Advances in Civil Engineering

Volume 2018, Article ID 5190354, 10 pages

https://doi.org/10.1155/2018/5190354

## Calculation of Capillary Rise Height of Soils by SWCC Model

^{1}Geotechnical Engineering Department, Nanjing Hydraulic Research Institute, Nanjing 210029, China^{2}Key Laboratory of Ministry of Education for Geomechanics and Embankment Engineering, Hohai University, Nanjing, China^{3}Jiangsu Research Center for Geotechnical Engineering Technology, Hohai University, Nanjing 210089, China

Correspondence should be addressed to Yuhan Li; moc.qq@418791922

Received 21 March 2018; Accepted 11 June 2018; Published 15 August 2018

Academic Editor: Annan Zhou

Copyright © 2018 Yuhan Li 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 maximum capillary rise height of soil is a complex system which is mainly determined by the distribution characteristics of soil pores. The tests of the rising height of capillary water on 8 kinds of soils by the method of vertical tube are widely conducted to measure the maximum capillary rise height. Based on the BCC model and principles of thermodynamics, the soil-water characteristic curve test is designed for the purpose of calculating the pore distribution of soil samples. A new method for calculating the maximum capillary rise height of soil is proposed by the author by using the distribution function of the soil pore. The coefficient which reflects the relationship between the maximum capillary rise and the average pore radius of soils is utilized during the calculation process, and then the reference range of for different soils is obtained according to series of experiments corresponding. The proposed calculation method offers an effective way to calculate the maximum capillary rise height, which can be applied to analyze the capillary effect area of relevant engineering problems.

#### 1. Introduction

Capillary-driven liquid flow is the main transport mechanism in the soil system of which the water erodes continuously by capillary rise from a lower elevation to higher elevation. Such capillary rise phenomena lead to an increase of the saturation of the soil, which will not only decrease the strength of the soil but also alter the elastic modulus of substructure soils, thereby leading to the corresponding changes in stress and strain response under the external load, for example, the traffic load. Therefore, the defect of the roadbed is closely related to capillary rise erosion. Seasonally frozen ground has always been an important problem in highway construction and channel slope at high latitudes. In the research of frost heaving zone, it is inevitable to determine the height of capillary rise of the substructure. For channel slope and embankment close to the riverside, capillary action path is shortened as well as the effect of capillary action on the supply of water is accelerated. As a result, these infrastructures are more prone to defect and frost heave in such particular areas because of capillary rise. To sum up, study of capillary rise, particularly the maximum capillary rise height, is of great significance to the design of the substructure and channel because the maximum capillary rise height is tightly connected to the strength reduction region and frost area.

A series of studies have been carried out on the capillary rise; LU offered a complete analytical solution for the relationship between the rate and time of capillary rise in soils [1]. However, in the equation, the maximum height of capillary rise is a known soil parameter. In other words, the accurate determination of the maximum height of capillary rise is the prerequisite to calculate the rate of capillary rise. The maximum height of capillary rise has an important influence on the overall engineering behavior of unsaturated soils and is a highly complex system of both the soil and pore water properties. It is extremely difficult to calculate the maximum capillary height accurately in real soils. In order to overcome this, scholars have done a lot of studies and have put forward some empirical formulas which established the correlation between the maximum capillary height and certain measured soil parameters. The earliest formula was proposed by Lane and Washburn [2, 3], after conducting the capillary rising test for 8 kinds of different soils, and the result shows that the maximum capillary height is linear with :

On the basis of (1), Peak and Hansen put forward another empirical formula [4]:

In this formula, 10% particle size , void ratio , and the coefficient are used to calculate the maximum capillary rise height. However, the coefficient is difficult to choose because the range of is relatively large, and the value of depends hugely on the real condition of soil. Kumar and Malik by carrying out indoor tests summarized as follows [5]:where is the height corresponding to air-entry pressure value of soils and is the equivalent of capillary radius of soils. In this formula, the unit of is *μ*m, so it has little influence on the result of the calculation. Therefore, is the only key computational parameter which can be determined by the soil-water characteristic curve. However, it requires an instrument to control the matric suction very precisely especially when the suction is less than 1 kPa [6].

We summarized that according to previous research results, using the micropore distribution of soils and using the pore radius parameter instead of the gradation parameter and void ratio are effective methods to accurately calculate the maximum capillary rise height. In this paper, a new method is proposed to calculate the maximum capillary rising height by using the radius of microscopic pore distribution. A large number of capillary rise tests as well as soil-water characteristic (SWCC) tests have been done for different kinds of soils, from which the parameters of different soils required for the calculation are obtained, and the feasibility of this method will be verified.

#### 2. Theoretical Framework

##### 2.1. Capillary Rise Equilibrium Equation in Soil System

In a single capillary when water column reaches the maximum height, the gravity of the water column is balanced by the surface tension along water-solid interface, as shown in Figure 1. The balance equation is as follows:where is the liquid-solid contact angle; is the density of water; is the radius of the capillary channel (); and is the surface tension of water.