# Discrete Element Study on Bending Resistance of Geogrid Reinforced Cement-Treated Sand

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## Abstract

**:**

## 1. Introduction

## 2. Laboratory Test

#### 2.1. Material and Methods

^{3}and the thickness is 3 mm. The schematic diagram of the working condition with different geogrid layers is shown in Figure 2.

#### 2.2. Results and Discussion

_{1}of the key node are P

_{1}(the first obvious nonlinear point of the load–deflection curve, the corresponding load value is called P

_{1}, and the corresponding deflection value is called δ

_{1}, corresponding to the bending strength f

_{1}) and deflection L/150 (corresponding to the residual strength f

_{2}).

_{1}), the mechanical responses of the specimens under different working conditions are similar. The loads both experience linear increases until the deflection increase to P

_{1}, then the load drops rapidly from point P1 onwards. However, the load of the CTS specimen decreases sharply to 0 after P

_{1}, while the loads of the CTSG specimens increase after decreasing, which illustrates that the reinforced specimens exhibit better bearing capacity. In addition, the bearing capacity of the double-layer reinforced condition is better than that of the single-layer reinforced condition. Comparing the bending strength index f under different geogrid layers, it can be seen that the bending strength f1 changes slightly with the increase in the number of layers, while f

_{2}increases significantly. The CTS specimen, due to its quick fracturing, fails to demonstrate any toughness. For the geogrid-reinforced specimens, the rate of toughness increase (slope of the toughness–deflection curve) for the double-layer reinforced specimens is faster than that of the single-layer reinforced specimens.

## 3. Simulated Test

^{2D}to simulate the three-point bending test of the CTS and CTSG specimens with different geogrid stiffness and layer number, and analyzes the reinforcement mechanism and deformation failure mechanism of geogrid on the bending resistance of the CTSGs.

#### Numerical Modeling

^{−5}. According to the actual loading situation of the three-point loading test, the clump simulation actuator and bearers are created according to the response size and spacing, as shown in Figure 5 The single-layer reinforced CTSG and particle contact relationship are shown in Figure 5a and the double-layer reinforced CTSG is shown in Figure 5b.

## 4. Results and Discussion

_{1}, but a significant effect on the second peak strength f

_{2}. The quantitative comparison of f

_{2}for each specimen indicates that for single-layer reinforcement specimens, the f

_{2}of CTSG-3-S is 184.84 kPa higher than that of CTSG-1-S and 67.87 kPa higher than that of CTSG-2-S; for double-layer reinforcement specimens, the

_{f}

_{2}of CTSG-3-D is 271.49 kPa higher than that of CTSG-1-D and 141.52 kPa higher than that of CTSG-2-D. The f

_{2}value increases significantly with the increase in geogrid stiffness, and the increase in the number of reinforcement layers will enhance the effect above, resulting in a larger growth rate. This is because in the early stage of loading, the cement mortar of the specimen has not been cracked yet, and the geogrid and cement mortar undergo coordinated deformation under external forces. The load is mainly controlled by the cement mortar part which occupies a higher stiffness, leading to the similar f

_{1}values for different specimens. However, when the specimen reaches f

_{2}, corresponding to a deflection of 2.0 mm or L/150, the cement mortar in the cross-section has cracked at this point. The geogrid plays its reinforcing role, and as a result, the stiffness and number of layers of the geogrid significantly affect the value of f

_{2}.

_{1}, because the specimen has not yet cracked and the geogrid has little effect at this time. After the deflection of the CTS specimen reaches δ1, the specimen is destroyed, the area surrounded by the normal contact force distribution diagram decreases rapidly and it no longer changes with the increase in the deflection. Comparing CTSG-1-S and CTSG-3-S, when the stiffness of the geogrid is low, the normal contact force of the specimen reaches its maximum when the deflection is δ1, and then the area surrounded by the normal contact force distribution graph is significantly reduced. With the further increase in the deflection, although the area increases, it still cannot reach its maximum value. Under high stiffness, the normal contact force of the specimen decreased after the deflection exceeds δ1, but could be restored to a level higher than that at δ1 due to a stronger reinforcement effect.

_{n}decreased with increasing geogrid stiffness (which means anisotropy of mortar decreased). Comparing CTSG-3-S and CTSG-3-D, it can be seen that the contact force of double-layer reinforced specimens decreased smaller at cracking and had a greater contact force value when deflection come to 2 mm. The Fourier fitting coefficient a

_{n}of double-layer reinforced specimens increased, as the double-layered reinforcement increased the range of the mortar tensile area (as shown in Figure 18d), resulting in a more significant increase in the contact force in the horizontal direction inside the mortar, enhancing the anisotropy.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 2.**Schematic diagram of cement-treated sand reinforced with geogrids in laboratory test. (

**a**) Single-layer geogrid CTSG specimen. (

**b**) Double-layer geogrid CTSG specimen.

**Figure 3.**The evolution of deflection with load and the variation of the bending strength and toughness in three-point bending tests.

**Figure 5.**Model of three-point bending test in DEM simulation. (

**a**) Single-layer geogrid CTSG specimen. (

**b**) Double-layer geogrid CTSG specimen.

**Figure 10.**Comparison of toughness of CTSG specimens under different working conditions (

**a**) The change in toughness of different specimens with deflection. (

**b**) Comparion of toughness of different stiffness geogrid specimens.

**Figure 11.**Specimen crack tip force chain amplification diagram. (

**a**) The state of mortar inside the box before cracking, (

**b**) The state of mortar inside the box after cracking.

**Figure 12.**Force chain diagram of ctsg specimen in bending process (local amplification near geogrid). (

**a**) before cracking, (

**b**) Initial cracking, (

**c**) cracking development.

**Figure 14.**Crack development of different specimens. (

**a**) CTS. (

**b**) CTSG-2-S. (

**c**) CTSG-2-D. (

**d**) CTSG-3-D.

**Figure 16.**The evolution of internal force with loading for different working conditions. (

**a**) CTS. (

**b**) CTSG-2-S. (

**c**) CTSG-2-D. (

**d**) CTSG-3-D.

**Figure 18.**Composition diagram of normal contact force chain. (

**a**) CTS. (

**b**) CTSG-1-S. (

**c**) CTSG-3-S. (

**d**) CTSG-3-D.

Parameter | Cement Mortar | Geogrid |
---|---|---|

Density (kg/m^{3}) | 2660 | 1350 |

Normal stiffness (N/m) | 5 × 10^{8} | 1 × 10^{7}, 5 × 10^{7}, 1.0 × 10^{8} |

Normal-tangential stiffness ratio (N/m) | 1.2 | 1.2 |

Parallel bond normal stiffness (N/m ^{3}) | 2 × 10^{11} | 1.2 × 10^{10}, 6 × 10^{10}, 1.2 × 10^{11} |

Parallel bond tangential stiffness (N/m ^{3}) | 1.67 × 10^{11} | 1 × 10^{10}, 5 × 10^{10}, 1 × 10^{11} |

Tensile strength (N/m^{2}) | 7 × 10^{5} | 1 × 10^{8} |

Cohesion (N/m^{2}) | 7 × 10^{5} | 1 × 10^{8} |

Specimen Code | Geogrid Stiffness (N/m) | Geogrid Layers |
---|---|---|

CTS | —— | —— |

CTSG-1-S | 1 × 10^{7} | One-layer |

CTSG-2-S | 5 × 10^{7} | One-layer |

CTSG-3-S | 1 × 10^{8} | One-layer |

CTSG-1-D | 1 × 10^{7} | Double-layer |

CTSG-2-D | 5 × 10^{7} | Double-layer |

CTSG-3-D | 1 × 10^{8} | Double-layer |

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**MDPI and ACS Style**

Luo, H.; Wang, X.; Zhang, Y.; Zhang, J. Discrete Element Study on Bending Resistance of Geogrid Reinforced Cement-Treated Sand. *Materials* **2023**, *16*, 2636.
https://doi.org/10.3390/ma16072636

**AMA Style**

Luo H, Wang X, Zhang Y, Zhang J. Discrete Element Study on Bending Resistance of Geogrid Reinforced Cement-Treated Sand. *Materials*. 2023; 16(7):2636.
https://doi.org/10.3390/ma16072636

**Chicago/Turabian Style**

Luo, Hao, Xuan Wang, Yu Zhang, and Jiasheng Zhang. 2023. "Discrete Element Study on Bending Resistance of Geogrid Reinforced Cement-Treated Sand" *Materials* 16, no. 7: 2636.
https://doi.org/10.3390/ma16072636