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Rate-dependent drag instability in granular materials

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Abstract

We investigate the conditions leading to large drag force fluctuations in granular materials. The study is based on a set of experimental drag tests, which involve pulling a plate vertically through a cohesionless granular material. In agreement with previous observations, drag force exhibits significant and sudden drops-up to 60%—when the plate is pulled out at low velocities. We further find that this instability vanishes at higher pullout velocities and near the surface. We empirically characterise the frequency and amplitude of these fluctuations and find that these properties are not consistent with a classical stick-slip dynamics. We therefore propose an alternative physical mechanism that can explain these force fluctuations.

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Funding

Funding was provided by Australian Research Council Discovery Project (Grant No. DP200101927).

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  1. School of Civil Engineering, The University of Sydney, Sydney, NSW, 2006, Australia

    T. Hossain & P. Rognon

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  1. T. Hossain
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Correspondence to P. Rognon.

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Appendix: Testing of the experimental setup

Appendix: Testing of the experimental setup

Two tests were conducted to assess the effect of the shaft and to quantify the stiffness of the loading frame and plate.

1.1 Effect of the shaft

An uplift test was performed without any plate attached to the shaft, as a way to isolate its influence on the drag force. The 4 mm diameter shaft was initially embedded at a depth 120 mm and then uplifted at a constant velocity of 5 mm/min. The measured drag force versus displacement response is shown in Fig. 18a. It evidences a shape similar to the one obtained with a plate. However, the maximum drag force is significantly lower. It is about 3.2 N with the shaft only and 18 N with a plate. Also, drag fluctuations did not significantly develop with the shaft only. This confirms that the drag instability is linked to the presence of the plate.

1.2 Stiffness of the loading frame/plate system

A specific test was conducted to quantify the effective stiffness \(k_0\) of the system comprised of the load cell, shaft and plate. This test involves restraining the edges of the plate to a steel frame fixed to the ground, applying an external force on the middle of the plate via the shaft and measuring the displacement P of the loading frame. This displacement includes elastic deformations of the load cell and shaft and the bending deflection of the plate. Results shown in Fig. 18b indicate a linear relationship between force and displacement, which we model as: \(F \approx k_0 P\). This relationship is valid in the range of forces considered in this study, from zero to 20 N. Best fit of the data is obtained for \(k_0 = 2.27 \times 10^5\) N/m.

Fig. 18
figure 18

Testing of the uplift experimental device: a drag force measured with a shaft only and no plate b stiffness test performed by holding the plate’s edges while applying a vertical force in it centre via the shaft

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Hossain, T., Rognon, P. Rate-dependent drag instability in granular materials. Granular Matter 22, 72 (2020). https://doi.org/10.1007/s10035-020-01039-5

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