# Comment on Maraveas, C. Concrete Silos: Failures, Design Issues and Repair/Strengthening Methods. Appl. Sci. 2020, 10, 3938

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## Abstract

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## 1. Introduction

- The silo is loaded with the material before discharge. The load due to the material causes the silo to deform elastically—bulging of the container, elongation of the container, and shortening of the columns (Figure 1). Conservation of Energy suggests that the potential energy is stored in the elastic deformations in the silo structure;
- When the gate is opened to discharge the material inside the silo, the forces that cause the initial elastic deformations are lost. The sudden loss of such forces causes the elastic deformations to spring back to their unloaded positions (Hooke’s law); therefore, the potential energy is converted to kinetic energy (Conservation of Energy);
- As suggested by the Conservation of Energy, the potential energy (elastic deformations) is equal to the kinetic energy (motions of the silo structure). As such, the rate of loss of the forces that caused the elastic deformations prior to discharge is compensated by the rate of development of the spring-back forces (Newton’s laws of motion). There are many examples of this phenomenon, for example, a simple spring-mass system. When the rate of loss in mass is insignificant, it can be observed that the spring returns to its original position slowly compared to a much quicker rate of loss of the mass. One can install strain gauges, accelerometers and other instruments on the silo to validate;
- Prior to discharge, the silo is initially stretched longitudinally, radially, and the columns are shortened, causing it to behave like a slingshot (Figure 1). Upon the release of the loads that cause the elastic deformations, the stored material is lifted and dropped.
- The impact forces caused by the stored material being lifted and dropped can cause buckling in the short term and induce accelerations that cause fluctuating pressures as per Newton’s laws of motion for the entire duration of the discharge cycle;
- The amplitudes of the motion are dependent on the dynamic structural properties of the silo and its supporting structure such as mass, damping and stiffness; and
- The fluctuating pressures will cause the entire silo to vibrate. Strong vibrations can result in fatigue failures in the long term.

- Correlation between the pressures developed during discharge with the elastic deformations of the overall silo prior to discharge, the motions of the overall silo, dynamic structural properties of the overall silo, the flow rate and the spring back force due to the overall silo being lighter need to be included in the analysis and design methods; and
- Fatigue design needs to be considered to ensure the silo and its supporting structure are structurally adequate for their intended use.

## 2. Theoretical Background

## 3. Solution Procedure

#### 3.1. Prior to Discharge

#### 3.2. During Discharge

- The support mechanism and resistant forces provided by the gate are lost;
- The material layers spanning across the hopper at the gate level must provide the lost forces supplied by the gate before open to prevent the material from flowing out of the silo;
- Assuming that the hopper is not subjected to any external force or acceleration that induces the material to flow, thus the only force causing the material to flow is gravity;
- Each particle must overcome the resistant forces surrounding it to flow, and if it cannot overcome the resistant forces, it will adhere to another particle beside it, forming a collection of particles or adhere to the boundary;
- The particles will stop flowing if the resistant forces are sufficient to prevent the particles from flowing. This is evident in Figure 5, where the dome formed by the particles having sufficient strength to prevent the other particles from flowing further, causing a blocked condition. Such dome formation is an active area of research, and some recent contributions include Lee, Wu, Chen and Chiang [24] and Khezri, Mohamad, HajiHassani and Fatahi [25]. The hopper shown in Figure 5 was designed in accordance with relevant granular theories to prevent blockage. However, the blockage suggests that such theories need fundamental improvements as well;
- If all of the particles can overcome the resistant forces and move together, then the flow is considered mass flow [26,27]; if some of the particles near the boundary cannot overcome the resistant forces and adhere to the boundary while other particles far away from the boundary flow out of the silo, then the flow is considered funnel flow [28,29]. Intermediate or transition flow happens when the forces causing the material to flow near the boundary fluctuate between being higher and lower than the forces resisting the flow, thus causing intermittent material to build up inside the silo [30,31]. Therefore, whether the flow is mass, funnel or intermediate is dependent on forces inducing flow and the ability of the particles to overcome the resistant forces, such as cohesion, adhesion, friction and interlocking forces, which exist to prevent the particles from flowing whether individually or lumped together; and
- If gravity alone is insufficient to enable flow, then other forces such as external accelerations can be introduced to enable the particles to flow [32,33,34,35,36]. This phenomenon can be readily observed in a saltshaker, where the salt particles do not flow out of the saltshaker readily without the user shaking it because outlets are small; thus, the resistant forces are significantly higher than the gravity force that causes the particles to flow. However, to get more salt particles from the saltshaker, the user needs to shake it. Therefore, the flow rates need to be determined from the overall motions of the structure and the material properties, as suggested by Equation (1)

#### 3.2.1. Granular-Structure Interactions

#### 3.2.2. Flow Properties

#### 3.2.3. Structural Dynamics and Acoustics

## 4. Applications of Equation (1)

## 5. Dynamic Response of the Structure Due to Sudden Mass Loss

## 6. Conclusions

## 7. Patents

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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Column | Length (m) | Stiffness (N/mm) | Mass (kg) | Vertical Load (kN) | Deflection (mm) | Peak Acceleration (m/s^{2}) |
---|---|---|---|---|---|---|

101.6 $\times $ 2.6 CHS | 2 | 80,668 | 12.7 | 10 | 0.124 | 88.525 |

101.6 $\times $ 2.6 CHS | 2 | 80,668 | 12.7 | 20 | 0.248 | 176.501 |

101.6 $\times $ 2.6 CHS | 2 | 80,668 | 12.7 | 30 | 0.372 | 264.477 |

101.6 $\times $ 2.6 CHS | 2 | 80,668 | 12.7 | 40 | 0.495 | 352.454 |

101.6 $\times $ 2.6 CHS | 2 | 80,668 | 12.7 | 50 | 0.619 | 440.430 |

219.1 $\times $ 3.0 CHS | 2 | 202,559 | 32 | 10 | 0.050 | 35.436 |

219.1 $\times $ 3.0 CHS | 2 | 202,559 | 32 | 20 | 0.099 | 70.325 |

219.1 $\times $ 3.0 CHS | 2 | 202,559 | 32 | 30 | 0.148 | 105.214 |

219.1 $\times $ 3.0 CHS | 2 | 202,559 | 32 | 40 | 0.197 | 140.102 |

219.1 $\times $ 3.0 CHS | 2 | 202,559 | 32 | 50 | 0.246 | 174.991 |

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**MDPI and ACS Style**

Tu, P.; Vimonsatit, V. Comment on Maraveas, C. Concrete Silos: Failures, Design Issues and Repair/Strengthening Methods. *Appl. Sci.* 2020, *10*, 3938. *Appl. Sci.* **2021**, *11*, 5675.
https://doi.org/10.3390/app11125675

**AMA Style**

Tu P, Vimonsatit V. Comment on Maraveas, C. Concrete Silos: Failures, Design Issues and Repair/Strengthening Methods. *Appl. Sci.* 2020, *10*, 3938. *Applied Sciences*. 2021; 11(12):5675.
https://doi.org/10.3390/app11125675

**Chicago/Turabian Style**

Tu, Phung, and Vanissorn Vimonsatit. 2021. "Comment on Maraveas, C. Concrete Silos: Failures, Design Issues and Repair/Strengthening Methods. *Appl. Sci.* 2020, *10*, 3938" *Applied Sciences* 11, no. 12: 5675.
https://doi.org/10.3390/app11125675