# Analysis of the Working Response Mechanism of Wrapped Face Reinforced Soil Retaining Wall under Strong Vibration

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^{2}

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## Abstract

**:**

## 1. Introduction

Reference | Test Type ^{a} | Height Model | Length to Height Ratio | Input Motion ^{b} | Reinforcement | A_{max} ^{c} |
---|---|---|---|---|---|---|

Krishna [8,9] | ST | 0.60 m | 1.25 | Sine. | geotextile | 0.2 g |

Sakaguchi [10] | ST | 1.50 m | 2.30 | Sine. | geogrid | 0.72 g |

Sakaguchi [10] | CST | 0.15 m | 2.30 | Sine. | geotextile | 12 g |

Ramakrishnan [11] | ST | 0.81 m | 2.50 | Sine. | geotextile | 0.6 g |

Huang [12] | ST | 0.60 m | 1.40 | Sine. | geotextile | 1.72 g |

Roessing [13,14] | CST | 0.38 m | 1.60 | EQ | geotextile/metallic strips | 1.0 g |

Yang [15] | CST | 0.16 m | 1.20 | Sine. | geotextile | 1.0 g |

Zhu [16] | ST | 1.60 m | 1.56 | EQ | geogrid | 0.616 g |

Duan [17] | ST | 2.00 m | 1.40 | EQ | geogrid | 0.616 g |

Sabermahani [22] | ST | 1.00 m | - | Sine. | geotextile/geogrid | 0.3 g |

^{a}: ST = Shaking table test, CST = Centrifuge shaking table test.

^{b}: Sine. = sinusoid, EQ = scaled earthquake.

^{c}: Amax = peak acceleration, g = acceleration of gravity. The backfill behind the panel is inviscid soil in all tests.

## 2. Shaking Table Model Test

#### 2.1. Similitude Laws

#### 2.2. Model Design

#### 2.3. Backfill Material

^{3}and the minimum dry density was 1.52 g/cm

^{3}. According to the Unified Soil Classification System (USCS), the sand used in this paper is classified as poorly graded sand (SP). In the process of model construction, each 100 mm thick sand layer was compacted once. By controlling the quality of each layer of sand, the relative density of sand was controlled to Dr = 0.7, and the corresponding sand density was 1.82 g/cm

^{3}.

#### 2.4. Reinforcement

_{2%}of the geogrid under 2% strain is 17.4 kN/m and the ultimate tensile strength, T

_{ult}= 57.9 kN/m, was measured by MTS electro-hydraulic servo universal testing machine. Due to the limitation of material types, it is impossible to strictly scale the geogrid according to the similarity ratio design. Therefore, the mechanical properties of materials were used as the key points of similarity design [25,26] to scale the materials. The geogrid was treated with rib removal at the similarity ratio of 1:3, and 2/3 of the geogrid longitudinal ribs were eliminated. The geogrids were horizontally arranged in the reinforcement area, and the reinforcement spacing was 0.2 m. The length of geogrid-reinforced section was 0.7 m.

#### 2.5. Panel

#### 2.6. Input Motions

## 3. Results

#### 3.1. Model Damage Phenomena

#### 3.2. Acceleration Response

_{rms}stands for root mean square acceleration; T

_{d}for vibration duration; a(t) for acceleration time histories.

_{m}is the design acceleration; A is the peak acceleration; a for acceleration amplification factor; H is the height of retaining wall; F

_{V}is site coefficient; S

_{1}is the spectral acceleration of period 1 s; h

_{i}for retaining wall toe to section i height.

_{i}for retaining wall toe to section i height.

#### 3.3. Deformation

#### 3.4. Earth Pressure

_{AE}is total dynamic earth force; γ is the sand weight; H is the wall height; K

_{AE}is seismic earth pressure coefficient; P

_{S}is static earth pressure; ΔP

_{dyn}is dynamic earth force increment; K

_{a}is the static earth pressure coefficient; K

_{dyn}is the dynamic increment active earth pressured coefficient; k

_{h}is the horizontal seismic coefficient; φ is the internal friction angle of sand; θ is the seismic inertia angle; δ is the soil-wall interface friction angle; α is the wall-back inclination.

^{2}) to obtain the measured seismic earth pressure increment coefficient K

_{dyn}. Figure 12 compares the measured values with the standard values, and the measured coefficient increases with the increase of peak acceleration. In the range of 1.0 g, the measured coefficient is always in the range of M-O method and S-W method, and the maximum measured value is 0.54. The distribution law of the S-W method coefficient is consistent with the measured value, and the value is slightly conservative, so it can be used as the upper limit. When the peak acceleration reaches 0.8 g, the M-O method will overestimate the dynamic increment active earth pressured coefficient. The S-W method considers that the normalized point of application for the resultant of the dynamic earth force increment acts on the height of 0.6 H, but the measured height is variable, with the increase of peak acceleration, the measured height gradually decreases from 0.63 H to close to H/3 height, which is consistent with the conclusion of Bathurst [35].

#### 3.5. Connection Loads

_{dyn}is the increment of reinforcement tensile force; K

_{dyn}is the dynamic increment active earth pressured coefficient; A

_{c}

_{(n)}is contributory area to determine force in reinforcement, for the lowermost layer A

_{c}

_{(n)}= A

_{c}

_{(1)}, for the topmost layer A

_{c}

_{(n)}= A

_{c}

_{(N)}; E

_{(n)}is the elevation of layer n above reference datum.

_{i}is internal inertia force due to the weight of backfill within the active zone; n is the total number of reinforcement layers in the wall; W

_{a}is the weight of the active zone.

## 4. Discussion

## 5. Conclusions

- (1)
- Affected by the nonlinear characteristics of soil, the acceleration amplification coefficient decreases with the increase of peak acceleration, and the maximum acceleration appears at the top of the retaining wall, which is consistent with the whiplash effect of high-rise structures. When HPGA reaches 1.0 g, the acceleration amplification coefficient increases, the range of acceleration amplification coefficient at the top of the wall is 1.36–1.69. Based on the Chinese Highway Specification and test results, this paper suggests that the acceleration amplification factor distribution formula is suitable for the reinforced soil-retaining wall with wrapped-face.
- (2)
- The lateral residual displacement increases with the increase of peak acceleration, and the residual displacement at the top of the retaining wall is the largest. When HPGA is 1.0 g, the maximum cumulative residual displacement is 2.96% H, exceeding the failure index of WSDOT, and the maximum uneven settlement of sand is 3.57% H, exceeding the limit value of AASHTO. According to the WSDOT lateral displacement control index, the deformation range of the reinforced soil-retaining wall with wrapped-face is divided into three stages: quasi-elastic stage, plastic stage, and failure stage.
- (3)
- When HPGA is 1.0 g, the measured total dynamic earth force is 10.68 kN/m, which is greater than 8.57 kN/m predicted by the S-W method, but the measured K
_{dyn}is slightly smaller than the theoretical value of the S-W method. This is because the traditional S-W and M-O methods do not consider the reinforcement effect of geogrid on sand, resulting in a gap between the predicted value and the actual value. The calculation of earth pressure of reinforced soil-retaining walls still needs to be studied. - (4)
- AASHTO and NCMA guidelines check the stress distribution of geosynthetics based on the limit equilibrium theory, allowable stress, and safety factor. This method is designed for the limit working state of retaining walls, it is considered that the load and resistance are in the limit state, and it is assumed that all reinforcements can reach the same stress state, which will lead to conservative results. The measured maximum value is 0.189 kN/m, less than the predicted values of the two guidelines.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Wrapped-face reinforced soil-retaining wall not damaged during the 2011 Tohoku earthquake, off the pacific coast [7].

**Figure 4.**Ground motion time history curve: (

**a**) WL wave time history curve; (

**b**) Fourier spectrum of WL wave; (

**c**) El wave time history curve; (

**d**) Elwave Fourier spectrum.

**Figure 11.**The total dynamic earth force and the normalized point of application for the resultant of total dynamic earth force.

**Figure 12.**The dynamic increment active earth pressured coefficient and the normalized point of application for the resultant of the dynamic earth force increment.

**Figure 15.**Comparison between the increment of reinforcement tensile force at the connection and the dynamic earth force increment: (

**a**) WL wave; (

**b**) El wave.

**Figure 17.**The normalized point of application for the resultant of reinforcement tension increment and dynamic earth force increment.

Parameter | Unit | Scale Factor (Prototype/Model) | Scale Factor Used in This Study (Prototype/Model) |
---|---|---|---|

Length | m | N * | 3 |

Elastic modulus | kPa | 1 | 1 |

Density | Kg/m^{3} | 1 | 1 |

Stress | kPa | 1 | 1 |

Time | s | N^{0.5} | 1.73 |

Velocity | m/s | N^{0.5} | 1.73 |

Acceleration | g | 1 | 1 |

Gravity | g | 1 | 1 |

Frequency | Hz | N^{−0.5} | 0.58 |

Case Number | Input Wave | PGA/g | Case Code |
---|---|---|---|

1, 2 | WL, El | 0.1 | WL 0.1 g, El 0.1 g |

3, 4 | WL, El | 0.2 | WL 0.2 g, El 0.2 g |

5, 6 | WL, El | 0.4 | WL 0.4 g, El 0.4 g |

7, 8 | WL, El | 0.6 | WL 0.6 g, El 0.6 g |

9, 10 | WL, El | 0.8 | WL 0.8 g, El 0.8 g |

11, 12 | WL, El | 1.0 | WL 1.0 g, El 1.0 g |

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**MDPI and ACS Style**

Xu, H.; Cai, X.; Wang, H.; Li, S.; Huang, X.; Zhang, S.
Analysis of the Working Response Mechanism of Wrapped Face Reinforced Soil Retaining Wall under Strong Vibration. *Sustainability* **2022**, *14*, 9741.
https://doi.org/10.3390/su14159741

**AMA Style**

Xu H, Cai X, Wang H, Li S, Huang X, Zhang S.
Analysis of the Working Response Mechanism of Wrapped Face Reinforced Soil Retaining Wall under Strong Vibration. *Sustainability*. 2022; 14(15):9741.
https://doi.org/10.3390/su14159741

**Chicago/Turabian Style**

Xu, Honglu, Xiaoguang Cai, Haiyun Wang, Sihan Li, Xin Huang, and Shaoqiu Zhang.
2022. "Analysis of the Working Response Mechanism of Wrapped Face Reinforced Soil Retaining Wall under Strong Vibration" *Sustainability* 14, no. 15: 9741.
https://doi.org/10.3390/su14159741