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Experimental investigation on the impact force of the dry granular flow against a flexible barrier

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Abstract

To reveal the composition and distribution of the impact force of the dry granular flow against a flexible barrier, five groups of physical experiments in different slope angles have been carried out. The flow velocities, flow heights and tensile forces of the cables were measured using the high camera and the load cells. Then we developed a model to calculate the total impact force of the dry granular flow against the barrier based on the tensile force of each cable. The results show that the main components the distribution of the maximum impact force vary with the pileup characteristics of the dead zone. The distributions of the maximum impact force change from linearity to nonlinear with the increase in the proportion of the impact force of flowing layer in the maximum impact force. The hydro-static model, the hydro-dynamic model and the limit equilibrium method were using for the estimation of the maximum impact force, respectively. Compared with the estimated results, the hydro-static model is more suitable for estimating the maximum impact force of the dry granular flow when the pileup height is five times greater than the flow height. The empirical static coefficients have close relationship with the ratio of the pileup length to the pileup height.

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Acknowledgements

First of all, the authors give sincere acknowledgement to the Strategic Priority Research Program of Chinese Academy of Sciences (XDA 20030301) and the “Belt & Road” International Collaboration Team of the CAS “Light of West China” Program (Su Lijun) for the completion of this research. The research presented in this paper was also supported by the CAS Pioneer Hundred Talents Program (Jiang Yuanjun). The authors wish to acknowledge these financial contributions and convey their appreciation of these organizations for supporting this basic research.

Author information

Author notes

  1. Xiao Siyou and Su Lijun contributed equally to this work.

Authors and Affiliations

  1. Key Laboratory of Mountain Hazards and Earth Surface Processes, Institute of Mountain Hazards and Environment, CAS, Chengdu, 610041, China

    Xiao Siyou, Su Lijun, Jiang Yuanjun, Hu Xiaobo & Liu Zhenyu

  2. University of Chinese Academy of Sciences, Beijing, 100049, China

    Xiao Siyou, Su Lijun, Jiang Yuanjun, Hu Xiaobo & Liu Zhenyu

  3. CAS Center for Excellence in Tibetan Plateau Earth Sciences, Beijing, 100101, China

    Su Lijun

  4. School of Civil and Architecture Engineering, Anyang Institute of Technology, Anyang, 455000, China

    Qu Xin

  5. Geobrugg AG Protection Systems China, Chengdu, 611731, China

    Xu Min

Authors
  1. Xiao Siyou
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  2. Su Lijun
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  3. Jiang Yuanjun
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  4. Qu Xin
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Corresponding author

Correspondence to Jiang Yuanjun.

Appendices

The steps to control the slope angle of the flume

The steps are as follows: Firstly, the pointer of the protractor is pointing to 0 when the slope angle of the flume is 0. Secondly, the level device launches a horizontal green light which is in line with the pointer of the protractor. Thirdly, the pointer of the protractor is set to the required angle. At last, the flume is hoisted to make the pointer and the green line coincide.

The tests of the repose angle of the granular flow and the basal friction angle

The experimental steps to measure the basal friction angle are as follows (Al-Hashemi and Al-Amoudi 2018): (1) Set the slope angle of the flume to 0. Put a cylindrical barrel, with the radius of 7.5 cm, the height of 25 cm filled materials fully into the flume. (2) Hoist the flume to make the barrel instability. (3) Measure the slope angle when the barrel begins to slide, as shown in Fig. 34. According to the above experiment, the friction angle between the test material and the basal of the flume ϕs is 21°. The angle of repose of the test materials was measured using the accumulation experiment, as shown in Fig. 35. The radius and the height of the cylindrical barrel using for this experiment are 20 cm and 60 cm, respectively. The pileup height is measured by the projection length of vertical green light on the ruler. The angle of repose φ is 40.5° according to this experiment.

Fig. 34
figure 34

Inclined slope experiment

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Fig. 35
figure 35

Accumulation experiment

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The test of the elastic modulus and the strength of the cable

We measured the tensile strength of the cable using MTS tensile machine, as shown in Fig. 36a. The length and radius of the testing sample Ls are 14.4 cm and 0.1 cm, respectively. To measure the static elastic modulus Estatic, the cable was stretched at the tensile rate of 1/1000. This test was numbered as group 1. The tensile rate of the cable impact by the granular flow can be estimated as follows:

$$ {v}_{\varepsilon }=\frac{T_{\mathrm{max}}}{E_{\mathrm{static}}A{t}_{\mathrm{max}}} $$
(37)

where A is the cross-sectional area of cable, Tmax is the maximum tensile force of the cable impacted by the granular flow and tmax is the duration from the beginning of the interaction between the flexible barrier and the granular flow to the moment of the maximum impact force. The ranges of Tmax/EA and tpeak are about 0.0024 to 0.01 and 0.2 to 0.6 as the slope angles increase in 5° increments from 30° to 50°, respectively. Based on Eq. 37, the range of vε is 1/400 and 1/50. Therefore, the tensile ratio of the group 2 is determined to 1/100. The failure of the cable corresponding to the group 1 is plotted in Fig. 36b. Figure 16 shows that the relationship between the tensile force and the tensile displacement. The peak tensile force of Tpeak cables are 2.71 kN and 2.66 kN corresponding to the tensile rate of 1/100 and 1/1000. The tensile strength Ts of the cable can be calculated as:

$$ {T}_{\mathrm{s}}=\frac{T_{\mathrm{peak}}}{A}=\frac{T_{\mathrm{peak}}}{\pi {r}^2} $$
(38)
Fig. 36
figure 36

The tensile experiments of cables. a The tensile experiment. b The failure of the cable

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The tensile strength of the cable is determined to the average value of these two group tests. Based on Eq. 14, the tensile strength of the cable is 855.1 N/mm2.

The elastic modulus E can be written as:

$$ E=\frac{\varDelta T{L}_{\mathrm{s}}}{\varDelta LA} $$
(39)

where ΔT/ΔL is the tangent slope of the curve in Fig. 37. In this study, ΔT/ΔL is the secant slope between the points corresponding to the tensile displacements of 1 cm and 2 cm. According to Eq. 38, the elastic moduli are 4.53 GPa and 4.84 GPa when the tensile rates are 1/100 and 1/1000, respectively. We determined the average value 4.67 GPa as the elastic modulus of the cable.

Fig. 37
figure 37

The curve of displacement of cable to tensile force

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Siyou, X., Lijun, S., Yuanjun, J. et al. Experimental investigation on the impact force of the dry granular flow against a flexible barrier. Landslides 17, 1465–1483 (2020). https://doi.org/10.1007/s10346-020-01368-9

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