# Cushion Layer Effect on the Impact of a Dry Granular Flow Against a Curved Rock Shed

• Yuan-Jun Jiang
• Zheng-Zheng Wang
• Yue Song
• Si-You Xiao
Original Paper

## Abstract

The dry granular flow produced by a landslide or mountain collapse represents an intense threat to road structures, including rock sheds in mountainous areas. In this study, we designed a set of experiments to investigate the impact mechanism of dry granular flow against a rock shed. The experimental rock shed model was characterized by a curved surface and a cushion layer of granular materials. Based on a video recording and the time history of the impact force, we determined the impact force characteristics and found that for cases without a cushion layer, the maximum normal and tangential force components are close to the end of the rock shed directly facing granular flow impact. With the addition of a cushion layer, the maximum impact force decreases and shifts approximately 30°–45° away from the end, which indicates that a cushion layer can not only reduce the magnitude of the impact force, but also change its distribution mode. We also verified the stronger energy dissipation capability of a cushion layer made of finer granular material. Finally, we performed a stiffness analysis, calculated the internal forces, and found that cushion layers can reduce the internal bending moment and internal shear force and increase the internal axial force. From the engineering perspective, all the changes introduced by a cushion layer positively contribute to rock shed safety.

## Keywords

Dry granular flow Curved-surface rock shed Impact Cushion layer

## List of symbols

$$\beta$$

The polar angle from 0°

$$F$$

Total normal force (N)

$$F_{i}$$

Normal sub-forces (N), i = 1–8

$$T$$

Total tangential force (N)

$$T_{i}$$

Tangential sub-forces (N), i = 1–8

$$D_{ 5 0}$$

Mean particle diameter (m)

$$\gamma_{\hbox{max} }$$

Maximum dry unit weight (N/m3)

$$\gamma_{\hbox{min} }$$

Minimum dry unit weight (N/m3)

$$X$$

Vector of primary unknowns for a tunnel

$$X_{i}$$

Component of X, i = 1, 2, 3

$$E$$

Elastic modulus of the rock shed (GPa)

$$E^{{\prime }}$$

Elastic modulus of the load cell (GPa)

$$I$$

Inertia moment of the cross section of the rock shed (m4)

$$I^{{\prime }}$$

Inertia moment of the cross section of the load cell (m4)

$$A$$

Area of the cross section of the rock shed (m2)

$$A^{{\prime }}$$

Area of the cross section of the load cell (m2)

$$\Delta_{i,j}$$

The displacement in X i direction caused by unit force in F j direction (m), i = 1–3, and j = 1–16

$$\delta_{i,j}$$

The displacement in X i direction caused by unit force in X j direction (m), i = 1–3, and j = 1–3

$$M_{i}^{i}$$

Internal bending moment caused by the unit force which is in X i direction (N/m)

$$N_{i}^{i}$$

Internal axial force caused by the unit force which is in X i direction (N)

$$Q_{i}^{i}$$

Internal shear force caused by the unit force which is in X i direction (N)

$$M_{j}^{e}$$

Internal bending moment caused by the unit force which is in F j direction (N/m)

$$N_{j}^{e}$$

Internal axial force caused by the unit force which is in F j direction (N)

$$Q_{j}^{e}$$

Internal shear force caused by the unit force which is in F j direction (N)

$$s$$

The domain along the rock shed periphery (m2)

$$\mu$$

Bending moment stiffness (Pa)

$$\delta$$

Basal friction angle (°)

$$\Delta W$$

The energy increment (J)

$$\Delta D_{i}$$

The corresponding normal displacement increment (m), i = 1–8

$$\Delta T_{i}$$

The tangential force increment in a time interval on segment (m), i = 1–8

$$\Delta \omega_{i}$$

The corresponding deflection increment (m), i = 1–8 (m)

$$H$$

The height of the load cell (m)

## Notes

### Acknowledgements

First, the authors sincerely acknowledge the CAS Pioneer Hundred Talents Program for making possible the completion of this research. The research presented in this paper was also jointly supported by the National Natural Science Foundation of China (Grant No. 41502334) and fund of the Institute of Mountain Hazards and Environment (Grant No. SDS-135-1705 and Grant No. SDS-135-1704). The authors wish to acknowledge these financial contributions and convey our appreciation to these organizations for supporting this basic research.

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© Springer-Verlag GmbH Austria, part of Springer Nature 2018

## Authors and Affiliations

• Yuan-Jun Jiang
• 1
• Zheng-Zheng Wang
• 2
• Yue Song
• 1
• 3
• Si-You Xiao
• 1
• 3
1. 1.Institute of Mountain Hazards and EnvironmentChinese Academy of SciencesChengduChina
2. 2.School of Civil EngineeringDalian University of TechnologyDalianPeople’s Republic of China
3. 3.University of Chinese Academy of SciencesBeijingChina