosity structural soils, from the perspective of microporosity structure. Based on the Fredlund and Xing unimodal SWCC equation, a bimodal SWCC equation is presented. The bimodal PSD equation d v / d log r for mercury intrusion porosimetry (MIP) is derived theoretically, according to the relationship between the mercury intrusion process in MIP and the water desorption process along the drying SWCC. These two associated equations have the same set of parameters, so the corresponding relationship between the bimodal SWCC and bimodal PSD can be directly shown. Three main presenting forms of PSD in MIP tests are summarized. Regression analysis results show that the proposed PSD equation can well fit bimodal PSD experimental data of various soils in the literature, and the SWCCs are predicted at the same time.

A novel modeling method for the bimodal soil-water characteristic curve

This paper introduces a hypothesis to link the soil pore size distribution curve (PSDC) to the bimodal soil–water characteristic curve (SWCC). The relationships between the PSDC and the bimodal SWCC equations are discussed extending a novel modeling method using two equations; namely, the rigid equation and the simplified equation extending two well-known traditional unimodal SWCC equations from the literature. The calibration processes built for both the equations performance was evaluated for various types of soils. The results suggest that both the modified equations provide excellent comparisons with the measured data. The rigid equations provide comprehensive information about the macropores and the micropores of the bimodal SWCC; however, the simplified equations facilitate a flexible and simple curve-fitting process. The relationships between the proposed equations and the available methods for the bimodal SWCC from the literature are also discussed. In addition, a technique is developed based on regression analysis to estimate the key features for bimodal SWCC without bias. Similar to the unimodal SWCC equations the proposed equations are promising tools for predicting the properties of unsaturated soils; they are also valuable for use in numerical techniques for addressing complex nonlinear problems in engineering practice for unsaturated soils.

Variability of Bimodal Soil-Water Characteristic Curves under Different Confining Pressures

Soils with two subcurves of Soil-Water Characteristic Curve (SWCC) (dual porosity soils) might be found within various residual soils. Soils located in different depths have different confining pressure. Residual soils are found in the unsaturated zones due to the deep groundwater table. There is a linear correlation between the hydraulic properties of the soil in the unsaturated area and that of its unsaturated properties. This study aims to examine the influence of the confining pressure towards the SWCC of dual porosity soil. The scope of this study involves measurements of the drying and wetting SWCC using Tempe cells, pressure plates, and an advanced triaxial apparatus. In this study, the mathematical equations were developed to explain the effect of confining pressure on SWCC. The experimental results indicated that the dual porosity soil exhibits bimodal characteristics for the drying curve of SWCC and it exhibits unimodal characteristics for the wetting curve of SWCC. As the confining pressure increases, the air entry values, the inflection points, and the standard deviation of drying SWCC increase. In addition, the hysteresis of SWCC is becoming smaller with the increasing confining pressure.

Moisture-dependent resilient modulus of chemically treated subgrade soil

Traffic loads induce cyclic loading under influence of environmental factors, and is affected by the variation of moisture content and suction (s). These parameters are difficult to quantify, and the methods for determination are cumbersome. This paper presents extensive experimental studies used to obtain the resilient modulus-suction (MR-s) relationship of the treated subgrade soil. An optimum design of bentonite‑magnesium-alkalinization (BMA) was used an additive. The cyclic Triaxial frame with ELDYN system was employed to measure MR values and the suction was estimated using the filter paper test. A bimodal soil water characteristic curve (SWCC) was observed for treated soil with unheated BMA additive and pre-treatment at heated (BMAH) conditions due to the presence of cementitious products. The MR-s relationship was also developed for the stabilized soil using a normalized model. Results showed that the BMAH samples had a significant level of improvement of MR at higher suction levels as compared to BMA samples but this behaviour of BMAH didn't sustain under fully saturated condition. The change in moisture contents under seasonal variation affects the subgrade performance. This study shows the soil additive can effectively improve the mechanical properties of the soil under various moisture contents. The MR for the treated soil can be estimated using the normalized model under the worst-case scenario of a subgrade when the soil is at a fully saturated condition

Analysis of water retention in soil horizons of two open trenches on a slope of Serra do Mar, Brazil, susceptible to landslides

This research presents and analyzes the results of Soil Water Characteristic Curves (SWCC) for the soil horizons (A, B and C) of two different trenches (TR3 and TR7) opened along a slope located in the Serra da Mar mountain range, Brazil. Microaggregations were observed in soil horizons of both trenches, which changed the textural classification of the soils. TR7 showed more macropores than TR3, especially on horizon C. Unimodal SWCC were obtained for soils of the horizon A for both trenches. Instead, bimodal SWCC were obtained for soils of the deeper horizons (B and C). All soil horizons showed the phenomenon of hysteresis, and it’s more expressive in the macroporosity part. In TR7 the water retention capacity is lower in B and C, facilitating the drainage, however, horizons B and C of TR3 presented greater water retention capacity for the same matric suction value. Depending on the intensity and duration of rainfall, the horizons B and C of both trenches may suffer a decrease of shear strength, without necessarily saturating. The A horizon of TR3 can undergo an erosive process for heavy and short rains.

Soil-pipe-atmosphere interaction under field conditions

Unsaturated clay deposits swell and shrink as a result of seasonal variations in climatic conditions and affect the performance of underground infrastructure systems. This paper investigates the response of a 150-mm PVC pipe buried in a highly plastic clay deposit under field conditions. A numerical model was established to integrate the daily climatic conditions. To accurately model field performance, the developed numerical model incorporated the use of a bimodal soil water characteristic curve (SWCC) and the simulation of the hydraulic characteristics of a cracked soil structure. The model results showed that the response of both the soil and the pipe was influenced by soil properties (native and backfill), the depth below the ground surface, and most importantly, the surface boundary condition (sealed versus unsealed surface). Although the pipe trench was covered by a pavement structure, the backfill material consisting of granular materials (i.e., mixed concrete) showed a noticeable variation in volumetric water content (VWC) with time. It was also observed that the effects of the atmosphere extended below the pipe burial depth to a depth of 4 m in the clay soil surrounding the trench. While the pipe trench was backfilled with a non-expansive material, the pipe experienced fluctuating displacements throughout the year. Finally, the model was utilized to give insight into the actual flux transferred through the pavement structure to the backfill material surrounding the pipe. It was predicted that approximately 30% of the surface net flux permeated the pavement structure and interacted with the underlying backfill materials.

Unsaturated shear strength of soil with bimodal soil-water characteristic curve

Many research works have been carried out to develop equations for shear strength of unsaturated soil. However, most of the equations are limited to soils with unimodal soil-water characteristic curves (SWCC). The objective of this study is to propose an equation for estimating the unsaturated shear strength of soils with bimodal SWCCs. Several series of unsaturated consolidated drained triaxial tests were carried out on statically compacted sand–kaolin specimens to evaluate the proposed equation. The experimental results indicated that the ϕb angle of the soil with bimodal SWCC at suctions between the first air-entry value (AEV1) and the second air-entry value (AEV2) was less than the ϕb angle at suctions below AEV1. However, the relationships between shear strength and suction at suctions between AEV1 and AEV2 were still linear. At suctions beyond AEV2, the ϕb angle of the soil with bimodal SWCC started to decrease non-linearly. The evaluation results showed that the estimated bimodal shear strength using the proposed equation in this study had good agreement with the shear strength data from the experimental works.

Pore-scale model for estimating the bimodal soil–water characteristic curve and hydraulic conductivity of compacted soils with different initial densities

This paper proposed a pore-scale model to simulate the effect of initial soil density on the bimodal soil water characteristic curve (SWCC) of compacted soils. The pore-scale model is developed based on the bimodal pore-size distribution. Soils with bimodal pore-size distribution is assumed to have dual porosity, namely the macropore structure and the micropore structure, and hypothesized that the micropore structure is hard to be compressed under mechanical loading. The water stored in the macropore structure is divided into two parts, the bulk water and the meniscus water, respectively. The deformation of soil (bulk water flow) is obtained by horizontal shifting and vertical scaling of the pore-size distribution (PSD) function. A toroidal model is used to describe the influence of initial density on the meniscus water. The pore structure of compacted coal gangue was qualitatively imaged as an evidence of the pore structure changes, and the SWCC of the compacted coal gangue was quantitatively analyzed. Finally, a numerical method is advised for simulating bimodal permeability function by using the proposed model with Mualem function. Laboratory test results in published literature are employed to validate the proposed model and permeability function, and the model predictions showed good agreement with the experimental data in the literature.

Physically based soil water characteristic curves function for soils with inner porosity

ABSTRACTMany unimodal models have been developed to describe the soil water characteristic curves (SWCC). However, for soils with inner porosity the independent draining of the structural and matrix pores frequently results in two distinct air-entry values, which any single unimodal function does not reproduce adequately. In the presented study, a bimodal lognormal (BLN) SWCCs function have been developed for soils with inner porosity. The model involved two overlaying continua pore systems, the pore probability density functions of systems were assumed as lognormal distribution and them can be superposed to obtain the overall probability density function of the soil. The experimental SWCCs data were used to verify the proposed method. The fitted result showed that the BLN approach resulted in the best agreement between measurement and simulation (R2 > 0.99, RSME < 0.66). Another advantage of proposed function was capable of simulating bimodal SWCC using parameters which can be related to physical properties of the structural soils. These physically based parameters could more intuitively analyse the measured data. The BLN approach can potentially be used as effective tool for identifying mechanical and hydraulic porosities in the structural mediums.

Effect of bimodal soil-water characteristic curve on the estimation of permeability function

Soil-water characteristic curve (SWCC) defines the relationship between water content and suction in soil. Many unsaturated properties can be estimated from SWCC such as permeability function and unsaturated shear strength. Therefore, SWCC is considered as the key information of unsaturated soil properties. Permeability function, which defines the relationship between hydraulic conductivity and matric suction, is essential information for seepage analysis in understanding water flow in unsaturated soil. The permeability function is commonly determined indirectly from the SWCC rather than from direct measurement in the laboratory because the direct measurement is time consuming and costly. On the other hand, it has been reported that SWCC can have unimodal and bimodal characteristics. Many models have been proposed for the estimation of permeability function from a unimodal SWCC while limited numbers of model have been proposed for a bimodal SWCC. In this paper, experimental works in laboratory were carried out for measurements of the unsaturated permeability of soils with bimodal SWCC. Zhai and Rahardjo's (2015) equation was used to estimate the permeability function of soils with bimodal SWCC. The experimental results show good agreement with the estimated permeability function. Therefore, Zhai and Rahardjo's (2015) equation was recommended for the estimation of the permeability function from bimodal SWCC. This study also shows that the variability in bimodal SWCC has significant effect on the estimation of the permeability function.

Estimation of unimodal water characteristic curve for gap-graded soil

Soils with a bimodal grain-size distribution (gap-graded soils) can be associated with unimodal or bimodal soil-water characteristic curves (SWCCs). Many equations have been developed to estimate SWCCs using grain-size distribution curves to overcome the high cost and long duration of SWCC experiments. Most of the equations are limited to the estimation of the SWCCs of soils with a unimodal grain-size distribution. Few studies have been conducted on the estimation of unimodal SWCCs for gap-graded soils. In this paper, procedures, equations and computer codes are proposed for estimating the unimodal SWCCs of gap-graded soils. The proposed equations are found to perform well in estimating the unimodal SWCCs of gap-graded soils.

A novel modeling approach for the simulation of soil–water interaction in a highly plastic clay

Formulation of unsaturated soil properties in a mathematical form is necessary for the computational modeling of water flow in soil deposits. To achieve this objective, it is essential to determine the soil–water characteristic curve (SWCC) in order to identify the soil response to transient water flow conditions. The volume–mass constitutive surfaces are other key properties that provide an overall theoretical framework for the soil state variables. In this paper, a bimodal SWCC equation was developed for a native clay deposit based on laboratory soil moisture-suction measurements. The proposed bimodal SWCC equation was formulated based on two distinct logistic power regression models. A factor quantifying the change in the soil hydraulic conductivity was also used to simulate the increase in the hydraulic conductivity of a cracked soil structure. The constitutive surfaces were then established based on the developed bimodal SWCC and representative consolidation test results. This study also attempted to perform an unsaturated seepage modeling analysis using the developed mathematical framework. The model was utilized to simulate the application of net surface flux on a soil column consisting of a highly plastic clay over a clay till. The sensitivity of the seepage analysis, attributable to variations in the SWCC and the hydraulic characteristics, was demonstrated. The results showed that the SWCC is a critical property controlling the modeling of the soil–water interaction, and it has a theoretical weight in performing a water seepage analysis. The use of a bimodal SWCC was capable of capturing the behavior of the top cracked clay layer leading to a rapid change in the volumetric water content with time.

Equation for unimodal and bimodal soil–water characteristic curves

Soil–water characteristic curve (SWCC) data are usually curve fitted with an equation whose parameters were obtained by using optimization procedures. Due to the interdependency of the parameters in the SWCC equation, the parameters are non-unique and thus it is difficult to relate the parameters to other soil properties. This becomes more prominent for bimodal SWCC equations which have more curve-fitting parameters. In order to overcome this limitation, a new equation for both unimodal and bimodal SWCCs is proposed. The new equation uses parameters that can be obtained graphically and no curve-fitting procedures are necessary. Hence, its parameters are unique. The proposed equation was shown to be accurate in representing both unimodal and bimodal SWCCs with several examples.

Effect of compaction state on the soil water characteristic curves of sand–natural expansive clay mixtures

Proper understanding and interpretation of the performance of sand–clay liners requires the consideration of its unsaturated behaviour. A cornerstone in the understanding of the unsaturated hydraulic efficiency is the soil water characteristic curve (SWCC). This study discusses the results of an experimental programme performed to investigate the influence of clay content and compaction state on the SWCCs of a proposed sand–natural clay liner. The proposed liner is a mixture of sand and natural expansive clay obtained from the city of Al-Qatif, Saudi Arabia. Experimental results revealed that the SWCC of sand–natural clay mixture is mainly dependent on the sand–clay composition and compaction state. The influence of clay content on the SWCC of sand–natural clay mixtures was marked by an increase in water retention capacity with increase in clay content ranging between 0% and 60%. This increase in water retention capacity was attributed to the formation of micropores due to the addition of clay. In addition, compacted specimens simulating optimum, dry-of-optimum and wet-of-optimum conditions showed two forms of SWCCs: unimodal and bimodal SWCC. The unimodal SWCC was observed to be dominant for sand–clay mixtures with low clay content (less than 5%) and for specimens compacted at wet-of-optimum conditions. The bimodal SWCC was observed for optimum and dry-of-optimum water content specimens. These forms of SWCCs were used to interpret mixture structure and pore size distribution arising from different clay content and compaction conditions.

Effect of coarse content on shear behavior of unsaturated coarse granular soils

The effects of coarse content on the microstructure, soil-water characteristics, shearing behavior, and critical state characteristics of three types of unsaturated coarse granular soil with different coarse contents are investigated in an integrated manner through an extensive laboratory test program. The tests were performed on samples with the same void ratio of 0.62. As the coarse content increases, the pore-size distribution of the soil changes from unimodal to bimodal. Accordingly, the soil-water characteristic curve (SWCC) changes from unimodal to bimodal. The whole drainage process of the bimodal SWCC is divided into four stages based on the role of the pore water. The contribution of suction to the peak state parameters and critical state parameters, except for the intercept of the critical state line in the stress plane (μ(s)) of a bimodal soil, reaches its maximum in the first drainage region. The pore water in the two pore series of a bimodal soil contributes to the shear strength differently during the desaturation process. Hence, the variations of the maximum dilatancy and the shear strength parameters with degree of saturation are highly nonlinear and μ(s) shows bimodal features. The contributions of suction to the shear strength parameters decrease with increasing coarse content.

Predicting bimodal soil–water characteristic curves and permeability functions using physically based parameters

Experimental evidence shows that a gap-graded soil or a widely-graded granular material may have a bimodal soil–water characteristic curve (SWCC) and a bimodal permeability function. A bimodal SWCC or a bimodal permeability function originates from a dual-porosity structure. To date, the prediction of bimodal SWCCs for gap-graded soils is still a difficult task. In this paper, a bimodal SWCC model is proposed to describe the drying process of granular soils considering a dual-porosity structure. The new SWCC model shows powerful capability in fitting the SWCCs for soils varying from gravel to silt. Regression analysis is conducted to establish empirical relations between the model parameters and the indexes of soil grain-size distribution (GSD). Based on these relations, the new model predicts well both the bimodal SWCCs for gap-graded soils and the unimodal SWCCs for well-graded soils and uniform soils. A bimodal permeability function is also proposed and linked to the new SWCC model. In the absence of experimental SWCCs and permeability functions, the new model can be used to obtain preliminary SWCCs and permeability functions for granular soils. It should be mentioned that the prediction of the SWCC from the GSD is still empirical and does not address the cyclic wetting/drying process. Measurement of the SWCC should be performed wherever an accurate SWCC is required.

Physically based closed-form expression for the bimodal unsaturated hydraulic conductivity function

Simulation of flow and contaminant transport through the vadose zone requires accurate parameterization of the soil hydraulic properties. This requirement is particularly important for soils with a complex structure. In the present study, a physically based closed-form expression for the bimodal unsaturated hydraulic conductivity function is proposed for soils with bimodal pore-size distribution. It combines the bimodal representation of the soil-water characteristic curve (SWCC) function of Liu with the conductivity representation model of Mualem. The proposed equations are defined by parameters that have physical significance, which can be related to the properties of the materials. Experimental data for the representation of bimodal SWCCs and corresponding hydraulic conductivity curves were used to demonstrate the applicability of the proposed functions. The proposed approaches resulted in good agreement with experimental data. These functions can potentially be used as an effective tool for identifying hydraulic porosities in mediums with a complex structure.

Unsaturated characteristics of undisturbed expansive shale from Saudi Arabia

The aim of this paper is to evaluate the soil water characteristic curves (SWCC) of undisturbed expansive shale identified at different locations of Kingdom of Saudi Arabia. The SWCCs were evaluated for suction ranging from 0.5 to 400 MPa. Based on test results, all SWCCs reveal a bimodal curve indicating the presence of two distinct pore size distributions referred to as small and large micropores. Volume change measurements were performed to evaluate void ratio–suction relationships which confirmed the expansive nature of shale. Similarities between measured SWCCs and void ratio–suction relations developed for expansive shale originating from same geological formation suggests the impact of geological and environmental conditions on the unsaturated behavior of shale samples. Finally, a modified approach based on Mckeen’s classification methodology was proposed to assess the swelling potential using bimodal SWCCs. The modified approach was used to assess the relative contribution of different micropores on the swelling potential of shale.