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The soil-water characteristic curve (SWCC) is the basis for describing seepage, strength, and constitutive model of unsaturated soil. The existing SWCC models do not work accurately for evaluating loess, because they do not consider the pore deformation that is induced by wetting. The present study develops a new SWCC model for unsaturated loess. The model considers the effect of wetting-induced pore deformation (WIPD) on the SWCC. The new model includes 6 parameters, which could be confirmed by laboratory tests. The pore volume function (PVF) was described by the WIPD. The shift factor

Loess covers a considerable part of China, especially in northern China’s Loess Plateau, where thick, unsaturated, and collapsible loess abounds. The properties of unsaturated loess are sensitive to water content [

Much research has been conducted on the theoretical model of the SWCC. According to some studies, the SWCC is influenced by multiple factors, including temperature [

In follow-up studies, scholars have gradually realized this limitation [

Previous research has shown that the size distribution of soil pores evolves with changes in the hydraulic path and stress history [

Unsaturated loess could be taken as a porous medium composed of pores and particles with different sizes. The radius of the pores is

Given the assumption that the radius of all pores in the loess falls in the range between the minimum radius

When the definition of the soil water-holing capacity curve (capillary pressure distribution function) is taken into consideration [

The study of Zhou et al. [

The water-holding capacity curve function in equation (

When the soil suction is infinite

Effective saturation is defined as [

And it is expressed using the water-holding capacity curve function thusly

Judging from equations (

According to the local equilibrium assumption raised by Mualem [

And

The radius of all pores in the soil falls between the minimum radius

The typical diagram of pore distribution is shown in Figure

Typical diagram of pore distribution.

The moisture content ratio is gained by the following:

Based on the definition of PVF from the research of Della Vecchia et al. [

Moreover, according to the Young-Laplace equation, the relationship between pore radius and suction is as follows:

The function of the relationship between saturation and suction satisfies the following:

The classical V-G model was used for the derivation. The SWCC function of the V-G model is represented as [

The derivation process involves the following: based on the definition of the volumetric moisture content, the following is obtained thusly:

The pore density function that takes volumetric moisture content into consideration is as follows:

The PVF is

In equation (

After the PVF of the soil is obtained, the description of the influence of WIPD on the SWCC must be preceded by establishing how the PVF changes with variations in WIPD. This means that the influence of WIPD on the PVF should be determined first. In the next section, we will consider the patterns in the influence exerted by WIPD on the PVF of the loess.

Much research has been conducted on the influence of processes like loading [

MIP results of dromedary soil [

MIP results of bimodal soil [

Based on the assumed pattern of the influence of WIPD of unsaturated loess on the PVF, the soil simplification may be regarded as a dromedary structure without considering the pore variation in the aggregate. The influence of WIPD on the PVF of the loess can be obtained by shifting and scaling from an initial state. This means that the PVF of any pore deformation state can be obtained through the PVF of the initial state. By introducing the shift factor

Influence of pore deformation on PVF.

It can be imagined that so long as the relationships between the indicator of the soil pores (such as void ratio, porosity factor, etc.) and the shift factor and the compression factor are established, the PVF of any state under different pore indicators can be obtained, based on which the SWCC under any pore deformation state can be obtained by integration from equation (

Taking the V-G model as the basis and assuming an initial state in which the void ratio of any pore is proposed as

First, to obtain the peak value

Assume that

Substitute

In the same way, the PVF at any state can be gained as

Combining the PVF with the definition of the compression factor

Then, we solve for the shift factor

According to the definition in equation (

It can be found that to solve and obtain the shift factor

We associate this with the Young-Laplace equation in equation (

To simplify the derivation process, we select the B-C model with relatively few model parameters to solve

We convert it into

We substitute this into the above equation and obtain

Further, we obtain the average pore radius:

We substitute it into equation (

We simplify and dispose it and get:

The PVF

The SWCC (equation (

We introduce the SWCC of any state into the SWCC integration function (equation (

We simplify this and obtain

We introduce

Thus, we find that the SWCC at any pore state is expressed as the function between the suction and void ratio. The SWCC changes with the void ratio changes. This can be construed as the three-dimensional space curve composed of saturation degree, suction, and void ratio. When the void ratio is not taken into consideration, we take the reference state

The SWCC test methods [

15 bar pressure membrane.

The working mechanism of the pressure membrane meter is as follows: it blocks the air from entering the pressure chamber through the ceramic plate; the membrane will produce surface tension as the pores of the ceramic plate shrink; the shrunk membrane covers the small hole of the whole ceramic plate; the difference between the gas pressure above the shrunk membrane and the water pressure below it is equal to the suction value; and the maximal suction value that can be maintained by the ceramic plate is

In this work, we set out to conduct tests of the SWCC of loess during the loess drying process. Remolded loess samples with different void ratios were prepared in the process that took the impact of the WIPD of unsaturated loess into consideration. The samples were prepared by fully disturbing the undisturbed soil, which was directly obtained from a construction site, packaged, and transported to the laboratory. The fundamental parameters of the undisturbed soil were tested and recorded, as shown in Table ^{3}, 1.51 g/cm^{3}, 1.55 g/cm^{3}, 1.60 g/cm^{3}, 1.65 g/cm^{3}, and 1.70 g/cm^{3}, respectively. The pressure boost values during the test process were set, respectively, at 0.1 bar, 0.2 bar, 0.4 bar, 0.6 bar, 0.8 bar, 1 bar, 1.5 bar, 2 bar, 2.5 bar, 3 bar, 3.5 bar, 4 bar, 4.5 bar, and 5 bar; the corresponding suction values were, respectively, 10 kPa, 20 kPa, 40 kPa, 60 kPa, 80 kPa, 100 kPa, 150 kPa, 200 kPa, 250 kPa, 300 kPa, 350 kPa, 400 kPa, 450 kPa, and 500 kPa.

Parameters of undisturbed loess.

Specific gravity ( |
Density (g/cm^{3}) |
Water content (%) | Void ratio | Compression modulus (MPa) | ||
---|---|---|---|---|---|---|

2.72 | 1.52 | 14.1 | 30.66 | 0.82 | 21 | 12.6 |

The remolded soil sample was prepared by fully disturbing the undisturbed soil, and the remolded samples with different void ratios were prepared using the sampler (Figure

Preparation of remolded loess sample.

According to the requirements of the tests, samples were saturated by the capillary saturation method. The saturation of the ring cutter sample was measured after saturation for 72 hours. The samples were deemed to meet the requirements if the saturation was greater than 95%. We wet the ceramic plate to a saturated state before the test. We weighed and recorded the total weight of the ring cutter plus the soil and then sealed the pressure chamber and exerted pressure step by step. After each stage of pressure balance, we read and recorded the reading of the water-collecting tube and used the difference between the two balance readings to determine the drainage weight that corresponded to each stage of pressure

The test results of the SWCC of remolded loess with different void ratios were used to verify the reliability of the new model. To calculate the SWCC at different void ratios, a certain void ratio was used as the initial void ratio to calibrate the parameters. This paper adopts an initial void ratio of

Calibration curve of the model.

Calibration of model parameters.

Item | ||||
---|---|---|---|---|

Parameter values | 0.455 | 0.095 | 2.0 | 0.015 |

Under the condition that the calibrated model parameters are obtained, the SWCC of loess that at any void ratio can be predicted according to equation (

Result comparison at the void ratio of 0.8.

Result comparison at the void ratio of 0.75.

Result comparison at the void ratio of 0.7.

Result comparison at the void ratio of 0.65.

Result comparison at the void ratio of 0.6.

The pore deformation has an obvious influence on the SWCC of the unsaturated loess. After introducing the void ratio parameter, we found that the model prediction results were closely related to parameters

Figure

Influence of

Figure

Influence of

Figure

Influence of

Figure

Relation of volumetric water content and void ratio.

In this paper, we established a new SWCC for predicting the hydraulic characteristics of unsaturated loess with different pore states, and we conducted tests of remolded loess to validate the capability of the new model. The conclusions are as follows:

Based on the assumption of local equilibrium, we defined the expression of the pore density function, discussed the pore distribution of the porous soil medium, and provided the PVF of any WIPD state

By introducing the compression factor and shift factor, we provided a description of the variation law of the pore distribution curve caused by the WIPD of unsaturated loess, and we inferred the relationship between pore indicator

Based on the PVF, we introduced the pore indicator into the classical V-G model, and we built an SWCC model of unsaturated loess considering the influence of WIPD. The model contains six parameters. When the pore deformation was not considered, the model regressed into a classical V-G model

We carried out the soil-water characteristics tests of unsaturated loess under different pore conditions. The model parameters were calibrated, and the model results were verified under different pore conditions. The results showed that the model has good simulation ability and can accurately predict the evolution of the SWCC of loess under different pore deformation conditions

The impact of parameters of

The data used to support the findings of this study are available from the corresponding authors upon request.

The authors declare that they have no conflicts of interest.

This research was financially supported by grants of the National Science Foundation of China (51378004 and 51578447), Postdoctoral Science Foundation of China (2018M643809XB), and Talent Foundation of Xi’an University of Architecture and Technology (RC1803).