# Determining Shrinkage Cracks Based on the Small-Strain Shear Modulus–Suction Relationship

^{1}

^{2}

^{*}

## Abstract

**:**

_{0}) at various moisture contents. The small-strain moduli from the SASW tests on the intact ground were generally higher than those from the FFR tests due to the effect of confining stress. A drop in the small-strain modulus determined using the SASW test was observed as an increase in suction-induced cracks and it relieved the horizontal stress. The crack depth measured in the field was then modelled using a semi-empirical procedure that can be used to predict crack depth relative to suction.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area and Instrumentation

^{6}kPa, were installed at a depth of 0.5 m at the top, middle, and base of the embankment. TDR sensors were installed at a depth of 0.1 m in the same locations as the MPS6 sensors, so that the surface boundary condition could also be investigated. The measurements from the low-capacity tensiometers (A1, A2, A3) and flushable tensiometers (UNSUC1, UNSUC2) during the dry season were not considered in further shrinkage analysis due to cavitation problems, as higher suctions than the working range of the tensiometers were observed in the field in this period.

_{c}), defined as the ratio of the plasticity index to clay fraction was also considered as an indicator for expansion potential of the soil. A

_{c}based on the soil properties in Table 1 was 0.54, which indicates possible clay minerals of kaolinite or illite [19]. Despite the medium expansion potential based on the Atterberg’s limits, it is not uncommon for shrinkage cracks to occur even for soil with a PI as low as 6.9 or clay with illite mineralogy [13]. According to [20,21,22], swelling potential is not necessarily equal to that of shrinkage, and it is the soil properties such as initial density, initial moisture content, and magnitude of suction change that are the main factors affecting the swelling and shrinkage behavior.

#### 2.2. Soil Water Retention Curve (SWRC)

#### 2.3. Free-Free Resonant Frequency (FFR) Test

_{s}, and the shear modulus, G

_{0}, using Equations (1) and (2):

#### 2.4. Spectral Analysis of Surface Waves (SASW) Test

#### 2.5. Measurement of Shrinkage Cracks

## 3. Results and Discussions

#### 3.1. Instrumentation Results

#### 3.2. Soil Water Retention Curve (SWRC)

#### 3.3. FFR Results

_{0}with moisture content and suction is bi-linear, with the turning point at a moisture content of about 10% and suction about 26 MPa.

_{0}with decreasing moisture content (or increasing suction) at the initial stage of drying (suction from zero to 26 MPa) was expected and due to the greater influence of suction stress on the modulus [37] in this stage, as well as the initial decrease in the void ratio on the initial drying that could further induce a rise in modulus (Figure 6b and Figure 9b). This process continued until the turning point (at a suction of around 26 MPa) was reached where shrinkage became minimal, after which the rate of change in G

_{0}became less. It is noteworthy that the moisture content at 26 MPa suction was 10.2%, which was lower than the soil’s shrinkage limit of 13.5% and smaller than the second air-entry point of the SWRC (Figure 6 and Figure 7). As drying continued, the sample showed a more gradual rate of increase in G

_{0}for suction higher than 26 MPa as shrinkage became progressively less with increasing suction.

#### 3.4. SASW Results

_{0}) with varying in-situ suctions. Shear wave velocity (Vs) profiles for the embankment at different periods are shown in Figure 10. Only the Vs values obtained from zero to 0.5 m depth were used to calculate the G

_{0}of the upper layer of soil where the shrinkage crack was observed.

_{0}as shown in Figure 11. The G

_{0}values from May to November 2018 positively correlate with measured suctions, while from January to March 2019, after the shrinkage crack occurred in December, the G

_{0}appeared to decrease significantly and varied disproportionately with suction. In general, G

_{0}values from January to March should have been higher than those from May to November, since the suction values were higher for those periods, if they were to follow the trend of intact soil. A possible explanation is that the crack was responsible for the reduced values of G

_{0}.

#### 3.5. Suction–Small-Strain Shear Modulus Relationship

_{0}) is dependent on net stress, suction history, void ratio, over-consolidation ratio (OCR), strain rate, and plasticity index [24,36,38,39,40,41]. Many empirical and semi-empirical expressions have been proposed for describing the relationship between suction and modulus. In this study, a modelling approach by [42] was used to determine the relationship between G

_{0}, suction ($\mathsf{\psi}$), and water content due to its viability and directness. Amongst various modeling options, the model that considers the influence of suction stress and net stress separately is depicted in Equation (6),

^{2}) and is the void ratio function given by [43] for sands and clays, A, C, and k are empirical parameters for obtaining the best fit between measured and predicted values.

^{2}ranging between 0.77 and 0.98) was observed for the relationships G

_{0}—$\mathsf{\psi}$ (Figure 12a) and G

_{0}—${\mathsf{\sigma}}_{\mathrm{s}}$ (Figure 12b) for both the SASW and FFR results. In the FFR tests, the soil followed a bilinear relationship for both G

_{0}—$\mathsf{\psi}$ and G

_{0}—${\mathsf{\sigma}}_{\mathrm{s}}$ as explained earlier. Regarding the SASW, the G

_{0}—$\mathsf{\psi}$ relationship holds well (R

^{2}= 0.905) until the initiation of the crack after which, despite the increase of suction, G

_{0}decreased. It is interesting to note that after the crack, the values of G

_{0}, in comparison to the expected G

_{0}—$\mathsf{\psi}$ and G

_{0}—${\mathsf{\sigma}}_{\mathrm{s}}$ relationships, reduced and became similar to the FFR test. This may be because the effect of the crack was to reduce the net confining stress effect and thus to reduce the constant D in Equation (7). The values of D and C obtained by curve fitting (Figure 12b) for different test conditions are listed in Table 4.

#### 3.6. Modelling of Crack Depth

#### 3.7. Potential Use of the Proposed Technique

_{0}—$\mathsf{\psi}$ or G

_{0}—${\mathsf{\sigma}}_{\mathrm{s}}$ were dependent on test conditions and the presence of cracks. The G

_{0}value of intact ground determined using the SASW test was normally greater than that of FFR at a given suction due to the influence of net confining pressure. However, as the increase in suction induced cracks in the ground, the horizontal stress was relieved, and the SASW tests yielded the G

_{0}value similar to that of FFR as shown in Figure 14. Thus, with periodic measurement of suction and small-strain modulus using the SASW method, the presence of shrinkage cracks could be predicted underneath the soil layer where visual inspection may not be possible.

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**Experimental setup and an example of data acquisition through the free-free resonant frequency (FFR) test. (

**a**) Sample with an accelerometer attached at one end. (

**b**) Accelerometer data of the frequency domain with the fundamental frequency indicated by a peak.

**Figure 3.**Shrinkage crack at the top of the embankment on 15 February 2019 (

**a**) Top (drone) view of the crack (

**b**) Measurement of the crack.

**Figure 4.**Results from MPS sensors and rain gauge for a period of one year. (

**a**) Pore water pressure (kPa) and rainfall intensity (mm/hr). (

**b**) Rainfall intensity (mm/hr) and cumulative rainfall (mm).

**Figure 6.**Soil water retention curve (SWRC) results. (

**a**) A plot of degree of saturation against soil suction. (

**b**) A plot showing the change in void ratio with respect to suction.

**Figure 9.**Bilinear variation of the small-strain shear modulus (G

_{0}) from the FFR tests with (

**a**) moisture content (

**b**) suction.

**Figure 12.**Modelling of the suction modulus relationship (

**a**) G

_{0}—$\mathsf{\psi}$ plot (

**b**) G

_{0}—${\mathsf{\sigma}}_{\mathrm{s}}$ plot. SASW = spectral analysis of surface wave.

**Figure 14.**G

_{0}—${\mathsf{\sigma}}_{\mathrm{s}}$ relationship for a range of suction stresses occurring in the embankment.

**Table 1.**Basic physical properties of soil along with the unified soil classification system (USCS) classification. CL = low-plasticity clay.

Depth of Soil Sample Taken from on Top of the Embankment | Gravel (%) | Sand (%) | Silt (%) | Clay (%) | Liquid Limit (LL) % | Plasticity Index (PI) | Shrinkage Limit (SL) % | USCS |
---|---|---|---|---|---|---|---|---|

(>4.75 mm) | (4.75–0.074 mm) | (0.074–0.002 mm) | (<0.002 mm) | |||||

0.0–0.5 m | 12.0 | 22.8 | 23.9 | 41.3 | 43.8 | 22.4 | 13.5 | CL |

Month | Crack Depth (cm) | Suction (kPa) |
---|---|---|

09 January | 17.5 | 527.3 |

15 February | 27.0 | 815.9 |

29 March | 28.0 | 863.0 |

28 April | - | 167.9 |

Fitting Parameters | ||||||||
---|---|---|---|---|---|---|---|---|

$\mathrm{a}$ | ${\mathsf{\psi}}_{\mathrm{b}1}$ | ${\mathsf{\psi}}_{\mathrm{r}\mathrm{e}\mathrm{s}1}$ | ${\mathrm{S}}_{\mathrm{r}\mathrm{e}\mathrm{s}1}$ | ${\mathsf{\psi}}_{\mathrm{b}2}$ | ${\mathrm{S}}_{\mathrm{b}2}$ | ${\mathsf{\psi}}_{\mathrm{r}\mathrm{e}\mathrm{s}2}$ | ${\mathrm{S}}_{\mathrm{r}\mathrm{e}\mathrm{s}2}$ | ${\mathrm{S}}_{\mathrm{m}\mathrm{a}\mathrm{x}}$ |

0.05 | 3.5 | 12 | 0.85 | 8500 | 0.8 | 365621 | 0.007 | 0.94 |

G_{0}—${\mathsf{\sigma}}_{\mathbf{s}}$ Relationship | C | D (MPa) | R^{2} |
---|---|---|---|

SASW (before crack) | 271.1 | 78.7 | 0.905 |

FFR ($\mathsf{\psi}$ = 0.02–26 MPa) | 33.65 | 31.5 | 0.976 |

FFR ($\mathsf{\psi}$ = 26–220 MPa) | 2.57 | 624 | 0.773 |

Properties | Values | Units |
---|---|---|

Suction value at the onset of crack | 318 | kPa |

H modulus at that suction | 9683 | kPa |

k_{0} | 0.53 | - |

Poisson’s ratio, µ | 0.35 | - |

Young’s Modulus, E (large-strain) | 650 | kPa |

Total unit weight, γ | 18.3 | kN/m^{3} |

σt/(k_{0}*γ) | 3.36 | m |

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**MDPI and ACS Style**

Shrestha, A.; Jotisankasa, A.; Chaiprakaikeow, S.; Pramusandi, S.; Soralump, S.; Nishimura, S.
Determining Shrinkage Cracks Based on the Small-Strain Shear Modulus–Suction Relationship. *Geosciences* **2019**, *9*, 362.
https://doi.org/10.3390/geosciences9090362

**AMA Style**

Shrestha A, Jotisankasa A, Chaiprakaikeow S, Pramusandi S, Soralump S, Nishimura S.
Determining Shrinkage Cracks Based on the Small-Strain Shear Modulus–Suction Relationship. *Geosciences*. 2019; 9(9):362.
https://doi.org/10.3390/geosciences9090362

**Chicago/Turabian Style**

Shrestha, Avishek, Apiniti Jotisankasa, Susit Chaiprakaikeow, Sony Pramusandi, Suttisak Soralump, and Satoshi Nishimura.
2019. "Determining Shrinkage Cracks Based on the Small-Strain Shear Modulus–Suction Relationship" *Geosciences* 9, no. 9: 362.
https://doi.org/10.3390/geosciences9090362