# A two stage model for moisture-induced deformations in expansive soils

- Maki Ito
^{1}, - Shahid Azam
^{1}Email author and - Yafei Hu
^{2}

**3**:19

https://doi.org/10.1186/s40068-014-0019-5

© Ito et al.; licensee Springer 2014

**Received: **15 March 2014

**Accepted: **3 June 2014

**Published: **24 June 2014

## Abstract

### Background

Moisture-induced suction changes in expansive soils due to infiltration and evaporation result in failure of civil infrastructure. The objective of this paper was to develop a two stage deformation model by simultaneously calculating soil suction and stress state. The model predictions were validated using a one-year field monitoring data.

### Results

Deformations in expansive soils closely match cyclical suction changes corresponding to seasonal weather variations. Volume changes fluctuated close to the ground surface and gradually decreased with depth (overburden pressure) due to isolation from meteorological effects. The top 2 m depth was found to be the active zone susceptible to moisture variations.

### Conclusions

The model agreed well with the monitoring data trends with deviations attributed to analytical assumptions in the equations, ineffective capture of antecedent soil conditions, possible soil heterogeneity and anisotropy, and hysteresis in soil saturation and desaturation.

### Keywords

Numerical modeling Unsaturated soils Expansive soils Swelling Shrinking## Background

Expansive soils exhibit volumetric deformations when their water content changes. The moisture flux is governed by climatic conditions prevalent in an area. In arid and semi-arid regions of the globe, where most expansive soils occur, the moisture loss through evaporation generally exceeds the moisture gain through precipitation thereby rendering the soil unsaturated. Consequently, the soil undergoes swelling due to rainfall and shrinkage between successive rainfall events. The effect of these alternate movements exhibits differently under various types of covers. For example, longitudinal cracks in highway embankments (Jotisankasa et al. [2011]), heaved domes in residential basements (Ito and Azam [2013]), settlement in the vicinity of trees (Driscoll [1983]), and vegetation induced movements in pipelines (Clayton et al. [2010]). The cost of infrastructure repair is comparable to other natural disasters such as the estimated $1 billion in the United States of America (Phanikumar and Sharma [2006]).

Few investigations have been reported on the field behavior of expansive clays. Zhan et al. ([2007]) analyzed infiltration through a grassed expansive soil slope in Zaoyang, Hubei, China that was subjected to artificial rainfall. Likewise, Fityus et al. ([2004]) summarized a seven year monitoring data highlighting the effect of soil covers and trees on volume changes in expansive soils at a test site near New Castle, Australia. Finally, Hu et al. ([2010]) presented a one-year field data at a water distribution pipe site in the expansive soil deposit of Regina, Saskatchewan, Canada. The scarcity in reported case histories is because such undertakings are time consuming, labour intensive, and quite costly. The above-mentioned issues can be addressed through the alternative approach of numerical modeling.

Roscoe et al. ([1958]) developed the Original Cam Clay Model (OCCM) for saturated soils. Utilizing the constitutive stress–strain relationships, the elasto-plastic constitutive model consists of the following pillars: (i) elastic property; (ii) yield surface; (iii) plastic potential; and (iv) hardening rule. Roscoe and Burland ([1968]) subsequently modified the original model by incorporating elastic shear strains and an improved yield surface. To capture the behavior of unsaturated soils, Alonso et al. ([1990]) developed the Barcelona Basic Model (BBM) by correlating soil hardening with suction. Alonso et al. ([1999]) extended the above model to expansive soils by including a conceptual fabric representation: elastic deformations in microstructure and plastic deformations in macrostructure (Gens and Alonso [1992]). The Barcelona Expansive Model (BExM) was validated using laboratory test data to understand the combined effect of vertical stress and soil suction on net volumetric strains. Farulla et al. ([2007]) confirmed that the BExM model predicts the behaviour of fissured clays possessing dual porosity. These authors concluded that successive swell-shrink cycles gradually reduce plastic strains thereby converting the soil to an elastic medium.

Vu and Fredlund ([2004]) developed an elasticity based vertical displacement model for unsaturated expansive soils. The nonlinear strain was accounted for by using the coefficient of compressibility as a function of net normal stress and soil suction. The model is appropriate for predicting monotonic paths of the above two stress state variables. Adem and Vanapalli ([2013]) proposed the Modulus of Elasticity Based Method (MEBM) for deformation prediction in similar soils by using a semi-empirical estimation of the modulus of elasticity (Vanapalli and Oh [2010]) along with transient changes in soil suction (Wilson [1997]). The overestimated vertical displacement in this model is attributed to the one-dimensionality and considering soil suction as the only stress state variable.

Derived from Ito and Hu ([2011]), this study develops a two-dimensional model (by including lateral volume changes in calculating vertical deformations) that captures normal stress (overburden soil pressure) and soil suction (net atmospheric flux). The current work is based on a one-dimensional soil atmosphere model where the swelling potential was determined using laboratory test results (Azam and Ito [2012]). The two-dimensional nature of the present model helps improve the capture of actual field conditions. This was confirmed through model validation using field monitoring data, reported by Hu et al. ([2010]).

The objective of this paper was to develop a two stage model for moisture-induced deformations in expansive soils. This included a coupled soil-atmosphere model for seepage through the soil that generated suction data and suction-based displacement model that takes into account the effect of overburden soil pressure. The predicted results were validated using a one-year field instrumentation data.

## Results and discussions

The model predictions generally correlated well with the measured trends in data at the investigated site (obtained from Hu et al. [2010]). The variations between the predicted and the measured data are attributed to the following: (i) analytical assumptions in the equations for calculating net flux; (ii) ineffective capture of antecedent weather conditions by the model; (iii) possible soil heterogeneity, anisotropy, and vegetation at the investigated site; (iv) hysteresis in soil saturation and desaturation during the year; and (v) lack of meterological data at the investigated site.

## Conclusions

Moisture-induced deformations in expansive soils are governed by the net flux at the soil-atmosphere interface and by the suction regime within the soil deposit. A two-stage two-dimensional model was developed. The model predictions generally correlated well with the trends in monitoring data at the investigated site. Deformations in expansive soils closely match cyclical suction changes corresponding to seasonal weather variations. Volume changes fluctuated widely close to the ground surface and gradually reduced with depth due to isolation from meteorological parameters and overburden pressure. The top 2 m depth was found to be the active zone susceptible to moisture variations. The variations between the predicted and the measured data are attributed to analytical assumptions in the equations for calculating net flux, ineffective capture of antecedent soil conditions by the model, possible soil heterogeneity, anisotropy, and vegetation at the investigated site, hysteresis in soil saturation and desaturation during the year, and lack of meteorological data at the investigated site. Clearly, the current model depends on an effective capture of site conditions and material properties.

## Methods

### Modeling process

*SWCC*and hydraulic conductivity functions. The

*SWCC*was estimated by using SoilVision software based on measured index properties (

*w*,

*Gs*, and

*γ*

_{ d }) and a grain size distribution (

*GSD*) curve. Similarly, using the saturated hydraulic conductivity

*k*

_{ s }= 4.22 × 10

^{−9}m/s (Shah [2011]), the estimated hydraulic conductivity function (

*k(ψ*)) was calculated. The climate data provided the infiltration and exfiltration fluxes to determine the boundary condition and then the net flux was calculated in relation to soil properties to obtain a suction profile. The complete theoretical details of the soil-atmospheric modeling process are described by Azam and Ito ([2012]).

*σ - u*

_{ a }) and matric suction, (

*u*

_{ a }

*- u*

_{ w }), where

*σ*is the total stress,

*u*

_{ a }is pore-air pressure, and

*u*

_{ w }is pore-water pressure (Fredlund and Morgenstern [1977]). The two-dimensional soil deformation analysis required soil elasticity parameters, namely:

*E,*soil elasticity with respect to net normal stress and

*H,*soil elasticity with respect to matric suction (Fredlund and Rahardjo [1993]). The volume change index

*C*

_{ s }(obtained from the net normal stress plane) was obtained from the consolidation curve (Ito and Azam [2009]). Likewise,

*C*

_{ m }(obtained from the matric suction plane) was obtained from the

*SWCC*and the shrinkage curve (Ito and Azam [2013]). The elasticity parameters for both the net normal stress plane and the matric suction plane were calculated using a Poisson’s ratio

*μ*(estimated from the typical values of similar soils) for the soil structure as follows (Vu and Fredlund [2004]):

The net normal stress acting on a model profile before applying the weather conditions is the total vertical stress resulted from the overburden pressure. The applied atmospheric conditions adjust the void ratio along with the matric suction plane and the maximum variations in water content from full saturation to desiccation gives about 5 kPa/m stress difference, but it is almost equalized by daily fluctuations. Due to negligible variation in net normal stress state induced by the water content change, the model solely captured the simultaneous cancellation of swelling with the overburden pressure.

*p*is density of soil,

*g*is acceleration due to gravity,

*C = E/(1-2 μ)(1 + μ)*, and

*G = E/2(1 + μ)*.

The model consisted of a homogeneous soil deposit having a 6 m wide x 4 m deep geometry. To understand the effect of meteorological conditions on the soil deposit, one half of the top boundary was treated as the exposed surface (closely mimicking the vegetated park) and the other half was considered to be the covered surface (pertaining to the asphalt-pavement) at the investigated site. Zero water flux was applied at the bottom boundary to represent no ground water table at 15 m depth at the investigation site. Daily climate data from May 1, 2009 to April 30, 2010 was obtained from the Regina International Airport weather station (located about 3 km from the investigation site). An initial matric suction of 1600 kPa based on the field measurement reported by Vu et al. ([2007]) was used. In the soil-deformation model, free movements of soil in the vertical direction were allowed at the top boundary and the horizontal directions were fixed. Likewise, the lower boundary was fixed in both directions.

A general purpose partial differential equation solver, FlexPDE was used for the analysis. The solver utilized the finite element method generating a triangular mesh over a two dimensional geometry. The adequacy of the mesh was constantly calculated and the automatic mesh refinement feature of the solver was applied to reduce error within a tolerance of 0.001. Using the script editor, the governing equation and material properties were directly input in the model compiler. An equation analyzer expanded the defined equation and the material properties, performed spatial differentiation, and applied integration by parts thereby reducing second order terms to create symbolic Galerkin equations for use in the weighted residual method. The Galerkin equations were further differentiated to form the Jacobian coupling matrix for improved convergence. Likewise, the solution curvature was also calculated to include time integration for better accuracy. The model outputs were in the form of soil suction (kPa) and vertical deformation (mm) for the soil-atmosphere model and the soil-deformation model, respectively.

### Material properties

*SWCC*. The curve exhibited the desaturation typical of fine-grained soils comprises of gradual decrease in the gravimetric moisture content as soil suction increases due to the presence of small pore spaces. Figure 6(c) shows the hydraulic conductivities as a function of soil suction. The curve also well captured the pore-size distribution derived from the grain size distribution curve shown in Figure 6(a). The reduction in hydraulic conductivity occurred slowly for the investigated clay and it only started to deviate from the saturated hydraulic conductivity value at a suction value around 100 kPa. Table 1 presents the soil properties used for the soil-deformation analysis. The elasticity parameter functions for the soil were calculated from equation [1] and [2] by using the volume change indices

*C*

_{ s }(from net normal stress plane) and

*C*

_{ m }(from matric suction plane) and an assumed Poisson’s ratio.

**Summary of soil properties**

Soil property | Value |
---|---|

Dry unit weight, | 12.0 |

Initial void ratio, | 1.2 |

Saturated volumetric moisture content (%) | 0.56 |

Hydraulic conductivity, | 4.22 × 10 |

Swelling index with respect to net normal stress, | 0.09 |

Swelling index with respect to matric suction, | 0.1 |

Poisson’s ratio, μ | 0.33 |

### Climate data

The above data implies that during the summer time, the average temperature remained high (14.4°C), the average wind speed was consistent (17.8 km/hour), the average relative humidity was low (64%), and the average net radiation was high (13.9 MJ/m^{2}/day). Such conditions generally render the surface layer of Regina clay desiccated. Therefore, in any sporadic rainfall event during the summer, the expansive clay can readily adsorb all of the available water thereby resulting in swelling.

## Declarations

### Acknowledgement

The authors would like to acknowledge for the financial support provided by the Communities of Tomorrow Inc. Sincere thanks to Dr. Hung Vu and Mr. Imran Shah for their help during numerical modeling and soil data collection, respectively.

## Authors’ Affiliations

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This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited.