# Accounting for Expansive Soil Movement in Geotechnical Design—A State-of-the-Art Review

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## Abstract

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## 1. Introduction

## 2. Expansive Soil Behaviour

## 3. Problems with Expansive Soils

## 4. Investigations of Expansive Soil Behaviour

#### 4.1. Laboratory Investigations

_{m}, and total suction, u

_{t}) and the water content of the filter paper (w

_{fp}) based on best-fit regressions. To determine the solute suction (u

_{s}) using the EC method, Equation (3) can be used. Equation (3) incorporates the actual moisture content (amc) to represent field conditions in which soil and water at a ratio of 1:5 are used to estimate the salinity of the soil–water suspension in the laboratory.

_{r}is the residual volumetric moisture content; θ

_{s}is the saturated volumetric moisture content; ψ is the soil suction; and a, n, and m are empirical fitting parameters related to the SWCC, with $m=1-\frac{1}{n}$.

_{s}), plasticity index (PI), and fine content, Witczak et al. [61] proposed Equations (5)–(10) to estimate the SWCC relating θ and the soil suction (in kPa).

_{f}= 5 for a

_{f}< 5 and c

_{f}= 0.03 for c

_{f}< 0.01

_{s}can be estimated using Equation (12) [62].

_{c})–capillary force-associated saturation and adhesive saturation (S

_{a})–adhesive force-associated saturation, as shown in Equation (13) (mathematically rearranged by Fredlund et al. [64], Bussière [65]). The proposed MK model comprises Equations (13)–(23) to estimate the SWCC relating S

_{a}and S

_{c}. This model requires basic soil properties, i.e., grain size distribution and liquid limit.

_{c}and suction is represented by Equation (14).

_{co}is the equivalent capillary rise (cm), ψ is the soil suction (cm), and m is a unitless pore size distribution parameter.

_{a}and the suction is represented by Equation (15).

_{c}is the dimensionless adhesion coefficient, e is the void ratio, ${\psi}_{0}$ is the suction of the soil under completely dry conditions (cm) (${\psi}_{0}={10}^{7}$ cm of water, which approximately corresponds to S = 0), ψ

_{n}is a normalisation parameter for maintaining unit consistencies (equal to 1 cm if the ψ values are in cm), and ${\psi}_{r}$ is the residual suction (cm).

_{co}, m, ${\psi}_{r}$, and a

_{c}. For granular soil, these parameters are expressed as follows:

_{10}is the particle size corresponding to the tenth percentile of the particle size distribution curve, and ${C}_{u}$ is the uniformity coefficient, which is equal to ${D}_{60}/{D}_{10}$. Here, D

_{60}is the particle size corresponding to the sixtieth percentile of the particle size distribution curve.

^{3}), and ${w}_{L}$ is the liquid limit (%).

_{sat}) can be determined through various permeability tests, such as falling head or constant head tests. However, the measurement of K for unsaturated conditions (K

_{unsat}) is difficult in laboratory or field tests as K

_{unsat}is dependent on the soil suction. The hydraulic conductivity function can be estimated using correlations proposed in various studies [54,66,67], which generally take the soil suction and K

_{sat}as input parameters, as shown in Equation (24), proposed by Van Genuchten [54]. Using this equation, K

_{unsat}can be estimated through a back-analysis of the field data as a function of K

_{sat}, as demonstrated by Karim et al. [15].

#### 4.2. Field Investigations

#### 4.3. Numerical Investigations

_{w}is the soil suction, and S

_{r}is the degree of saturation. The incremental stress (dσ′) can be expressed as shown in Equation (26) [97].

_{o}is the initial void ratio, ${\epsilon}_{ms}{}^{\prime}$ is the volumetric strain obtained through laboratory shrinkage experiments, and ${\sigma}_{o}^{eq}$ and ${\sigma}^{eq}$ are the initial and final equivalent stress components, respectively, of the orthogonal stresses.

## 5. Australian Design Practice for Residential Footings on Expansive Soils

_{s}). Here, y

_{s}is defined as the movement of the ground in the vertical direction owing to long-term suction changes in the soil. The site classes ranges from mostly sandy and rocky non-reactive sites (y

_{s}= 0 mm) to extremely reactive sites (y

_{s}> 75 mm). y

_{s}is also used in the design of other structures on expansive soils, such as road pavements [99,100].

#### 5.1. Characteristic Surface Movement Prediction

_{s}, can be calculated as the cumulative movement of the individual sublayers of soil within the design suction change depth (H

_{s}), as shown in Equation (27) [75].

_{pt}is the instability index (%/pF), $\overline{\Delta u}$ is the average soil suction change of a particular layer (pF), h is the thickness of a particular layer (m), and N is the number of soil layers within H

_{s}.

#### 5.1.1. Instability Index

_{ss}) and can be estimated using Equation (29) [104].

_{ls}) and can be estimated using Equation (30) [103].

_{o}is the water content of the sample trimmings, w

_{f}is the final water content of soil (%), u

_{o}is the mean soil suction of the sample trimmings, and u

_{f}is the mean soil suction determined from the sub-samples acquired after the sample’s removal from the apparatus (pF).

_{cs}) and can be estimated using Equation (33) [102,105].

_{wc}is the variation in the moisture content (%), and c is the soil moisture characteristics, defined as below:

_{c}is the water content of a soil disc (%) at the mass equilibrium point when the specimen is kept in a chamber with supersaturated ammonium chloride solution, w

_{o}is the initial water content of the sample trimmings, and u

_{o}is the initial total suction (pF).

_{ss}involves both swelling and core shrinkage tests; however, controlling the suction can be difficult, and lateral confinement of the sample during the swelling test allows only vertical movement to occur. In addition, neglecting the solute suction expected from mineralised soil by using distilled water may affect the accuracy of the results. Despite the limitations of I

_{ss}, it captures the shrink–swell properties, and thus it can be considered a more reliable reactivity index than I

_{cs}. This observation was supported by Fityus et al. [107] and Cameron [108]. Furthermore, the shrink–swell test method does not require tests for suction and can be applied to any given initial moisture condition of the soil [109].

_{ps}), as shown in Equation (35) [75]. Please note that I

_{ps}is used here as a generic reactivity term, and, depending on the method used, I

_{ps}can be I

_{ls}or I

_{cs}or I

_{ss}.

_{pt}can be defined as the field reactivity index after adjustment of the laboratory-deduced index for field conditions. In the cracked zone, lateral confinement is not expected, and α can assume a value of 1 [107]. To account for the lateral confinement beneath the cracked portion, the relationship presented in Equation (36) has been used [75]. Here, α is again assumed to be equal to 1 for depths of greater than 5 m to achieve a value of I

_{pt}that is at least equal to I

_{ps}.

_{pt}is determined, soil can be classified as of low, moderate, high, and very high expansive nature, as shown in Table 2 below. It is to be noted that other index properties (liquid limit and plasticity index) have also been used for deducing the soil’s classification, and this is also presented in Table 2. Others have correlated the reactivity with linear shrinkage strain, even though the correlation can have low reliability [110].

#### 5.1.2. Depth of the Design Soil Suction Change (H_{s})

_{s}is the soil depth under which the soil moisture content is not affected by seasonal climate variations; hence, no suction changes occur, and soil below this depth does not contribute to ground movement. The location of the water table and bedrock affects H

_{s}[75]. In such situations, adjustments to H

_{s}and the suction profile can be made, as shown in Figure 13. For example, when a shallow depth water table is present, the suction triangle should end at the top of the water table. In presence of bedrock, the triangle reaches to the full depth of suction change but the calculation from rock layer is ignored.

#### 5.1.3. Soil Suction Change at the Ground Surface (Δu)

#### 5.1.4. Mound Shape and Soil’s Stiffness

_{m}) across a foundation are used to define the mound shape, with flat mounds having parabolic edges, as shown in Figure 15, where y

_{m}can be considered as 0.5y

_{s}and 0.7y

_{s}for the edge heave and centre heave, respectively [75]. Likewise, different values of edge distances (m) are given for edge heave and centre heave, as shown in respective Equations (37) and (38).

_{m}is in mm.

_{m}is in mm and H

_{s}is in m.

_{m}can be considered as 0.7y

_{s}for both conditions (edge heave and centre heave) [75]. The profile of the mound in the x and y axes can be obtained from the following Equation (39).

_{m}is in mm, H

_{s}is in metres, and D

_{e}is the embedment depth of the edge beam in metres.

_{t}can be calculated using the equation below [75]:

_{t}is the distance of the tree from the building, D

_{i}is the influence distance. For a single tree, D

_{i}should be taken equal to HT of a group of 4 or more trees in a row; D

_{i}can be taken as twice the design height of the tree group. y

_{t-max}is the maximum potential surface movement induced by tree-related suction change. This is in addition to the usual design suction profile suggested by the design code. A similar method as of y

_{s}for a regular site can be used to calculate y

_{t-max}. The depth of cracking can be taken equal to the maximum design drying depth.

#### 5.2. Effect of Climate on H_{s} and Correlation with TMI

_{s}. A reliable value of H

_{s}can be achieved based on long-term site data of ground movements and suction changes, including moisture variations with depth. However, obtaining these data requires not only an extensive site investigation program but also a longer period of up to decades for data acquisition and accumulation [117]. Few investigations have been performed to predict H

_{s}for various locations in Australia. For example, Hu et al. [118] estimated H

_{s}values for three locations in Western Australia and compared them with the available site data [119], while Walsh et al. [117] developed H

_{s}maps for south Western Australia and South-Eastern Queensland, and Fityus et al. [74] generated a H

_{s}map of the Hunter Valley region of New South Wales, with a discussion of the H

_{s}values at three locations within the Hunter Valley region. With limited field observations, AS2870 [75] presents values of H

_{s}for specific locations, where higher values of H

_{s}correspond to hotter climate zones; this can be extrapolated to other areas based on the suitability of the climate. Alternatively, the TMI is a widely accepted moisture index for incorporating the effect of climatic boundary conditions in geo-infrastructure design; hence, AS2870 [75] provides relationships between H

_{s}and TMI values (Table 3) so that H

_{s}can be estimated based on the TMI of a particular site. One limitation of AS2870 was that it provides the H

_{s}recommendation for ranges of TMI values which may create confusion in certain cases. Fityus et al. [74] presented a continuous relationships between H

_{s}and TMI. It is expected that climate change will cause changes in TMI, which will influence H

_{s}which can be an important problem requiring future investigation.

#### 5.3. Comparison with American Practice on Expressing Expansion Potential

#### 5.4. Summary

_{s}) and classifies sites according to their characteristic ground movement, e.g., sandy and rocky sites (class A) to extremely reactive clay sites (class E). A subscript D is added to the classification if the depth of suction change is >3 m. The current standard provides the basic requirements for the design of slabs and footing for residential buildings, emphasising expansive soil issues. It also provides guidelines on the estimation of the depth of suction change based on TMI. However, the available TMI maps may not reflect the current climate [98]. Furthermore, the suction depth to TMI relationship has been developed based on limited field investigations [76]. It is also believed that the change in suction assumed at the ground surface (used in ground movement calculation) is a function of soil type and climate conditions. AS2870 [75] provides very limited guidance on its value.

## 6. Conclusions

- The behaviour of expansive soil can be complex. The expansive soil movement can be influenced by several factors, including its mineralogy and hydraulic and atmospheric boundary condition.
- Many different types of structures can be affected. Some of the specific examples found in the literature are lightweight residential buildings, road pavements, underground pipelines, slopes, and other infrastructures.
- It is expected that, due to climate change, the problems due to expansive soils will worsen in many parts of the world and should be given proper consideration for building climate-resilient structures.
- The effect of climate change may not be uniform across a state or other jurisdiction, and the local condition needs to be taken into account (calculation of local TMI and other variables may be needed).
- Laboratory tests commonly used for the quantification of reactivity are simplified and can be time-consuming. The number of field studies is also limited due to the expenses and effort involved.
- Current practice is based on a simplification of a complex process and caution should be exercised when estimating the soil reactivity as a function of conventional soil parameters such as the liquid limit or plasticity index.
- Numerical tools have been used to capture the behaviour of expansive soil and its interactions with different types of structures and can be a useful tool for a better understanding of the process or site-specific designs. They can be categorised into three groups, i.e., (1) modelling of the seepage due to interaction with the atmospheric boundary; (2) modelling of volume change and related ground movement, and (3) modelling of the interaction between the soil and structure constructed on or within the shallow depth of it.
- Advanced numerical methods for unsaturated seepage will require inputs of the SWCC and unsaturated hydraulic conductivity function and can be a complex process.
- Several past studies have attempted modelling of the interaction between soil–atmospheric boundaries and structures. However, several assumptions have been made, including some on the calculation of effective stress, which can have important consequences for the outputs of the numerical model.
- This review recommends further studies to incorporate the effects of the future climate, as geo-structures are designed to achieve a 50- to 100-year service life.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

## Appendix A

SWCC | Hydraulic Conductivity Function | Thermal Properties | Climate Data | Vegetation Influence | Boundary Condition | Reference |
---|---|---|---|---|---|---|

Developed through the measured soil suction with corresponding moisture content in Vadose/w software | The equation proposed by Fredlund et al. [67] was used to develop this function in the Vadose/w model. K _{sat} was measured. | The measured thermal conductivity, including the specific heat capacity variation with the moisture content, was taken from another site near the study area [126]. | Weather data collected from the nearest weather station were assigned in the Vadose/w model. | Considered in Vadose/w through LAI, RD, and PML factors. | - Applied in a surface layer.
- Assumed bedrock at the bottom layer and non-flow conditions.
- Adaptive time-stepping.
| [93] |

Obtained from Li et al. [94] | K_{unsat} was formulated based on Forchheimer [127]. K _{sat} = 1 × 10^{−7} to 1 × 10^{−9} (m/s). | - | - | - | A soil column of height:width:length = 11:11:11 m was considered to avoid the impact of boundary conditions. | [85] |

Suction Change | H_{s}(m) | Strain | Reference |
---|---|---|---|

SWCC from Vadose/w model captures the suction profile | 0.6 to 3 | $\Delta {\epsilon}_{sh}=\mathsf{\alpha}\Delta w$, α = 0.28 [128] | [93] |

1.2 pF | 1.3 to 4 | ${\epsilon}_{T}={\epsilon}_{es}+{\epsilon}_{ms}$ | [85] |

_{sh}is the linear swelling strain, Δw is the change in water content, α is the linear expansion coefficient, ${\epsilon}_{T}$ is the total strain, ${\epsilon}_{es}$ is the strain resulting from the effective stress of the soil, and ${\epsilon}_{ms}$ the volumetric strain resulting from the swelling of soil based on the moisture level.

Stress Equation | Bulk Modulus | Elastic or Shear Modulus | Poisson’s Ratio | Boundary Condition | Reference | |
---|---|---|---|---|---|---|

$\Delta {\sigma}_{sh}=3k\Delta {\epsilon}_{sh}$ [128] | $K=\frac{E}{3\left(1-2\nu \right)}$ | Second-order polynomial equation in the FLAC3D model was developed from lab tests of the soil to generate the soil stiffness (E) and gravimetric moisture relationship. | ν_{soil} = 0.45 | Same as Table A1. | [93] | |

Equation (25) Equation (26) $d{\sigma}_{dev}=2Gd{\epsilon}_{dev}^{el}$ | Log bulk modulus, κ, commonly adopted values were 0.01–0.06. | E = tensor of soil elastic constants | ν_{soil} = 0.1 to 0.4 | - Symmetry in the x- and z-direction of the inner parts of a slab.
- Symmetry in each direction exerts a restraining force to the respective directions and restrains rotation in the other directions.
- Horizontally restrained outer edges allow vertical movement.
- The bottom part of the soil mass is restrained horizontally and vertically.
- Friction coefficient (soil–structure contact) = 0.35.
| Mechanical behaviour of soil | [85] |

$G=\frac{3\left(1-2{\nu}_{soil}\right)\left(1+{e}_{o}\right)}{2\left(1+{\nu}_{soil}\right)\kappa}\times \left({\sigma}^{eq}\right)exp\left({\epsilon}_{vol}^{el}\right)$ | ||||||

${\sigma}_{t}=\left(1-{d}_{t}\right){E}_{o}\left({\epsilon}_{t}-{\epsilon}_{t}^{pl}\right)$ ${\sigma}_{c}=\left(1-{d}_{c}\right){E}_{o}\left({\epsilon}_{c}-{\epsilon}_{c}^{pl}\right)$ | Elastic modulus of concrete (E_{c}) = 20–25 GPa | ν_{concrete} = 0.2 | Slab-on-grade model |

_{o}is the initial void ratio, ${\sigma}_{t}$ is the uniaxial tensile stress, ${\sigma}_{c}$ is the uniaxial compressive stress, d

_{t}and d

_{c}are damage variables ranging from zero (undamaged concrete) to one (damaged concrete), and ${\epsilon}_{t}^{pl}$ and ${\epsilon}_{c}^{pl}$ are the tensile and compressive plastic strain rates, respectively.

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**Figure 1.**Schematic representation of mineral structures: (

**a**) Kaolinite; (

**b**) Illite; (

**c**) Montmorillonite, adapted from Nelson et al. [44].

**Figure 4.**Pipe movement in the vertical direction is attributed to seasonal moisture changes in expansive soils: (

**a**) dry season; (

**b**) wet season.

**Figure 5.**Surface cracks on the ground surface and settlement due to soil shrinkage around a manhole cover during dry season.

**Figure 9.**Soil movement associated with monthly rainfall. Data from Karunarathne [56].

**Figure 10.**Measured and predicted soil moisture at various depths. Data from Karunarathne [56].

**Figure 12.**Distribution of expansive soils in Australia. Source: [101].

**Figure 13.**Suction profile simplifications under various scenarios (

**a**) soil to depth ≥ H

_{s}; (

**b**) effect of bedrock; (

**c**) effect of groundwater. Adapted from [75] by the first author with the permission of Standards Australia Limited under licence CLF1022BD. Copyright in AS 2870-2011 vests in Standards Australia. Users must not copy or reuse this work without the permission of Standards Australia.

**Figure 14.**Field observations of suction changes for extremely dry and wet conditions. Data adapted from [114] by first author with the permission of Standards Australia Limited under licence CLF1022BD. Copyright in HB 28-1997 vests in Standards Australia. Users must not copy or reuse this work without the permission of Standards Australia.

**Figure 15.**The idealisation of mound shapes in Walsh’s method to depict ground movement in design: (

**a**) centre heave; (

**b**) edge heave.

**Figure 16.**The idealisation of mound shapes in Mitchell’s method to depict ground movement in design: (

**a**) centre heave; (

**b**) edge heave.

Phenomenon | Soil Reaction | Result |
---|---|---|

Heaving/ | Ground movement | Building failure |

Shrink–swell | Buried pipe failure | |

Road failure | ||

Cracking | Increased permeability | Contamination of underlying groundwater through the easy movement of contaminants |

Slope instability | Slope movement | Distortion of structures founded on slopes, e.g., road disconnection or interruption of water supply distribution networks |

Expansiveness | Liquid Limit (LL), % | Plasticity Index (PI) | Weighted PI (PI × % < 425 µm) | I_{pt} (% Strain/pF) | Modified PI (%) |
---|---|---|---|---|---|

Very high | >70 | >45 | >3200 | 4 to 7 for PI > 55 | - |

High | >70 | >45 | 2200 to 3200 | 2 to 4 for PI < 55 | ≥40 |

Moderate/ medium | 50 to 70 | 25 to 45 | 1200 to 2200 | 1 to 2 | ≥20 to <40 |

Low | <50 | <25 | <1200 | <1 | ≥10 to <20 |

**Table 3.**Relationship between TMI and H

_{s}. Adapted by first author with the permission of Standards Australia Limited under licence CLF1022BD from [75]. Copyright in AS 2870-2011 vests in Standards Australia. Users must not copy or reuse this work without the permission of Standards Australia.

TMI | H_{s} (m) |
---|---|

>10 | 1.5 |

≥−5 to 10 | 1.8 |

≥−15 to ≤−5 | 2.3 |

≥−25 to ≤−15 | 3 |

≥−40 to ≤−25 | 4 |

≤−40 | >4 |

**Table 4.**Expansion potential of soil. Adapted from Snethen et al. [120].

Liquid Limit, % | Plasticity Index, % | Soil Suction at Natural Water Content ( ${\mathsf{\tau}}_{\mathbf{n}\mathbf{a}\mathbf{t}}$), kPa | Swell Potential, % | Potential Soil Type |
---|---|---|---|---|

>60 | >35 | >429 | >1.5 | High |

50 to 60 | 25 to 35 | 161 to 429 | 0.5 to 1.5 | Marginal |

<50 | <25 | <161 | <0.5 | Low |

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**MDPI and ACS Style**

Devkota, B.; Karim, M.R.; Rahman, M.M.; Nguyen, H.B.K. Accounting for Expansive Soil Movement in Geotechnical Design—A State-of-the-Art Review. *Sustainability* **2022**, *14*, 15662.
https://doi.org/10.3390/su142315662

**AMA Style**

Devkota B, Karim MR, Rahman MM, Nguyen HBK. Accounting for Expansive Soil Movement in Geotechnical Design—A State-of-the-Art Review. *Sustainability*. 2022; 14(23):15662.
https://doi.org/10.3390/su142315662

**Chicago/Turabian Style**

Devkota, Bikash, Md Rajibul Karim, Md Mizanur Rahman, and Hoang Bao Khoi Nguyen. 2022. "Accounting for Expansive Soil Movement in Geotechnical Design—A State-of-the-Art Review" *Sustainability* 14, no. 23: 15662.
https://doi.org/10.3390/su142315662