# Mechanical Responses of Soil-Geosynthetic Composite (SGC) Mass under Failure Load

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

## 3. Results

#### 3.1. Influence of Reinforcement Vertical Spacing

#### 3.2. Influence of Reinforcement Axial Stiffness

#### 3.3. Influence of Secant Modulus ${E}_{50}$

#### 3.4. Influence of Angle of Internal Friction

## 4. Discussion

#### 4.1. Influence of Reinforcement Stiffness and Spacing on Lateral Displacement

#### 4.2. Influence of Reinforcement Strength and Spacing on Load-Carrying Capacity

#### 4.3. Failure Surface of SGC Mass

## 5. Conclusions

- In general, the variation of the reinforcement spacing, reinforcement stiffness, soil modulus, and angle of friction of the backfill had negligible effect on the level of the reinforcement’s maximum axial strain, which corresponded to the possible rupture or failure surface of the composite mass.
- The study showed that the influence of the reinforcement stiffness $EA$ on the load-carrying capacity of the composite mass was more apparent when $EA$ was between 333 kN/m and 1000 kN/m than between 1000 kN/m and 3000 kN/m. The result suggested that for a consistent performance, the geotextile reinforcement to be adopted should have an axial stiffness $EA$ of at least 1000 kN/m.
- Wu–Pham’s equation performed well in estimating the load-carrying capacity of the composite mass with reinforcement strengths ${T}_{f}$ of 23.3 kN/m and 70 kN/m, a range of internal friction angles of 40${}^{\circ}\le {\varphi}^{\prime}\le 50$${}^{\circ}$, and a range of reinforcement spacings of $0.2\phantom{\rule{0.277778em}{0ex}}\mathrm{m}\le {S}_{v}\le 0.4\phantom{\rule{0.277778em}{0ex}}\mathrm{m}$.
- Based on the result of the same reinforcement strength and reinforcement spacing ratio (Table 2), the reinforcement spacing was found to have a more profound effect than the reinforcement strength on the load-carrying capacity of the composite mass. This behavior was mainly attributed to the composite behavior created by the interface friction between the closely spaced geosynthetic-reinforcement layers and the backfill, in which a closer spacing resulted in an increased lateral confinement and hence, increasing the stiffness and load-carrying capacity of the SGC mass. A reasonable combination of $({S}_{v},{T}_{f})$ was recommended, which is between (0.1 m, 70 kN/m) and (0.4 m, 280 kN/m), for which the load-carrying capacity reduced linearly between 5600 kPa and 2500 kPa, respectively.
- The failure surface of the composite soil mass beneath the concrete pad was found to be different from that observed in the GRS–IBS system, and that of the unreinforced soil; using the Rankine active wedge theory and the Mohr–Coulomb failure criterion, the backcalculated angle of friction of the SGC mass was found to be about 15% to 25% less than that of unreinforced soil. Thus, the failure mode of the GRS composite was different from that of the unreinforced soil and did not follow the Rankine—Mohr–Coulomb failure mode.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

GRS | Geosynthetic-reinforced soil |

IBS | Integrated bridge system |

PP | Polypropylene |

SGC | Soil-geosynthetic composite |

GRS–IBS | Geosynthetic-reinforced soil–integrated bridge system |

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**Figure 1.**Materials properties: (

**a**) shear strength parameters of the study backfill; (

**b**) uniaxial tensile test of a 300 mm wide by 150 mm long Geotex 4 × 4 PP-woven geotextile; (

**c**) obtained tensile strength of the single- and double-sheet geotextiles (Pham [3]).

**Figure 2.**(

**a**) Schematic diagram and configuration of a typical SGC mass; (

**b**) uniformly distributed load adopted in the simulation of the compaction effect of the SGC specimen; (

**c**) a typical finite element mesh used in the numerical simulation.

**Figure 3.**(

**a**) Simulated and measured applied vertical pressure vs. axial strain and (

**b**) simulated (with a compaction pressure of 44 kPa) and measured lateral displacement along the specimen height of the three SGC tests performed by Pham [3].

**Figure 4.**Failure patterns observed from the experimental SGC masses performed by Pham [3]. (

**a**) Test no. 1; (

**b**) test no. 2; and (

**c**) test no. 3.

**Figure 5.**Influence of reinforcement vertical spacing, under a surcharge (service load) of 200 kPa, on the distribution of reinforcement’s axial strain at (

**a**) 0.8 H, (

**b**) 0.6 H, (

**c**) 0.4 H, and (

**d**) 0.2 H of the specimen.

**Figure 7.**Influence of reinforcement axial stiffness $EA$, under a surcharge (service load) of 200 kPa, on the distribution of reinforcement axial strain at (

**a**) 0.8 H, (

**b**) 0.6 H, (

**c**) 0.4 H, and (

**d**) 0.2 H of the specimen.

**Figure 8.**Relation between load-carrying capacity and reinforcement stiffness $EA$ of the study SGC mass.

**Figure 9.**Influence of secant modulus ${E}_{50}$ of soil, under a surcharge (service load) of 200 kPa, on the distribution of reinforcement axial strain at (

**a**) 0.8 H, (

**b**) 0.6 H, (

**c**) 0.4 H, and (

**d**) 0.2 H of the specimen.

**Figure 10.**Influence of angle of internal friction, under a surcharge (service load) of 200 kPa, on the distribution of reinforcement axial strain at (

**a**) 0.8 H, (

**b**) 0.6 H, (

**c**) 0.4 H, and (

**d**) 0.2 H of the specimen.

**Figure 11.**Relations between load-carrying capacity and angle of internal friction of the study SGC specimen with various vertical spacing.

**Figure 12.**Relation between the open face lateral displacement and the ratio of reinforcement stiffness and reinforcement spacing of the study GRS mass.

**Figure 13.**Relation between load-carrying capacity, reinforcement strength, and reinforcement spacing of the study GRS mass.

Materials Properties | Test No.1 | Test No. 2 | Test No. 3 |
---|---|---|---|

Soil^{a} | |||

Model | Hardening Soil | Hardening Soil | Hardening Soil |

Unit weight ${\gamma}_{\mathrm{soil}}$ (kN/m${}^{3}$) | 25 | 25 | 25 |

Dilation angle ${\psi}_{\mathrm{soil}}\phantom{\rule{0.277778em}{0ex}}{(}^{o})$ | 19 | 19 | 19 |

Peak internal friction angle, ${\varphi}_{\mathrm{soil}}^{\prime}\phantom{\rule{0.277778em}{0ex}}{(}^{o})$ | 50 | 50 | 50 |

Apparent cohesion ${c}_{\mathrm{soil}}^{\prime}$ (kPa) | 70 | 70 | 70 |

Maximum particle size ${d}_{\mathrm{max}}$ (mm) | 33 | 33 | 33 |

Secant modulus ${E}_{50}$ (kPa) | 62,374 | 62,374 | 62,374 |

Unloading modulus ${E}_{\mathrm{ur}}=3{E}_{50}$ (kPa) | 187,122 | 187,122 | 187,122 |

Stress dependence exponent m | 0.5 | 0.5 | 0.5 |

Poisson’s ratio ${\nu}_{\mathrm{soil}}$ | 0.2 | 0.2 | 0.2 |

${P}_{\mathrm{ref}}$ (kPa) | 100 | 100 | 100 |

Reinforcement | Single-sheet | Double-sheet | Single-sheet |

Geotex 4 × 4 | Geotex 4 × 4 | Geotex 4 × 4 | |

Model | Elastic–perfectly plastic | Elastic–perfectly plastic | Elastic–perfectly plastic |

Elastic axial stiffness $EA$ at 1% strain (kN/m) | 1000 | 2000 | 1000 |

Tensile strength ${T}_{f}$ (kN/m) | 70 | 140 | 70 |

Reinforcement spacing ${S}_{v}$ (m) | 0.2 | 0.4 | 0.4 |

Modular Block | |||

Model | Linear elastic | Linear elastic | Linear elastic |

Unit weight $\gamma $ (kN/m${}^{3}$) | 12.5 | 12.5 | 12.5 |

Poisson’s ratio $\nu $ | 0 | 0 | 0 |

Stiffness modulus (kPa) | 3 $\times {10}^{6}$ | 3 $\times {10}^{6}$ | 3 $\times {10}^{6}$ |

Block–Block Interface^{b} | |||

Model | Mohr–Coulomb | Mohr–Coulomb | Mohr–Coulomb |

Poisson’s ratio ${\nu}_{i}$ | 0.45 | 0.45 | 0.45 |

Friction angle ${\varphi}_{i}\phantom{\rule{0.277778em}{0ex}}{(}^{o})$ | 33 | 33 | 33 |

Apparent cohesion ${c}_{i}$ (kPa) | 2 | 2 | 2 |

Stiffness modulus ${G}_{i}$ (kPa) | 3 $\times {10}^{6}$ | 3 $\times {10}^{6}$ | 3 $\times {10}^{6}$ |

Soil–Block Interface^{b} | |||

Model | Mohr–Coulomb | Mohr–Coulomb | Mohr–Coulomb |

Poisson’s ratio ${\nu}_{i}$ | 0.45 | 0.45 | 0.45 |

Friction angle ${\varphi}_{i}\phantom{\rule{0.277778em}{0ex}}{(}^{o})$ | 33.33 | 33.33 | 33.33 |

Apparent cohesion ${c}_{i}$ (kPa) | 46.67 | 46.67 | 46.67 |

Stiffness modulus ${G}_{i}$ (kPa) | 74,830 | 74,830 | 74,830 |

Soil–Reinforcement Interface | |||

Model | Mohr–Coulomb | Mohr–Coulomb | Mohr–Coulomb |

Poisson’s ratio ${\nu}_{i}$ | 0.45 | 0.45 | 0.45 |

Friction angle ${\varphi}_{i}\phantom{\rule{0.277778em}{0ex}}{(}^{o})$ | 43.63 | 43.63 | 43.63 |

Apparent cohesion ${c}_{i}$ (kPa) | 56 | 56 | 56 |

Stiffness modulus ${G}_{i}$ (kPa) | 106,685 | 106,685 | 106,685 |

Geometrical Configuration | |||

Wall height H (m) | 2 | 2 | 2 |

Wall aspect ratio L/H | 0.7 | 0.7 | 0.7 |

**Table 2.**Load-carrying capacity of SGC mass under various combinations of reinforcement spacing and strength.

${\mathbf{S}}_{\mathbf{v}}$ | ${\mathbf{T}}_{\mathbf{f}}$ | ${\mathbf{T}}_{\mathbf{f}}/{\mathbf{S}}_{\mathbf{v}}$ | Numerical Result | Equation (5) | Difference between Proposed Equation (5) and Numerical Result |
---|---|---|---|---|---|

(m) | (kN/m) | (kPa) | (kPa) | (%) | |

0.1 | 35 | 350 | 3181 | 3372 | 6.00 |

0.2 | 70 | 350 | 2957 | 2384 | −19.38 |

0.3 | 105 | 350 | 1787 | 1947 | 8.95 |

0.4 | 140 | 350 | 1656 | 1686 | 1.81 |

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**MDPI and ACS Style**

Gui, M.-W.; Phan, T.T.T.; Pham, T.
Mechanical Responses of Soil-Geosynthetic Composite (SGC) Mass under Failure Load. *Sustainability* **2022**, *14*, 9629.
https://doi.org/10.3390/su14159629

**AMA Style**

Gui M-W, Phan TTT, Pham T.
Mechanical Responses of Soil-Geosynthetic Composite (SGC) Mass under Failure Load. *Sustainability*. 2022; 14(15):9629.
https://doi.org/10.3390/su14159629

**Chicago/Turabian Style**

Gui, Meen-Wah, Truc T. T. Phan, and Thang Pham.
2022. "Mechanical Responses of Soil-Geosynthetic Composite (SGC) Mass under Failure Load" *Sustainability* 14, no. 15: 9629.
https://doi.org/10.3390/su14159629