# Experimental Investigation on the Cyclic Shear Mechanical Characteristics and Dynamic Response of a Steel–Silt Interface in the Yellow River Delta

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Large-Scale CNL Cyclic Shear Tests

#### 2.1. Testing Apparatus

#### 2.2. Testing Materials

^{3}).

_{0}(smooth), R

_{1}(slightly rough), and R

_{2}(rough) (Figure 6). The sand filling method, average profile height, fractal dimension method, etc., typically determine the surface roughness. In this test, three parameters (the peak valley distance H, groove cross-section width L

_{1}, and platform spacing L

_{2}) were defined to determine the surface roughness according to the modified sand-filling method [16]. The steel plate had no material loss during the tests.

#### 2.3. Testing Scheme

## 3. Results and Discussion

#### 3.1. Interface Shear Strength

^{max}. The peak shear stress was equal to the average magnitude of the positive and negative maximum shear stress. Furthermore, the definition of the stress ratio D

_{τ}was introduced to characterize the relationship between the peak shear stress and the cycle number and between the stress ratio and the cycle number.

#### 3.1.1. The Influence of Normal Stress

- (1)
- The shear strength decreased with the increase in the number of cycles. At the beginning of shear, the soil particles occluded tightly under normal stress, and the cohesion between the steel soil interface was strong, resulting in the soil interface having a more remarkable ability to resist shear. With the increase in the shear cycle, the soil was compacted and the corners of the soil particles were rounded. After the first few shear cycles, the soil particles near the interface under the same repeated shear stress had a particular historical stress path, which led to the shear strength decreasing continuously and finally becoming stable.
- (2)
- With the increase in normal stress, the shear strength and residual shear strength (the peak shear stress of the 30th cycle) also increased.
- (3)
- The first two cycles showed hardening under the low-stress conditions of 100 kPa and 200 kPa. The results were inconsistent with the findings of Shang (2016), Li (2018), and others [19,20]. One possible reason could be attributed to the constant stress conditions used in the tests and the normal stress remaining unchanged during the whole test, resulting in a discontinuous reduction in normal stress under the low-stress conditions. Furthermore, combined with the direct test results, under the low-stress condition, the shear stress–shear displacement curve appeared to develop a hardening behavior, and so when the overall shear displacement was small (the first two cycles), the shear stress increased. The softening feature seemed to align with the rise in the overall shear displacement (after two cycles) [12].
- (4)
- Similar to the shear stress–shear displacement curve in the direct shear test, the peak shear stress–total shear displacement curve in the cyclic test could be used as the shear strength–cycle number curve. Three stages could be recognized, i.e., the elastic stage of the rapid change in shear stress (the first five cycles), the plastic stage of the slow evolution of the shear stress (5–10 cycles), and the shear failure stage of equilibrium of the shear stress (10–30 cycles).

_{nτ}was further adopted based on the stress ratio D

_{τ}to characterize the cumulative weakening degree of the first n cycles. The representative weakening coefficients S

_{5}

_{τ}, S

_{10}

_{τ}, S

_{15}

_{τ}, S

_{20}

_{τ}, S

_{25}

_{τ}, and S

_{30}

_{τ}under the three normal stresses were calculated. The results are shown in Figure 9. The maximum weakening coefficients S

_{30}

_{τ}under the three normal stresses were 9.84%, 11.84%, and 16.6%, respectively.

#### 3.1.2. The Influence of Shear Amplitude

- (1)
- With the increase in the shear amplitude, the peak and residual shear strength increased. However, with the increased shear amplitude, its increasing rate decreased and the residual shear strength was similar to those when the amplitude was 15 mm and 35 mm.
- (2)
- The test group with a shear amplitude of 5 mm showed hardening in the first two cycles. With the increase in the number of cycles, the shear strength decreased. The results were similar to the findings of Vieira et al. (2013), indicating that the cyclic loading of the interface under a small displacement would not reduce the shear strength, while the cyclic shear strength decreased significantly under a large displacement [23]. The explanation is the same as the previous one. In the case of large shear amplitude, the interface has reached the direct shear strength under the same conditions in the first few cycles (approximately 2–5), which affected the development of the subsequent cycle shear strength.

_{nτ}under the three shear amplitudes was calculated, as shown in Figure 11. The maximum weakening coefficients S

_{30}

_{τ}under the three shear amplitudes were 11.84%, 15.59%, and 25.51%, respectively.

#### 3.1.3. The Influence of Roughness

- (1)
- With the roughness increase, the shear strength of the first cycle increased, but the difference was insignificant. Referring to the conclusion of the direct test, the influence of roughness on shear stress decreased under a larger normal stress, which could reasonably explain the above phenomenon [12].
- (2)
- Smaller roughness levels reached the shear failure stage earlier, but the residual shear strength decreased with the roughness increase. The stress ratio–cycle number curve presented in Figure 12 demonstrates that the weakening of the shear strength became apparent with the increase in roughness. Taha and Fall (2014) drew a similar conclusion for their cyclic shear test on steel marine clay [25]. With the roughness increase, the dislocation and rearrangement process of the soil particles near the interface became intense. With the progressive number of cycles, the strength degradation became more significant.

_{nτ}under the three shear amplitudes were calculated, as shown in Figure 13. The maximum weakening coefficients S

_{30}

_{τ}under the three roughness conditions were 15.84%, 20.65%, and 25.51%, respectively, which verified the above conclusions.

#### 3.1.4. The Influence of Water Content

_{30}

_{τ}were 21.5%, 25.51%, and 28.6% under the three water content conditions, respectively.

#### 3.2. Shear Stiffness and Damping Ratio

_{1}and K

_{2}represent the shear stiffness in the positive and negative shear directions, respectively, and ${\tau}_{2}^{Max}$ is the peak shear stress, while A

_{w}is the shear amplitude.

_{1}and D

_{2}represent the damping ratio in the positive and negative shear directions, S is the hysteresis loop area, and S

_{1}and S

_{2}are shadow areas.

#### 3.2.1. The Influence of Normal Stress

#### 3.2.2. The Influence of Shear Amplitude

#### 3.2.3. The Influence of Roughness

#### 3.2.4. The Influence of Water Content

## 4. Conclusions

- (1)
- Generally, three distinctive stages appeared in the curve of the peak shear stress: the elastic stage, in which the shear stress changed rapidly (the first five cycles); the plastic stage, in which the shear stress changed slowly (5–10 cycles), and the shear failure stage, in which shear stress equilibrium was achieved (10–30 cycles). The shear strength, shear stiffness, and damping ratio decreased, and the energy dissipation tended to be asymptotic with the increase in the cycle number.
- (2)
- The normal stress conditions significantly influenced the action of the cyclic interface weakening. As the normal stress increased, the degree of interface weakening increased. At the same time, the shear strength and shear stiffness of the interface increased while the damping ratio decreased.
- (3)
- With the increase in the shear amplitude, the degree of the interface weakening, the shear strength, the damping ratio, and the energy dissipation increased, while the shear stiffness also decreased.
- (4)
- As the roughness increased, the shear strength’s weakening became apparent and the energy dissipation became fast.
- (5)
- The shear strength and stiffness increased when the water content decreased. The weakening degree of the interface reached its maximum near the optimal water content.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Silt in the Yellow River Delta. (

**a**) Concept map of the soil classification adapted from Ren et al., 2020 [11]. (

**b**) Dry condition. (

**c**) Wet condition.

**Figure 2.**The offshore structures in the Yellow River Delta. (

**a**) The Chengdao offshore oil platform. (

**b**) The Hekou jack-up marine ranching platform.

**Figure 3.**Large-scale shear instrument. (

**a**) 3D schematic diagram of the shear box. (

**b**) Displacement measuring device. (

**c**) Spring under the shear box.

Number | Normal Stress (kPa) | Shear Amplitude (mm) | Roughness (mm) | Water Content (%) | Others | |
---|---|---|---|---|---|---|

1 | 100 | 5 | 0.05 | 20 | Number of cycles = 30 Frequency = 0.01 HZ Shear rate = 1 mm/s | |

2 | 200 | |||||

3 | 15 | |||||

4 | 35 | 0 | ||||

5 | 0.025 | |||||

6 | 0.05 | 16 | ||||

7 | 24 | |||||

8 | 20 | |||||

9 | 300 | 5 |

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## Share and Cite

**MDPI and ACS Style**

Yu, P.; Dong, J.; Guan, Y.; Wang, Q.; Jia, S.; Xu, M.; Liu, H.; Yang, Q. Experimental Investigation on the Cyclic Shear Mechanical Characteristics and Dynamic Response of a Steel–Silt Interface in the Yellow River Delta. *J. Mar. Sci. Eng.* **2023**, *11*, 223.
https://doi.org/10.3390/jmse11010223

**AMA Style**

Yu P, Dong J, Guan Y, Wang Q, Jia S, Xu M, Liu H, Yang Q. Experimental Investigation on the Cyclic Shear Mechanical Characteristics and Dynamic Response of a Steel–Silt Interface in the Yellow River Delta. *Journal of Marine Science and Engineering*. 2023; 11(1):223.
https://doi.org/10.3390/jmse11010223

**Chicago/Turabian Style**

Yu, Peng, Jie Dong, Yong Guan, Qing Wang, Shixiang Jia, Meijun Xu, Hongjun Liu, and Qi Yang. 2023. "Experimental Investigation on the Cyclic Shear Mechanical Characteristics and Dynamic Response of a Steel–Silt Interface in the Yellow River Delta" *Journal of Marine Science and Engineering* 11, no. 1: 223.
https://doi.org/10.3390/jmse11010223