# Pre- and Post-Liquefaction Behaviors of Manufactured Sand Considering the Particle Shape and Stress History Effects

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Particle Shape Evaluation

_{max-insc}is the particle’s maximum inscribe cycle diameter, D

_{min-circ}is the minimum diameter of the circumcircle, D

_{c}and N

_{c}are the diameter and number of other cycles except the largest in-circle, respectively, and D

_{max}is the largest inscribed corner cycle.

#### 2.2. Relationships between the Particle Shape and Friction Angle

## 3. Experimental Apparatus and Methods

_{0}consolidation was imposed with the effective vertical stress σ

_{v}of 50 kPa for 30 min, which was identified as the first consolidation. A strain-controlled undrained CSS test was then carried out with a cyclic number of 250 and several cyclic shear strain amplitudes. Figure 8 depicts the cyclic loading waveform in one cycle of the CSS tests and the loading frequency was set to be 0.1 Hz, which applies to the continued wave loading condition [55]. The vertical displacement was maintained to keep the volume unchanged. The initial liquefaction was considered to occur when the loss of vertical stress reached 95% as in the cyclic shear condition, and the change in vertical stress in dry sand is equivalent to the true water pressure in saturated sand [56].

## 4. Results and Discussion

#### 4.1. Pre-Liquefaction Behaviors

#### 4.1.1. Relationships between the Shear Stiffness, Particle Shape, and Cyclic Number

#### 4.1.2. Liquefaction Resistance

#### 4.2. Post-Liquefaction Behaviors

_{γ}= 0) serve as a reference. Compared with the samples that did not go through liquefaction, the shear strength of the post-liquefaction samples was enhanced after the cyclic shearing and re-consolidation. The peak shear stress before the shear strain of 1% and the overall maximum shear stress of the MS samples were higher than that of the LBS sample during the post-liquefaction stage with a higher regularity under the same condition. For a specified regularity, the results showed that samples have higher shear strength if they had undergone larger shear strain amplitudes with the same cyclic number. This is because larger vibrations have caused greater rotation and slipping of particles, leading to larger volumetric strains in the re-consolidation stage and increasing the density of the samples. Under the coupling effect of the higher density and the particle shape, the internal structure became more stable and more difficult to slide over particles.

#### 4.2.1. Effects of Particle Shape on Maximum Shear Stress under Various Cyclic Shear Histories

_{τ}is the adjustment coefficient for maximum shear stress and I

_{τ}is a basic parameter.

_{τ}and I

_{τ}changes among the samples with different particle regularity, as listed in Table 4. It can be seen that the fitting line was gentle for the sample with the largest particle regularity of 0.803, which had the minimum adjustment coefficient K

_{τ}of 5.416, while the sample with the minimum particle regularity of 0.432 had the greatest adjustment coefficient K

_{τ}of 14.132. The results showed that the decrease of the particle regularity would lead to an increase of K

_{τ}and shear strength in the PMS tests. In addition, the change of the shear strain amplitude and particle regularity did not seem to influence the intercept of the linear relationship, while the slope could be influenced considerably by the variation of particle regularity ρ.

#### 4.2.2. Influences of Particle Shape and Shear History on the Pore Pressure

_{γ}. The results manifest that irregular particles of MS could effectively restrain the pore pressure generation. However, compared to the build-up of pore pressure in the pre-liquefaction stage, the liquefaction did not occur in this stage because the accumulation of pore pressure is induced by monotonic shear loading.

_{μ}is the adjustment coefficient for the peak pore pressure, E

_{A}is the scaling factor for shear strain amplitude A

_{γ}, and I

_{μ}is the state constant. In this study, the value of K

_{μ}was taken as the average and the other parameters were derived by linear interpolation. The values of K

_{μ}, E

_{A}, and I

_{μ}in this experiment were 30.096, −26.222, and 26.262, respectively.

## 5. Conclusions

- It was found that irregular shapes not only increase the friction angles, but also enhance the shear stability of the MS samples. In the undrained CSS tests, the samples with irregular particles showed better shear performance and required more cycles to reach liquefaction. A power correlation between shear stiffness and loading cycles was proposed to describe the decrease in shear stiffness. For a given shear amplitude, particle regularity has a noticeable effect on the cyclic shear resistance as the irregular shapes strengthen the interlocking of particles and make them more difficult to dislocate, thus enhancing the cyclic shear resistance of MS.
- In PMS tests, the samples that had undergone cyclic shearing were strengthened and their shear strength was higher than those that did not go through CSS tests. Moreover, the shear strength of the samples improved as the cyclic shear amplitude increased or the regularity of the particles decreased. The relationship between the shear amplitude and peak shear stress under monotonic shearing is proposed. Therefore, although the samples were tested in the same conditions, the MS samples had larger shear strength because the irregularity of the MS samples was generally higher than that of the LBS samples.
- The pore pressure of the samples in the post-liquefaction phase reached the maximum value and then decreased gradually under the monotonic shear. The liner regression between the peak pore pressure and particle regularity was established, which could serve as a reference for the prediction of the pore pressure and shear strength in geotechnical engineering.
- The test results indicated that, generally, MS has a higher friction angle and better mechanical response compared with natural quartz sand. Therefore, MS could serve as the replacement of natural sand in backfilling projects. The relationships discovered in this paper between the shear performance and particle regularity could support the application and selection of MS in offshore and geotechnical engineering.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 3.**Binary images of the particle shapes of: (

**a**) LBS; (

**b**) MSSR; (

**c**) MSB; (

**d**) MSS; and (

**e**) MSR.

**Figure 4.**Cumulative distribution curves of the shape parameters of the samples: (

**a**) sphericity and (

**b**) roundness.

**Figure 10.**Shear stiffness of samples against the cyclic number with different cyclic shear strain amplitudes (σ

_{v}= 50 kPa, D

_{r}= 46%): (

**a**) A

_{γ}= 0.1%; (

**b**) A

_{γ}= 0.2%; (

**c**) A

_{γ}= 0.3%; and (

**d**) A

_{γ}= 0.4%.

**Figure 13.**Volumetric strain development of re-consolidated samples with different shear histories: (

**a**) LBS; (

**b**) MSSR; (

**c**) MSB; (

**d**) MSS; and (

**e**) MSR.

**Figure 14.**Shear stress-strain behaviors in PMS tests of samples with different shear amplitudes: (

**a**) LBS; (

**b**) MSSR; (

**c**) MSB; (

**d**) MSS; and (

**e**) MSR.

**Figure 15.**Relationship between the maximum shear stress and cyclic shear history of different samples: (

**a**) LBS; (

**b**) MSSR; (

**c**) MSB; (

**d**) MSS; and (

**e**) MSR.

**Figure 16.**Pore pressure developments at the post-liquefaction stage of samples with different cyclic shear histories: (

**a**) LBS; (

**b**) MSSR; (

**c**) MSB; (

**d**) MSS; and (

**e**) MSR.

**Figure 17.**Relationships between the peak pore pressure and particle regularity with different cyclic shear histories: (

**a**) A

_{γ}= 0.1%; (

**b**) A

_{γ}= 0.2%; (

**c**) A

_{γ}= 0.3%; and (

**d**) A

_{γ}= 0.4%.

Material | LBS | MSSR | MSB | MSS | MSR |
---|---|---|---|---|---|

Specific gravity G_{s} (g/cm^{3}) | 2.65 | 2.65 | 2.65 | 2.60 | 2.70 |

Maximum void ratio e_{max} | 0.79 | 1.023 | 0.992 | 1.016 | 1.09 |

Minimum void ratio e_{min} | 0.52 | 0.606 | 0.589 | 0.585 | 0.636 |

Uniformity mean diameter D_{50} (mm) | 0.62 | 0.62 | 0.62 | 0.62 | 0.62 |

Material | Sphericity (S) | Roundness (R) | Regularity (ρ) |
---|---|---|---|

LBS | 0.76 | 0.846 | 0.803 |

MSSR | 0.702 | 0.512 | 0.607 |

MSB | 0.651 | 0.421 | 0.536 |

MSS | 0.604 | 0.392 | 0.498 |

MSR | 0.478 | 0.386 | 0.432 |

Pre-Liquefaction | Post-Liquefaction | ||||
---|---|---|---|---|---|

Testing No. | Consolidation stress (σ_{v}, kPa) | Samples | Cyclic shear strain amplitude (A_{γ}, %) | Re-consolidation stress (σ_{v}, kPa) | Monotonic shear |

1 | LBS | 50 | Along the x-direction | ||

2 | MSSR | ||||

3 | / | MSB | / | ||

4 | MSS | ||||

5 | MSR | ||||

6–10 | 50 | LBS | 50 | Along the x-direction | |

11–15 | MSSR | ||||

16–20 | MSB | 0.1, 0.2, 0.3, 0.4 | |||

21–25 | MSS | ||||

25–30 | MSR |

Material | Particle Regularity (ρ) | K_{τ} | I_{τ} |
---|---|---|---|

LBS | 0.803 | 5.416 | 3.267 |

MSSR | 0.607 | 8.132 | 4.526 |

MSB | 0.536 | 8.066 | 4.917 |

MSS | 0.498 | 11.382 | 4.654 |

MSR | 0.432 | 14.132 | 4.722 |

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**MDPI and ACS Style**

Wang, Z.; Chen, G.; Wu, D.; Li, Y.; Hu, J. Pre- and Post-Liquefaction Behaviors of Manufactured Sand Considering the Particle Shape and Stress History Effects. *J. Mar. Sci. Eng.* **2023**, *11*, 739.
https://doi.org/10.3390/jmse11040739

**AMA Style**

Wang Z, Chen G, Wu D, Li Y, Hu J. Pre- and Post-Liquefaction Behaviors of Manufactured Sand Considering the Particle Shape and Stress History Effects. *Journal of Marine Science and Engineering*. 2023; 11(4):739.
https://doi.org/10.3390/jmse11040739

**Chicago/Turabian Style**

Wang, Zhe, Guanyu Chen, Dazhi Wu, Yao Li, and Juntao Hu. 2023. "Pre- and Post-Liquefaction Behaviors of Manufactured Sand Considering the Particle Shape and Stress History Effects" *Journal of Marine Science and Engineering* 11, no. 4: 739.
https://doi.org/10.3390/jmse11040739