# Physical and Numerical Models of Mechanically Stabilized Earth Walls Using Self-Fabricated Steel Reinforcement Grids Applied to Cohesive Soil in Vietnam

^{*}

## Abstract

**:**

^{2}, which is 15 times greater than the design load of 20 kN/m

^{2}. The failure surface within the reinforced soil had a parabolic sliding shape that was similar to the theoretical studies. At the failure load level, the maximum lateral displacement at the top of the wall facing was small (3.9 mm), significantly lower than the allowable displacement for a retaining wall. Furthermore, a numerical model using FLAC software 7.0 was applied to simulate the performance of the MSE wall. The modeling results were in good agreement with the physical model. Thus, self-fabricated galvanized steel grids could confidently be used in combination with the local backfill soil for MSE walls.

## 1. Introduction

_{u}) of the backfill soil [18].

## 2. Full-Scale Experimental Model

#### 2.1. Model Design

^{2}and the experimental load was applied until the MSE wall collapsed, which included reinforcement rupture.

#### 2.1.1. Wall-Facing Panels

#### 2.1.2. Backfill Material

_{60}, D

_{30}, and D

_{10}were 0.09, 0.65, and 4.1 mm, respectively. The uniformity coefficient C

_{u}was determined to be 45.6. The friction angle and the unit cohesion were 34.3° and 5.1 kN/m

^{2}, respectively. The maximum dry density was 18.16 kN/m

^{3}when the optimum moisture content was 12.5%. The properties of the selected backfill material met the requirements of reinforced soil according to the standards from AFNOR [12], AASHTO [26], and TCVN [14] for MSE wall constructions.

^{2}in the backfill soil could affect the interaction between the steel reinforcement and the reinforced soil. In addition, this soil contained a remarkable amount of sulfate ion (SO

_{4}

^{2−}= 0.497 mg/g); thus, it could affect the long-term durability of the reinforcement due to corrosion. Therefore, to efficiently utilize the available local backfill material, the reinforcement used in the wall was galvanized to prevent corrosion and the soil–reinforcement interaction was enhanced by arranging steel ribs on the reinforcement mesh.

#### 2.1.3. Reinforcement

_{0}, was 49,000 N. However, we also considered the effect of the backfill soil, the service life of the wall, corrosion due to sulfate ions, and metal loss during the 100-year design life of the MSE wall. Regarding the service life of the wall, Haiun et al. [29] recommended that an MSE structure needs to be monitored and repaired when the values of the remaining tensile strength within the reinforcement are equal to 65% F

_{0}, with F

_{0}being the initial tensile strength of the reinforcement. Thus, in this study, the tensile strength of the reinforcement was 31,850 N at the initial stage, as illustrated in Table 2.

_{0}, as indicated in Table 2.

_{v}= 0.75 m (4 reinforcement layers along the height of the wall, H = 3 m). In each layer, 4 longitudinal steel reinforcement bars were installed with a space of 0.375 m. In addition, the horizontal spacing between the reinforcement bars (the transverse direction) was 0.45 m. Ribs that were 3 cm high were bonded to the reinforcement mesh to enhance the soil–reinforcement interaction, as shown in Figure 4. The steel reinforcement grids were rigidly connected to the facing panels.

#### 2.1.4. Ground Foundation

#### 2.1.5. Loading System

#### 2.2. Construction and Instrumentation of the MSE Wall

## 3. Numerical Modelling

- If z > z
_{0}= 6 m;

- If z ≤ z
_{0}= 6 m;

_{0}*(1 − z/z

_{0}) + (z/z

_{0})tan φ

_{0}* = 1.2 + log

_{10}(C

_{u});

_{0}* are the apparent friction coefficients for the steel reinforcement and backfill interfaces; C

_{u}is the coefficient of uniformity of the backfill soil; z is the depth of the reinforcement layers from the top of the wall, where z

_{0}= 6 m; and φ is the friction angle of the backfill soil. Table 4 illustrates the properties of the backfill–reinforcement interactions and facing-panel–backfill interactions.

## 4. Results and Discussion

#### 4.1. Full-Scale Model Results

#### 4.1.1. MSE Wall Loading

^{2}. The design load of the model was 20 kN/m

^{2}[12]. The maximum load (when the steel reinforcement bars were ruptured) was 302 kN/m

^{2}, approximately 15 times greater than the normal traffic loading of 20 kN/m

^{2}. The stress, strain, and displacement of the wall, the longitudinal reinforcement bars, and the reinforced soil mass were recorded at load levels of 12, 20, 50, 75, 100, 150, 200, 250, 275, 300, and 302 kN/m

^{2}.

#### 4.1.2. Tensile Forces in the Reinforcement Bars

^{2}; and L is the length of the longitudinal reinforcement bars, with L = 2.1 m.

^{2}to 302 kN/m

^{2}, the tensile forces in the reinforcement bars increased and created a sliding surface within the reinforced soil.

^{2}), the tensile forces in the deeper reinforcement layers were greater than the upper ones. However, when the test load was higher than 75 kN/m

^{2}, the tensile forces in reinforcement layers 3 and 4 were higher than layers 1 and 2. It is a fact that at a low load level, the total load (including the earth pressure, dead loads, and surcharge load) increases with the depth of the wall. Thus, the deeper reinforcement layers absorbed a greater load than the upper layers. Conversely, when the load test was high, reinforcement layer 4 achieved the highest tensile forces and this value decreased along the wall depth. In addition, the increasing tensile force distribution when the surcharge load increased indicated that the failure surface expanded in the passive area.

#### 4.1.3. Failure Load

^{2}. When the load level was 302 kN/m

^{2}, the maximum tensile force in the reinforcement layers was 31,881 N, which was higher than the ultimate tensile force of 31,850 N. Thus, at that moment, failure occurred in the MSE wall. The longitudinal steel bars suddenly ruptured at the drilled cross-sectional area where the tensile force reached its maximum value in the reinforcement bars.

^{2}, which was 15 times greater than the design load. In terms of the load-bearing capacity, the MSE wall structure in the experimental model could resist very high surcharge loads. However, in terms of long-term serviceability, the selected steel bars would be appropriate for the structure durability during a service life of 100 years under a design load of 20 kN/m

^{2}[3].

^{2}, the failure surface in the reinforced soil could be determined by connecting the maximum tensile force points in each reinforcement layer. Figure 10 demonstrates that the failure surface in this study was similar to the Rankine theory [2]. In detail, in the first half of the wall, the failure surface started from the top of the wall and further away from the wall face at approximately 0.3 H. In deeper positions, the failure surface stopped at the toe of the wall (wall base). This failure pattern was similar to the reports of Chang et al. [2], Lee et al. [8], Murray and Farrar [7], Schlosser and Guilloux [36], and Murray [11]. However, the failure surface at the toe of the wall was far from the wall facing (0.2 H). Murray and Farrar [7] explained that friction between the rigid foundation of an MSE wall and the soil reinforcement affects the failure surface of the reinforced soil mass.

_{a}in this study and the values calculated from the standards from AFNOR [12]. The L

_{a}values in reinforcement layers 4, 3, and 2 were close to the theoretically estimated values. The failure surface of the lowest layer was slightly different due to the strain gauge locations.

#### 4.1.4. Lateral Displacement of the Wall Facing

^{2}), the maximum lateral displacement at the top of the wall was 3899 µm, which was much smaller than the allowable lateral displacement for the wall (Δ = H/100 = 3 cm) [8,10]. The lateral displacement of the wall in this study had a similar pattern to the displacement profiles in previous studies [36].

#### 4.2. Numerical Model Results

^{2}). The numerical model results were similar to the report of Stuedlein et al. [38].

^{2}, the model results showed that the highest lateral displacement of the wall facing was 4270 mm, as shown in Figure 14. In addition, the maximum tensile load in the fourth reinforcement layer (near the top of the wall) was similar to the full-scale model and was located approximately 0.95 m further away from the facing panel. This value decreased close to the wall facing of the lower reinforcement layers, as shown in Figure 10.

## 5. Conclusions

- The retaining wall suddenly collapsed due to internal instability (reinforcement rupture) at a load level of 302 kN/m
^{2}, which was 15 times greater than the design load. At that failure mode, the maximum lateral displacement at the top of the wall facing was 3899 µm, which was much less than the allowable displacement of the wall (3 cm). The failure surface within the reinforced soil block was similar to theoretical studies. - It was noted that when the test load was lower than the design load (<20 kN/m
^{2}) the tensile forces in the deepest reinforcement layer showed the highest value. However, the upper reinforcement layers achieved the highest tensile forces when the test load increased. Thus, it is essential to enhance the bearing capacity of the reinforcement layers near the ground surface in special constructions with a very high surcharge load. - The measured data from the full-scale model were validated by the numerical model using FLAC software. The tensile load distribution pattern in the reinforcement layer and the lateral displacement of the wall were similar to the research results from other studies and were in good agreement with the current standards.
- The experimental results also demonstrated that when using a self-fabricated galvanized steel reinforcement (CB300V; Φ 10) for the MSE wall, the wall maintained its stability under the applied load considering a metal loss of 65% of the initial tensile strength. Deformations to the reinforcement were minimal, and the wall was capable of withstanding high surcharge loads. Therefore, self-fabricated galvanized steel reinforcement grids and the specific soil material in the Danang area could be used as the reinforcement material for MSE walls with high stability.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

MSE walls | Mechanically stabilized earth walls |

GSG | Galvanized steel grid |

F_{0} | Initial tensile strength of the reinforcement |

ΔF | Proportional loss of tensile strength of the reinforcement |

L_{a} | Length of the reinforcement bars in the failure zone |

L_{e} | Length of the reinforcement bars in the backfill zone |

f* | Apparent friction coefficient for the steel reinforcement and backfill interfaces |

C_{u} | Coefficient of uniformity of the backfill soil |

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**Figure 2.**Properties of the backfill material: (

**a**) local backfill soil; (

**b**) grain-size distribution of the backfill soil; (

**c**) Proctor compaction results.

**Figure 3.**Drilling to reduce the cross-sectional area of the reinforcement bars: (

**a**) drilling the steel bar; (

**b**) drilling positions.

**Figure 5.**Full-scale MSE model with full instrumentation: (

**a**) MSE model with full instrumentation; (

**b**) full-scale model after construction.

**Figure 7.**The tensile force distribution in the reinforcement layers at different test load levels: (

**a**) the fourth layer; (

**b**) the third layer; (

**c**) the second layer; (

**d**) the first layer.

**Figure 8.**Tensile force distribution in different reinforcement layers: (

**a**) load level of 0 kN/m

^{2}; (

**b**) load level of 20 kN/m

^{2}; (

**c**) load level of 75 kN/m

^{2}; (

**d**) load level of 300 kN/m

^{2}.

**Figure 13.**The numerical model results during the construction of the wall: (

**a**) displacement of the wall facing; (

**b**) distribution of tensile force in the reinforcement layers.

**Figure 14.**The numerical model results at a load level of 300 kN/m

^{2}: (

**a**) stress distribution in the retaining wall; (

**b**) displacement of the wall facing; (

**c**) the distribution of the tensile force in the reinforcement layers.

Parameter | Unit | Value |
---|---|---|

Saturated density, γ | kN/m^{3} | 2.070 |

Dry density, γ_{k} | kM/m^{3} | 1.816 |

Friction angle, φ_{soil} | Degrees | 34.3 |

Cohesion, c_{soil} | Pa | 5100 |

Plasticity index, IP | - | 8.55 |

Uniformity coefficient, C_{u} | - | 45.6 |

pH | - | 5.9 |

Ion, Cl^{−} | mg/g | 0.094 |

Ion, SO_{4}^{2−} | mg/g | 0.497 |

Parameter | Unit | Value |
---|---|---|

Initial tensile strength of the steel reinforcement | N | 49,000 |

Loss of tensile strength | N | 17,150 |

Remaining tensile strength within the reinforcement | N | 31,850 |

Drilling the reinforcement bars to reduce their cross-sectional area | % | 26.6 |

Drilling depth (Φ 5) | mm | 8.1 |

Parameter | Unit | Value |
---|---|---|

Concrete panel | ||

Width | m | 0.75 |

Height | m | 0.15 |

Length | m | 1.5 |

Young’s modulus | Pa | 2 × 10^{11} |

Compressive strength of concrete | Pa | 35,000 |

Foundation soil | ||

Unit weight, γ_{Found} | kg/m^{3} | 2700 |

Friction angle, φ_{Found} | Degrees | 51 |

Cohesion, c_{Found} | Pa | 5.51 × 10^{7} |

Bulk modulus | Pa | 4.39 × 10^{10} |

Shear modulus | Pa | 3.02 × 10^{10} |

Backfill soil | ||

Unit weight, γ_{soil} | kg/m^{3} | 2070 |

Friction angle, φ_{soil} | Degrees | 34.3 |

Cohesion, c_{soil} | Pa | 5100 |

Bulk modulus | Pa | 1.5 × 10^{7} |

Shear modulus | Pa | 6 × 10^{6} |

Steel reinforcement | ||

Length | m | 2.1 |

Steel bar thickness | m | 0.010 |

Calculation width | m | 1.5 |

Number of longitudinal bars per calculation width | Strip | 4 |

Young’s modulus | Pa | 2 × 10^{11} |

Tensile strength | N/m | 31,850 |

Tensile failure strain | % | 0.19 |

Shear stiffness | N/m^{2} | 2 × 10^{7} |

Parameter | Unit | Value |
---|---|---|

Backfill soil: concrete panel | ||

Normal stiffness | Pa/m | 2.4 × 10^{6} |

Shear stiffness | Pa/m | 2.4 × 10^{6} |

Friction angle | Degrees | 26 |

Backfill soil: steel reinforcement | ||

Shear stiffness | N/m^{2} | 2 × 10^{7} |

Cohesion | N/m | 1 × 10^{5} |

Initial apparent friction coefficient | ||

Layer 4 | 1.917 | |

Layer 3 | 1.751 | |

Layer 2 | 1.586 | |

Layer 1 | 1.420 |

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**MDPI and ACS Style**

Chau, T.-L.; Nguyen, T.-H.; Pham, V.-N.
Physical and Numerical Models of Mechanically Stabilized Earth Walls Using Self-Fabricated Steel Reinforcement Grids Applied to Cohesive Soil in Vietnam. *Appl. Sci.* **2024**, *14*, 1283.
https://doi.org/10.3390/app14031283

**AMA Style**

Chau T-L, Nguyen T-H, Pham V-N.
Physical and Numerical Models of Mechanically Stabilized Earth Walls Using Self-Fabricated Steel Reinforcement Grids Applied to Cohesive Soil in Vietnam. *Applied Sciences*. 2024; 14(3):1283.
https://doi.org/10.3390/app14031283

**Chicago/Turabian Style**

Chau, Truong-Linh, Thu-Ha Nguyen, and Van-Ngoc Pham.
2024. "Physical and Numerical Models of Mechanically Stabilized Earth Walls Using Self-Fabricated Steel Reinforcement Grids Applied to Cohesive Soil in Vietnam" *Applied Sciences* 14, no. 3: 1283.
https://doi.org/10.3390/app14031283