J. Cent. South Univ. (2018) 25: 432-447

DOI: https://doi.org/10.1007/s11771-018-3748-1

Prediction of soil–water characteristic curve for Malan loess in Loess Plateau of China

LI Ping(李萍)¹, LI Tong-lu(李同录)², S. K. Vanapalli³

1. Department of Geology, Northwest University, Xi’an 710069, China;

2. School of Geological & Surveying Engineering, Chang’an University, Xi’an 710054, China;

3. Department of Civil Engineering, University of Ottawa, Ottawa K1N6N5, Canada

Central South University Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Abstract: To predict the soil–water characteristic curve (i.e. SWCC) of natural and remoulded Malan loess from soil physical properties, one-point methods for determining the SWCC that are much simpler than experimental methods are proposed. The predicted SWCC is presented in the form of the BRUTSAERT equation, in which the four model parameters can be estimated from soil physical properties using the best correlations obtained in the present study along with one measured data point. The proposed one-point methods are validated using the measured SWCC data reported in the literature. The results of validation studies suggest that the proposed one-point methods can provide reasonable prediction of the SWCC for natural and remoulded Malan loess. The measured data point should be within the transition zone; the measured suction is suggested between 25 to 100 kPa for natural loess, while between 100 to 500 kPa for remoulded loess.

Key words: soil–water characteristic curve; Malan loess; natural loess; remoulded loess; one-point method; physical properties

Cite this article as: LI Ping, LI Tong-lu, S. K. Vanapalli. Prediction of soil–water characteristic curve for Malan loess in Loess Plateau of China [J]. Journal of Central South University, 2018, 25(2): 432–447. DOI: https://doi.org/10.1007/ s11771-018-3748-1.

1 Introduction

Loess soils are widely distributed in arid and semi-arid regions, covering about 10% land area of the world. Many countries in Asia, Europe, North America, South America and Africa have loess soil deposits. In China, the well-known Loess Plateau extends over 4.4×10⁵ km², occupying about 7% land area of the country [1, 2]. In the Loess Plateau, the arid to semi-arid climate condition and the basin-shaped landscape are favourable for the deposition of wind-blown loess soils. In China, loess soils have deposited since 2.4 million years (i.e. 2.4 Ma), spanning over the Pleistocene period (i.e. 2.4–0.01 Ma) and Holocene period (i.e. recent 0.01 Ma). Therefore, loess soils may behave differently with the depth due to the influence of climate factors over a long period of time. Geotechnical problems in loess deposits, such as landslide and wetting-induced collapse, are more commonly associated with loess soils that deposited during Late Pleistocene period (i.e. Malan loess) and Holocene period (i.e. Holocene loess) because of their relatively loose structure. Holocene loess is typically the vegetation layer; therefore, studies on loess soils are pervasively related to Malan loess.

Malan loess, which is a typical example of collapsible loess, has an open, potentially meta-stable structure. LI et al [3] developed a comprehensive understanding of the collapsible loess soil structure from four elements; namely,particles, contacts, pores and bonds. As a soil with open structure, Malan loess has a two-level structure (i.e. macro-level and micro-level) [4]. Each aggregate, the assemblage of elementary particles (i.e. sands, silts and clays) cemented by bonding materials (such as clay platelets and calcium carbonates) or held by some forces (for example, capillary tension), can be regarded as a micro-level structure. Whereas the arrangement of aggregates is referred to as the macro-level structure. Correspondingly, the pores can be divided into two series based on the pore size and location with respect to aggregates: inter-aggregate pores (or macro-pores) and intra-aggregate pores (or micro- pores). The former series of pores are larger in size and distributed among the aggregates, while the later series of pores are smaller and distributed within the aggregates. Essentially, collapse is a process of the failure of macro pores and transition from an open to a close structure due to wetting as well as loading [5, 6].

Loess soils are typically in a state of unsaturated condition. Since the 1990s, principles of unsaturated soil mechanics have been used to address geotechnical problems associated with loess soils, especially with respect to the shear strength and flow behaviour. The soil–water characteristic curve (i.e. SWCC) along with saturated soil properties has been widely used for the estimation of unsaturated soil properties [7–10]. This is because variation in the unsaturated soil properties is primarily function of the amount of water in the soil. For example, the coefficient of permeability of an unsaturated soil is a function of the volume of water in the soil, while the shear strength and volume change behaviour are primarily functions of the area of water on an unbiased cross section. The SWCC is defined as the relationship between soil suction and water content (volumetric or gravimetric) or degree of saturation. The soil suction is influenced by many factors, including soil structure, soil properties, temperature, degree of saturation, stress applied on the soil or stress history experienced by the soil [11, 12]. For a given soil, the SWCC is actually a three- dimensional curve in the (S_r : e : ψ) space (S_r=degree of saturation; e=void ratio; ψ=soil suction). This is because even at constant suction, degree of saturation varies when there are strains due to either consolidation or shearing) [13–15]. Furthermore, even under constant external stresses, volume change in terms of changes in pore-size distribution could arise during the SWCC measurement as soil suction changes [16].

In the laboratory, the SWCC is measured typically with no (or constant) net stress by changing the imposed matric suction; volume change is conventionally neglected for non- deformable soils. The measured SWCC is influenced by the test device, operators’ ability and experience, size of the specimen, experimental procedure and test temperature [17, 18]. Furthermore, the SWCC used in numerical calculation is influenced by the mathematical equation that is used to fit the measured data, number of measured data points and measurement range of suction [17]. Various methods for measuring soil suction include 1) direct methods using the pressure plate, pressure membrane and tensiometer; 2) indirect methods using the filter paper, porous blocks and heat dissipation sensors. Almost all of the methods are based on the equilibrium of pore-water pressure in the soil with matric suction in the measuring system or stabilization of variables that are sensitive to changes in water content. Therefore, typically a long-time period is required to measure soil suction, 1–2 d and 3–7 d are typically required to achieve the equilibrium at each matric suction in coarse- and fine-grained soil specimens, respectively, using the pressure plate [19]. The time varies depending on the level of suction; longer time is required at higher suction value.

The above discussion suggests that it is time-consuming and cumbersome to measure soil suction. In addition, the measured data may not provide an accurate representation of the SWCC. An interesting study was performed by ZAPATA et al [17] to evaluate the variability in the SWCC drawn using the measured data. The soil specimens of three soils (i.e. sandy, silty and clayey soils) were tested in ten laboratories around the United States for acquiring their SWCC information. A preliminary analysis found that the data provided by some laboratories significantly deviate from the potential best-fit SWCC. Some other laboratories’ data were found to misrepresent the potential best-fit SWCC over the entire suction range or within a certain range, with the variability as high as 54%. Besides, different methods (i.e. the pressure plate, pressure membrane and filter paper were involved in their study) were found to produce high variability for different soils and in different suction ranges (i.e. boundary effect zone, transition zone and residual zone). For these reasons, it is desirable to predict the SWCC from soil properties that are easy to measure and have lower variability from the measurements, such as dry density (or porosity) and grain-size distribution (i.e. GSD). Such methods that can be applied with ease are better choices for engineering practice to determine the SWCC with reasonable accuracy.

The SWCC is typically unimodal in nature for homogeneous soils. However, a bimodal SWCC may be associated with any soil with two-level structure, such as soils of dual-porosity structure and cracked soils [20–22]. For this reason, collapsible Malan loess may have a bimodal SWCC. Recent studies provide evidence of bimodal SWCC behaviour for several loess soils [23]. A bimodal SWCC can be visualized as the superposition of two unimodal SWCCs, one for the water stored in inter-aggregate pores and the other for the water stored in intra-aggregate pores. As per the experimental results on loess soils, the unimodal SWCC for the inter-aggregate pore water is within a low suction range (less than 10 kPa). It indicates that the relationship between soil suction and water content in the field (either during the drying or wetting stress paths) can be well represented using a unimodal SWCC that is for the intra-aggregate pore water. Reliable measurement of a bimodal SWCC using the presently available test facilities is of a great challenge for operators. In addition, the prediction and application of a bimodal SWCC are still evolving since both measured bimodal SWCC data and mathematical equations for representing the bimodal SWCC are rather limited [24–26]. To date, unimodal SWCCs are more widely used in numerical modelling and characterization of unsaturated soil behaviour. For these reasons, the present study is directed towards prediction of the SWCC that is unimodal. The key objectives include 1) to summarize the methods/models proposed for predicting the SWCC from soil physical properties; 2) to develop simple methods for predicting the SWCC of natural and remoulded Malan loess; 3) to validate the proposed methods using the measured data.

2 Summary of methods proposed for predicting the SWCC

As stated above, the SWCC is a three- dimensional curve in the (S_r : e : ψ) space. Even at constant void ratio, the hydraulic hysteresis during inflow and outflow of water through the individual voids makes the SWCCs during drying and wetting stress paths different. In addition, the SWCC behaviour is dependent on the drying–wetting cycling (i.e. main curves and scanning curves). Natural soils have experienced numerous drying– wetting cycles in the field and their SWCCs measured in the laboratory would be the scanning curves, especially within the suction range around the natural condition. However, the SWCCs measured using remoulded soil specimens would be the main curves. The typical main drying and wetting curves in terms of volumetric water content are illustrated in Figure 1. There are an infinite number of scanning curves that bridge between the main drying and wetting curves. The SWCC which is consistent with the process being simulated (i.e. drying or wetting) should be used in modelling the flow behavior of unsaturated soil. However, drying curves are more commonly used since they are easier to measure in the laboratory [19]. The SWCCs (both drying and wetting) are sigmoidal in shape; the two transition points on the drying curve are the air-entry value and residual suction value. The air-entry value, ψ_a, is defined as the matric suction at which air enters into the largest pores by drying. The residual water content, θ_r, is the water content at which water phase is discontinuous; the suction value corresponding to θ_r is called the residual suction, ψ_r. The air-entry value and residual suction divide the drying SWCC into three identifiable stages, namely, boundary effect zone, transition zone and residual zone [8].

Figure 1 Typical main drying and wetting soil–water characteristic curves

Typically, there are three different approaches to predict the SWCC for a soil; 1) database mining for the SWCC from similar soils; 2) prediction from the grain-size distribution (i.e. GSD) curve; 3) correlations relating parameters in the SWCC equations to soil properties [27]. Numerous studies have been performed on the last two approaches. The GSD has enjoyed a great popularity being used for prediction of the SWCC since information of the distribution of voids in the soil, which primarily controls the SWCC behaviour, can be extrapolated from the GSD. The method using the GSD for predicting the SWCC is referred to as pedo-transfer function (i.e. PTF), which includes the 1) physico- empirical methodology, and 2) functional parameter regression methodology [17, 27, 28].

The first category indicates the physico- empirical models using the GSD as a tool. ARYA and PARIS [29] were the first to propose a physico-empirical model for predicting the SWCC from the GSD. The GSD is translated into the pore- size distribution (i.e. PSD), which is then related to the SWCC through the capillary theory. The pore radius prediction was based on the assumption of spherical particles and cylindrical pores. The ARYA and PARIS [29] model was later modified and improved by considering the random packing of spherical particles and the influence of soil structure [30]. Recently, the PSD was directly measured and used to predict the SWCC and changes in the PSD during drying and wetting were also considered. SIMMS and YANFUL [31] developed a model for predicting the drying SWCC based on the evolution of measured PSDs for a compacted clayey soil. HU et al [15] proposed a hysteretic SWCC model based on changes in the PSD taking account of the influence of volumetric deformation on the SWCC. There are other physico-empirical models that do not have to translate the GSD into the PSD. The FREDLUND et al [32] model, for example, makes use of a combination of the capillary theory and an understanding of changes in the SWCC with respect to particle size. FREDLUND [32] modified the FREDLUND and XING [33] SWCC equation to permit the fitting of the GSD data by considering the similarity between the GSD and SWCC. The GSD can be divided into small divisions of uniform particle size and each division corresponds to a unique SWCC (for example, the SWCC for pure sands, pure silts and pure clays). The divisional SWCCs are then summed to form the SWCC of the soil. However, these physico-empirical models could not provide reasonable prediction for fine- grained soils due to the complex particle packing in fine-grained soils [32]. Also, they could not reliably predict the SWCC in the high range of suction, where capillary tension is overwhelmed by adsorption mechanism [23]. In addition, they involve complicated computation and hence are difficult to be used in routine engineering practice.

The second category is based upon statistical prediction of water contents at selected soil suction values. The water content is presented as a function of soil suction and various soil properties based on regression analysis of a dataset. Early studies focused on involving grain size properties (for example; contents of sands, silts and clays, medium particle size, geometric mean particle size, etc.), morphological properties (for example, organic matter, bulk density and porosity, etc.) and chemical properties (for example, CEC (cation exchange capacity) and SAR (soil adsorption ratio, etc.) into the equation. To increase the accuracy, the water contents at several specific suction values (for example, 33 and 1500 kPa that are commonly measured) were involved into the regression equations (for example, Refs. [34–36]). RAWLS et al [37] presented a comprehensive summary of the methods of this category. WILLIAMS et al [28] compared four methods using a dataset of 366 cores of Bernow soil and concluded that regression equations based on soil texture and bulk density provide poor prediction of the water contents, with large errors at some suction values. The results were however significantly improved when two measured water contents (i.e. at suction values 33 and 1500 kPa) are included as variables in the regression equations. Some investigators proposed equations to represent the SWCC of loess soils as functions of matric suction and soil properties (i.e. dry density is the most commonly used variable) [38, 39].

The third category includes the methods which relate the fitting parameters in mathematical equations to soil properties. The widely-known SWCC equations, such as the BROOKS and COREY [40] equation, GENUCHTEN [7] equation and FREDLUND and XING [33] equation, were commonly used for this purpose. Also, there were PTFs attempting to relate the parameters in the CAMPBELL [41] equation and modified Kovacs equation [42] to the grain-size and morphological properties. A summary of some PTFs of this category is presented in Table 1. Similar to the second category, these PTFs were proposed based on regression analysis of a dataset (including soils with the same structure and mineralogical composition or not). Most of them can provide satisfactory prediction only for the soil types that are available in their datasets. Nevertheless, these PTFs are simple and convenient for practicing engineers to determine the SWCC, and alleviate the need of cumbersome laboratory tests.

3 Introduction of the BRUTSAERT SWCC equation

The BRUTSAERT [52] equation is one of the earliest continuous SWCC mathematical expressions that can fit the SWCC data over the entire range of suction. This equation is chosen in the present study to propose simple methods for predicting the SWCC not only because it has less fitting parameters (i.e. it is a two-parameter equation), but it is the best equation to fit the SWCC data of a variety of soils among two- parameter equations [53]. In addition, both fitting parameters are physically meaningful and the effect of one parameter can be distinguished from that of the other. In a study by SILLERS [53], nine SWCC equations including both two-parameter and three- parameter equations were compared by using them to fit the SWCC data of 231 soils (8 USDA soil classification system groups). The results showed that the BRUTSAERT equation performs better than the other two-parameter equations, with the fitting capacity just behind the FREDLUND and XING equation and the van GENUCHTEN equation, which are three-parameter equations. The BRUTSAERT equation can be written in terms of the normalised volumetric water content, Θ, which is defined as the amount of water in the soil normalised between the residual and saturated volumetric water contents (see Eqs. (7) and (8)).

Table 1 Summary of PTFs relating fitting parameters in SWCC equations to soil properties

Continued

                           (7)

                            (8)

where Θ is normalised volumetric water content; θ(ψ) is volumetric water content at the suction, ψ; θ_s is volumetric water content at saturated state; θ_r is volumetric water content at residual state; a_b and n_b are fitting parameters.

Parameter a_b is a function of the air-entry value, and n_b is a function of the rate at which the soil desaturates once the air-entry value has been exceeded. Figure 2(a) presents a plot of the BRUTSAERT equation with constant n_b (i.e. 1.5) and varying a_b. a_b has the same unit as suction (i.e. kPa) and appears at the inflection point on the log-normal scale. The BRUTSAERT equation is symmetrical on the log-normal scale and the curve is translating toward the higher suction region as a_b increases [54]. Figure 2(b) presents a plot of the BRUTSAERT equation with constant a_b (i.e. 30 kPa) and varying n_b. The larger the value of n_b, the steeper the curve in the transition zone.

4 SWCC behaviour of Malan loess in the Loess Plateau of China

According to a comprehensive review of studies on the SWCC of loess soils in the Loess Plateau of China, some key findings are concluded as below:

Figure 2 Plots of BRUTSAERT equation with one varying parameter while the other is constant:

1) Studies on the SWCC of loess soils in the Loess Plateau were mostly undertaken during the last fifteen years and were published in the local language (i.e. Chinese).

2) Loess soils distributed in Gansu Province (especially around the city of Lanzhou) and Shaanxi Province (especially around the city of Xi’an) were extensively studied, while few studies were about that in other regions in the Loess Plateau. In addition, Malan loess deposited during the Late Pleistocene period was extensively studied, while few measurements of the SWCC were conducted on the loess soils deposited earlier (i.e. Lishi loess deposited during the Middle Pleistocene period, the upper Lishi loess is also potentially meta-stable upon wetting).

3) The pressure plate, pressure membrane, tensiometer and unsaturated triaxial test apparatus were commonly used to measure the soil suction. Due to this reason, the measured SWCC was limited to a low range of suction (i.e. less than 1500 kPa). Centrifuge and filter paper were also used in some studies.

4) For remoulded loess, both static compaction and proctor compaction techniques were used to prepare soil specimens for measuring the SWCC. The key variable that was mostly concerned is the dry density. In most cases, the soils collected from the same site were compacted at the same initial water content (for example, natural water content) to different dry densities by controlling the specimen volume. For such a scenario, soil structure that is dependent on the moulding water content and can have a significant influence on the SWCC behavior was rarely considered.

5) The drying SWCC was commonly measured in the laboratory applying the axis translation technique; however, the wetting curve was often measured using tensiometer. The hydraulic hysteresis among drying and wetting branches was rarely studied for loess soils.

These findings suggest that studies on the SWCC behaviour of loess soils in the Loess Plateau are limited. Some of the reasons can be attributed to 1) this is an emerging research area, which has been receiving attention only during the last two decades; 2) comprehensive test facilities and various devices for reliably measuring soil suction were rather limited; 3) highly qualified and trained operators for performing these tests are not widely available. Due to these reasons, it is rather difficult for geotechnical engineers to reliably determine the SWCC of loess soils from experimental results. In other words, there are difficulties in promoting the unsaturated soil technology in conventional engineering practice applications for addressing geotechnical problems related to loess soils. Therefore, it is desirable and urgent to develop simple methods to predict the SWCC for loess soils from soil properties that are easy to measure.

4.1 SWCC of natural Malan loess

In total, 24 Malan loess soils were tested using natural soil specimens for obtaining their SWCC information. Either the pressure plate or pressure membrane was used to measure soil suction.These soils were mostly collected from Gansu and Shaanxi Province. The measured data were fitted with the BRUTSAERT equation and the values of model parameters (i.e. a_b, n_b, θ_s and θ_r) were determined for each soil, which were then used to predict the volumetric water contents using the BRUTSAERT equation at given suction values for each soil. A comparison was made between the measured and predicted volumetric water contents at identical suction values, a good agreement was found between two sets of volumetric water contents (the deviation parameter R²=0.89, see Figure 3).

Figure 3 Predicted and measured volumetric water contents for natural Malan loess soils

Besides the SWCC, physical properties including dry density, liquid limit, plastic limit, clay content and silt content that were measured for all of the natural Malan loess soils, as summarized in Table 2. These soil properties can be easily and reliably determined from simple tests. They were classified into three groups, namely, dry density, Atterberg limits (i.e. liquid limit, plastic limit and plastic index) and GSD (i.e. clay content, silt content and sand content).

Table 2 Soil physical properties of natural Malan loess soils

One property from each group was chosen to obtain the best correlations that relate the BRUTSAERT model parameters (i.e. a_b, n_b and θ_r) to soil physical properties. This procedure was not followed for θ_s since it depends more on the technique used to saturate the soil specimen. Typically, the soil specimen is submerged in de-aired water inside a vacuum container for at least 24 h. The soil specimen by doing this can reach a degree of saturation typically greater than 97% [55].

The best correlations between the BRUTSAERT model parameters (i.e. a_b, n_b and θ_r) and soil physical properties (i.e. dry density, ρ_d, clay content, P_clay and plastic index, I_P) were obtained by means of a statistical multiple regression program, as expressed in Eqs. (9), (10) and (11), where g_i, b_i, c_i and d_i are constants. Their values are: g₁=0.451, b₁=2.991, c₁=0.003, d₁=0.010, g₂=0.001, b₂=5.996, c₂=–0.023, d₂=–0.015, g₃=8.813, b₃=–0.010, c₃= 0.034 and d₃=–0.016 for the available SWCC data. These values and the best correlations (i.e. Eqs. (9), (10) and (11)) are then used to estimate the BRUTSAERT model parameters for natural Malan loess soils from their soil properties (i.e. ρ_d, P_clay and I_P). The estimated model parameters (i.e. a_bp, n_bp and θ_rp) are compared with the best-fit values (i.e. a_b, n_b and θ_r), as shown in Figure 5. Reasonable agreement between a_bp and a_b as well as θ_rp and θ_r) (R²=0.76 and 0.73 for both parameters, respectively) suggests that a_b and θ_r for natural Malan loess can be estimated from soil physical properties through the best correlations obtained in the present study.

             (9)

           (10)

            (11)

Therefore, a simple method is suggested for predicting the SWCC that is presented in the form of the BRUTSAERT equation from soil physical properties for natural Malan loess. The four model parameters (i.e. a_bp, n_bp, θ_sp and θ_rp) can be determined from physical properties that can be reliably measured from simple tests. a_bp and θ_rp can be determined from ρ_d, P_clay and I_P through Eqs. (9) and (11); θ_sp can be calculated using ρ_d and specific gravity, G_s through the volume–mass relations. The estimated a_bp and θ_rp agree well with the best-fit values, a_b and θ_r (see Figures 4(a) and (b). However, there is considerable inconsistency between n_bp and n_b, with a relatively low R² of 0.63 (see Figure 4(c)). To increase the reliability, a measured data point with measured suction and the corresponding volumetric water content, along with a_bp, θ_rp and θ_sp that have been already estimated, are suggested to be used to determine the value of n_bp. Such a simple method for predicting the SWCC from soil physical properties along with one measured data point is referred to as one-point method.

Figure 4 Estimated model parameters in comparison to best-fit values for natural Malan loess:

4.2 SWCC of remoulded Malan loess

There is significant difference between the mechanical behaviour of natural and remoulded loess [56, 57]. A number of experimental studies reported in the literature focused on the comparison between natural loess and the same soil in remoulded state, especially with respect to the shear strength and volume change behaviour. For example, JIANG et al [58] conducted a series of triaxial tests on natural and remoulded loess soils. The results suggest that natural loess is more likely to exhibit strain-softening behavior than remoulded loess. The shear strength of natural loess is typically higher than that of remoulded loess under low confining pressures, while the opposite is true under high confining pressures. HU et al [57] highlighted the difference between the volume change behaviour of natural and remoulded loess. Remoulded loess is found more compressible than natural loess under low vertical stresses, while the opposite is true under high vertical stresses. The flow behaviour of natural and remoulded loess was also compared by some investigators [59, 60]. At high degrees of saturation (for example, higher than 60%), the coefficient of permeability of natural loess is larger than that of remoulded loess, while the opposite is true at low degrees of saturation [59]. In addition, several studies were conducted to compare the SWCCs of natural and remoulded loess [23, 61, 62]. For example, ZHANG and JI [61] found that remoulded loess has slower rate of water extracting from the soil and higher air-entry value. A similar conclusion was drawn by NG et al [23], who observed lower air-entry value, milder adsorption and desorption rates for remoulded loess than natural loess. However, in studies by YAO et al [59] and WEI et al [60], they found that at low suction values, the rate of water escaping from the soil is higher than that of remoulded loess, while the opposite is true at high suction values. These differences can be attributed to the different microstructure characteristics such as the PSD and bonding type between natural and remoulded loess. JIANG et al [63] carried out MIP (i.e. mercury intrusion porosity) and SEM (i.e. scanning electron microscopy) tests on natural loess and the same soil in remoulded state. They found from the results that the fabric of remoulded loess is featured by a relatively uniform distribution of pores, while the particles in natural loess are grouped in connected assemblages. In short, remoulded loess has a more homogenous fabric than natural loess. In addition, two peaks were observed on the pore size density curves of both natural and remoulded loess, which define two major pore series in the soil structure, namely, inter-aggregate pores and intra-aggregate pores. Natural loess has larger dominant macro- pore diameter than remoulded loess; however, interestingly, they have identical dominant micro- pore diameter. In other words, both the natural and remoulded loess samples tested have dual-porosity structure. That is because the remoulded loess soil sample in study by JIANG et al [63] was compacted at an initial water content equal to the natural water content (i.e. 15%), while the optimum water content is about 18%. For such a scenario, the compacted soil has a structure of flocculated type that exhibits dual-porosity. However, the soils compacted at wet side of the optimum water content have relatively homogenous or dispersed structure [4, 11]. They even observed that the volume of pores with small diameter (for example, smaller than 5 μm) is nearly identical in both natural and remoulded loess, irrespective of their different modes of formation. Besides the PSD, different bonding types can also explain the difference between the mechanical behaviour of natural and remoulded loess. In natural loess, the particles or aggregates are in contact with neighboring particles or aggregates by cementation bonding, and the bonding materials are always calcium carbonates and clays [3, 5, 64]. On the contrary, in remoulded loess, particles are predominantly bonded by matric suction [63, 65]. For these reasons, at low degrees of saturation, the structure of remoulded loess is more favorable for drainage of water since more pores in it are filled with water. On the contrary, at high degrees of saturation, the structure of natural loess is more favorable as large size pores in it are filled with water. On the other hand, under low confining pressures or vertical stresses, the bonding strength from cementation in natural loess contributes towards the shear strength and provides resistance to prevent the soil from being compressed. On the contrary, natural loess would experience quick and dramatic reduction in the shear strength and total volume as the confining pressure or vertical stress is high enough to destroy the bonding agents. This reasoning can explain the test results discussed above.

Remoulded loess has different microstructures in spite of having the same mineralogy and physical properties (such as GSD and dry density) from natural loess. For this reason, it is required to study the SWCC behaviour of remoulded loess especially when compacted loess is increasingly used in earth-fill structures in local regions [66]. Disturbed Malan loess soils extracted from 11 different sites around the cities of Lanzhou, Xi’an and Lvliang (Shanxi Province) of China were used to prepare remoulded soil specimens for measuring their SWCC information. Both static compaction and proctor compaction techniques were applied. In most cases, the soils from each site were compacted at the same initial water content (i.e. natural water content) to different dry densities by controlling the volume of soil specimens. For such a scenario, the produced soil specimens could have similar soil structure (i.e. flocculated or dispersed type). The influence of soil structure associated with the moulding water content on the SWCC is not considered. In total, 44 soil specimens with different dry densities were produced, and their SWCC information was measured using either pressure membrane or pressure plate apparatus. The measured data were fitted with the BRUTSAERT equation and the values of model parameters (i.e. i.e. a_b, n_b, θ_s and θ_r) were determined for each of the soil specimens. These values were then used to predict the volumetric water contents using the BRUTSAERT equation at given suction values for each soil specimen. The predicted volumetric water contents were compared with the measured values (see Figure 5). A good agreement was found between two sets of volumetric water contents with a high R² (i.e. 0.99). It is interesting to note that n_b shows little variation for remoulded Malan loess soils, with most of them lying between the values of 1 and 2 (see Figure 6(a)). However, this value varies between 0 and 3 for natural Malan loess.

Figure 5 Measured and predicted volumetric water contents for remoulded Malan loess soils

Similar to natural Malan loess, physical properties including Atterberg limits (i.e. liquid limit, plastic limit and plastic index) and GSD (i.e. contents of clays, silts and sands) were measured for most of the disturbed soils, the details are summarized in Table 3. The best correlations between the BRUTSAERT model parameters (i.e. a_b and θ_r) and soil physical properties (i.e. ρ_d, P_sand and w_P) were obtained as Eqs. (12) and (13), where f_i, r_i, s_i and t_i are constants. Their values are: f₁=0.0002, r₁=2.903, s₁=0.092, t₁=0.429, f₂=0.0001, r₂=2.258, s₂=0.091 and t₂=0.442 for the available SWCC data. These values and the best correlations are then used to estimate the BRUTSAERT model parameters for all of the remoulded loess soil specimens from their physical properties (i.e. ρ_d, P_sand and w_P). The estimated model parameters (i.e. a_bp and θ_rp) are shown in Figures 6(b)–(c) in comparison to the best-fit values (i.e. a_b and θ_r). There is reasonable agreement between a_bp and a_b as well as θ_rp and θ_r (R²=0.71 and 0.76 for both parameters, respectively), which suggests that a_b and θ_r for remoulded Malan loess can be estimated from soil physical properties through the best correlations obtained in the present study.

             (12)

             (13)

A simple method is suggested for predicting the SWCC for remoulded Malan loess from soil physical properties. The predicted SWCC is presented in the form of the BRUTSAERT equation and the four parameters (i.e. a_bp, n_bp, θ_sp and θ_rp) can be determined following simple procedures. θ_sp can be calculated from ρ_d and G_s through the volume- mass relations and a_bp and θ_rp can be determined from soil physical properties (i.e. ρ_d, P_sand and w_P) through the best correlations (i.e. Eqs. (12) and (13)). In spite of the value of n_b falling within a narrow range, between 1 and 2, for remoulded Malan loess (see Figure 6(a)), one measured data point is suggested to be used to determine the value of n_bp. Such a method for predicting the SWCC for remoulded Malan loess using one measured data point is referred to as one-point method.

Table 3 Soil physical properties of disturbed Malan loess soils

Figure 6 Estimated model parameters in comparison to best-fit values for remoulded Malan loess soil specimens:

In the proposed one-point methods for both natural and remoulded Malan loess, θ_sp can be determined through the volume-mass relations and a_bp and θ_rp are suggested to be determined through the best correlations obtained in the present study. One measured data point along with the values of θ_sp, a_bp and θ_rp that have been already determined is suggested to be used to determine the value of n_bp. The measured data point is suggested to be within the transition zone since n_b is strongly related to the rate of water escaping from the soil in the transition zone. In other words, the measured soil suction should be between the air-entry value and residual suction value. This suction range will be further discussed in later section.

5 Validation of proposed one-point methods

In this section, the proposed one-point methods are validated using the measured SWCC data reported in the literature. In total, 20 sets of SWCC data measured using pressure plate, pressure membrane, GCTS soil-water characteristic cell or centrifuge were used. The soils tested are mostly distributed in Shaanxi and Gansu Province and their physical properties collected from the literature are summarized in Table 4 and Table 5, for natural and remoulded Malan loess, respectively. The BRUTSAERT model parameters (i.e. a_bp and θ_rp) are estimated from soil physical properties (i.e. ρ_d, P_sand, P_clay, w_P and I_P) using the best correlations (i.e. Eqs. (9), (11), (12) and (13)) along with the constants (i.e. g_i, b_i, c_i, d_i, f_i, r_i, s_i and t_i) obtained in the present study. The value of θ_sp for each soil specimen is calculated from ρ_d and G_s through the volume–mass relations. The value of n_bp for each soil specimen is determined by substituting the values of a_bp, θ_rp and θ_sp along with one measured data point into the BRUTSAERT equation. The estimated values of a_bp, n_bp, θ_sp and θ_rp required for predicting the SWCC are summarized in Tables 4 and 5.

Table 4 Soil physical properties and estimated values of BRUTSAERT model parameters for natural Malan loess soils

Table 5 Soil physical properties and estimated values of BRUTSAERT model parameters for remoulded Malan loess soils

The results of validation studies are presented by providing comparisons between the measured volumetric water contents and that predicted using the proposed one-point methods at identical suction values (see Figures 7 and 8). There is a relatively good agreement between two sets of volumetric water contents (i.e. R²=0.95 and 0.89 for natural and remoulded Malan loess soils, respectively). These results suggest that the proposed one-point methods can provide relatively reliable prediction of the SWCC for natural and remoulded Malan loess in the Loess Plateau of China.

From the validation studies, it is found that the one measured data point required for determining the value of n_bp should be in the suction range between 25 to 100 kPa for natural Malan loess, while between 100 to 500 kPa for remoulded Malan loess. This indicates that natural loess has the transition zone in lower suction range than that of remoulded loess. This also can be seen from the measured SWCCs which are used for validation of the proposed methods (see Figure 9). Natural loess has a higher air-entry value than remoulded loess, as seen in the figure. Once the air-entry value is exceeded, natural loess has a relatively steeper desorption rate than remoulded loess; however, they tend to have the same desorption rate at high suction values. As discussed earlier, this can be attributed to the difference in microstructure between them. In general, remoulded loess has more homogenous structure than natural loess, which contributes to a gentle desorption rate in the transition zone of remoulded loess.

Figure 7 Comparison between measured volumetric water contents and that predicted using proposed one- point method for natural Malan loess soils

Fig. 8 Comparison between measured volumetric water contents and that predicted using proposed one-point method for remoulded Malan loess soils

Figure 9 Measured SWCCs of natural and remoulded Malan loess soils used for validation studies

From the results of validation studies, the predicted SWCCs for natural loess provide a better comparison with the measured data than remoulded loess, which is evidenced by the R² of both validation studies (i.e. 0.95 and 0.89 for natural and remoulded loess, respectively). The variation in soil structure of remoulded loess soils is not considered in the proposed method, which is thought to contribute to such a little inconsistency between the predicted and measured SWCCs for remoulded loess soils. In other words, soils compacted at dry and wet sides of optimum water content have different structures (i.e. flocculated and dispersed type) in spite of the same soil physical properties, which would contribute to different SWCC behaviour. For this reason, more experimental results for remoulded loess soils are required for calibration of the constants (i.e. f_i, r_i, s_i and t_i) with respect to soil structure, such that the SWCC can be predicted using the proposed method taking account of the influence of the soil structure.

6 Conclusions

The measured SWCC data of natural and remoulded Malan loess soils were fitted with the BRUTSAERT equation. The best correlations between the model parameters and soil physical properties were obtained, upon which one-point methods are proposed for predicting the SWCC from physical properties for natural and remoulded Malan loess. The predicted SWCC is presented in the form of the BRUTSAERT equation. Model parameters a_bp and θ_rp are suggested to be estimated from soil physical properties (i.e. ρ_d, P_sand, P_clay, w_P and I_P) using the best correlations obtained in the present study. One measured data point is suggested to be used for estimating parameter n_bp. Parameter θ_sp can be determined from ρ_d and G_s through the volume–mass relations. The proposed one-point methods are validated using the measured SWCC data reported in the literature. The relatively good agreement between the predicted SWCCs and measured data suggests that the proposed methods can provide reasonable prediction of the SWCC for natural and remoulded Malan loess. The measured data point should be within the transition zone; the measured suction is suggested between 25 to 100 kPa for natural loess, while between 100 to 500 kPa for remoulded loess. However, more experimental results on remoulded loess are required for calibration of the constants in the best correlations with respect to soil structure, such that the SWCC of remoulded loess can be predicted using the proposed method taking account of the influence of soil structure.

Acknowledgement

The first author gratefully acknowledges her appreciation to the Chinese Scholarship Council, which funded her Joint PhD research program. The third author thanks the support from Natural Sciences and Engineering Research Council of Canada (NSERC) for his research programs.

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(Edited by YANG Hua)

中文导读

基于物理特征的马兰黄土土–水特征曲线的预测方法

摘要：总结了已有的预测土–水特征曲线的方法；评价了已有的黄土土–水特征曲线的研究；提出并验证了基于物理特征预测原状及重塑马兰黄土脱湿土–水特征曲线的一点法；比较了原状和重塑马兰黄土的土–水特征曲线。

关键词：土–水特征曲线；马兰黄土；原状黄土；重塑黄土；一点法；物理特征

Foundation item: Project(41372329) supported by the National Natural Science Foundation of China; Project(2014CB744701) supported by the National Basic Research Program of China

Received date: 2016-06-14; Accepted date: 2017-12-10

Corresponding author: LI Tong-lu, PhD, Professor; Tel: +86–29–82339964; E-mail: dcdgx08@chd.edu.cn