Geofluids

Volume 2019, Article ID 1672418, 14 pages

https://doi.org/10.1155/2019/1672418

## A New Soil-Water Characteristic Curve Model for Unsaturated Loess Based on Wetting-Induced Pore Deformation

^{1}School of Civil Engineering, Xi’an University of Architecture and Technology, Xi’an 710055, China^{2}Shaanxi Key Laboratory of Geotechnical and Underground Space, Xi’an University of Architecture and Technology, Xi’an 710055, China^{3}School of Highway, Chang’an University, Xi’an 710064, China

Correspondence should be addressed to Yuwei Zhang; moc.qq@6769562301 and Zhanping Song; nc.ude.tauax@typhzgnos

Received 27 November 2018; Revised 24 January 2019; Accepted 20 February 2019; Published 15 April 2019

Academic Editor: Jaewon Jang

Copyright © 2019 Yuwei Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

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 and the compression factor were introduced into the model. The relationship between the void ratio and and was established using the average pore radius. The new SWCC model for saturated loess was improved based on the classical van Genuchten (V-G) model. If the WIPD had not been considered, the new model would regress into the classical V-G model. SWCC tests of unsaturated loess with different void ratios were carried out to verify the new model. The model parameters were calibrated in the original state, and the SWCCs of different void ratios were predicted by the new model and found to be in good agreement with the test results.

#### 1. Introduction

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 [1]. The inner pores of this material are obviously influenced by wetting. Wetting-induced pore deformation (WIPD) is the main reason for changes in the hydraulic characteristics of loess [2–5]. The loess material used in construction work is mostly in an unsaturated state. The unique solid-liquid-gas state of unsaturated loess complicates its mechanical properties. The soil-water characteristic curve (SWCC) is the basis of the study of loess mechanics, which is a field of study that describes the relationship between saturation or volumetric moisture content and suction . The hydromechanical properties of unsaturated soil, such as permeability [6, 7], strength [8–12], and deformation [13–19], are closely related to the SWCC. The constitutive model often involves the SWCC [20–28]; therefore, some scholars have pointed out that the SWCC has the same status in unsaturated soil mechanics as the compression curve has in saturated soil mechanics [29–33]. Measurement of the SWCC by laboratory and field methods is time-consuming and expensive; therefore, it is helpful to establish a mathematical SWCC model for predicting the hydraulic characteristics of soil [34–36].

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 [37], drying and watering cycles [38–40], stress history [41, 42], and initial density [43–45], in which the pore structure of the soil has a decisive influence on the SWCC [46–49]. Early SWCC models used the pore distribution coefficient to reflect the influence of the pore structure. In these models, the pore structure was usually assumed to consist of rigid pores that were unaffected by deformation [50–53]. This assumption is applicable to conventional soils. However, if pore deformation is not considered in the case of highly collapsible and unsaturated loess with large pores, the predictions will have significant errors.

In follow-up studies, scholars have gradually realized this limitation [54–56], and they have begun to explore the SWCC model with consideration of the influence of pore change. Researchers have conducted tests to obtain the SWCC with different void ratios, and some have established empirical models based on test results. For example, Sun et al. [57, 58] conducted an SWCC test of red clay, analyzing the variation law of the SWCC and the characteristics of wetting-drying hysteresis for different types of pores. Rahardjo et al. [59] carried out a complete dehumidification test of expansive soil, analyzing changes in the SWCC of different initial void ratios; Zhou et al. [45] analyzed the incremental relationship between saturation and initial density, introducing an initial density influence factor to build an SWCC model. Simms and Yanful gauged the variation pattern of pores in a clay dehumidification test, establishing a causality relationship between pore distribution and the SWCC [60]. Zhang and Chen [61] introduced the average pore, pore distribution index, and porosity, combining these factors with the Brooks and Corey model to construct an SWCC model for deformed soil. Other scholars introduced a variety of parameters (void ratio, dry density, etc.) into the existing classical model through a series of assumptions, to reflect the influence of the pore change on the SWCC. For instance, considering the influence of the void ratio on parameters such as the suction intake value and pore distribution index, Huang et al. [7] established an SWCC model based on the Brooks and Corey model. Gallipoli [31] defined the relationship between the parameters of the suction intake value and the void ratio and established an SWCC model. Nuth and Laloui [62] defined the influence pattern of soil compression deformation on soil pores and established a cooperative relationship between soil compression and the SWCC. Hu et al. [49] assumed that pore functions remain unchanged during compression deformation and established an SWCC model that considered deformation. Scholars have carried out much research on soil-water characteristics using experimental tests [39, 57, 58], theories [2, 3, 8, 10, 28, 31], and numerical modeling methods [63, 64]; however, studies on the impact of wetting-induced pore deformation (WIPD) on the SWCC of unsaturated loess are limited.

Previous research has shown that the size distribution of soil pores evolves with changes in the hydraulic path and stress history [2, 18, 39, 47]. The description of a pore distribution index has involved different analytical methods in different models. A reasonable pore evolution law can simulate the evolution of aggregate pore structures and the hydraulic changes of compact loess [47, 49, 52, 54, 65]. In this paper, the authors took the pore volume function (PVF) as the basis, considered the evolutionary characteristics of immersed pore structures, and assumed the influence law of WIPD on the PVF. The compression factor and the shift factor were introduced into PVF under the impact of WIPD. Based on the classical V-G model [66], a new SWCC model of loess that considers the effect of WIPD was established in this paper. There are six parameters (, , , , , and ) in the new model, all of which could be calibrated by simple laboratory tests. Finally, results from the SWCC tests of the reconstructed unsaturated loess with different void ratios are used to verify the capability of the new model. The influence of each parameter on the new model was discussed in detail. The research results of this paper can provide a new simplified and accurate method for predicting the SWCC of loess resulting from WIPD.

#### 2. Evolution Characteristics of WIPD in Loess

##### 2.1. Pore Distribution Function

Unsaturated loess could be taken as a porous medium composed of pores and particles with different sizes. The radius of the pores is , and the PVF of the porous medium is . So when the radius of the pores changes from to and the percentage taken up of the pores is , the pore volume in the soil can be expressed as

Given the assumption that the radius of all pores in the loess falls in the range between the minimum radius and the maximum radius and according to the definition of volumetric moisture content and the assumption of local equilibrium, pores with a radius that is smaller than that of a certain value will be filled by water. Therefore, the relationship between the volumetric moisture content and the PVF can be expressed as follows

When the definition of the soil water-holing capacity curve (capillary pressure distribution function) is taken into consideration [20],

The study of Zhou et al. [22, 44] holds that water in soil pores may be classified into two categories, one being the free water inside the pores with significant capillarity and the other being the water that is attached to solid particles. By means of the impact of chemical bonding, the latter kind of water is considered to be unchanged and thus equal to residual saturation . It corresponds to the residual volumetric moisture content . Since the saturation of soils was regarded as the sum of microsaturation and macrosaturation , then . Volumetric moisture content can also be regarded as being composed of the residual volumetric moisture content and the volumetric moisture content of the changing part. Therefore, the relationship between the volumetric moisture content and the PVF meets the following conditions:

The water-holding capacity curve function in equation (3) is expressed in the following way:

When the soil suction is infinite , the volumetric moisture content of soils is the residual volumetric moisture content , and the soil saturation is the residual saturation . When the soil suction is zero , the volumetric moisture content is , and the saturation is 1, .

Effective saturation is defined as [22] and is expressed using the PVF thusly

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

Judging from equations (7) and (8), we can find that to deduce the SWCC, the PVF or the water-holding capacity curve function must be known. The PVF can be also expressed by the pore density function. In this paper, the method proposed by Della Vecchia et al. [47] is used to deduce the pore density function , and is denoted as the contribution of pores with a radius less than to the overall void ratio. Variable is defined as follows:

According to the local equilibrium assumption raised by Mualem [6], water inside soil first fills up small pores due to the higher capillarity. The pore radius integral function at this time can be linked with the saturation of soils:

And is defined as the pore size density function of the porous medium, such that when the pore radius changes from to , the percentage occupied by the pores is . Hence,

The radius of all pores in the soil falls between the minimum radius and the maximum radius , and thus,

is denoted as the probability of pores with less-than radius, and the number of pores with radius that is smaller than is

The typical diagram of pore distribution is shown in Figure 1. A specific suction corresponds to a specific pore radius . Pores with a radius that is larger than in the soil are filled up by air, while those with less-than radius are filled up by water. According to the definition of soil saturation, the relationship between saturation and pore distribution is as follows: