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Multiscale analysis of rotational penetration in shallow dry sand and implications for self-burrowing robot design

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Abstract

In nature, seeds of some flowering plants such as Erodium and Pelargonium can bury themselves into the ground effectively for germination. Jung et al. (Phys Fluids 29:041702. https://doi.org/10.1063/1.4979998, 2017) hypothesized that rotation induced by the hygroscopic coiling and uncoiling movement of the awn reduces the penetration resistance. Rotational penetration was also studied in geotechnical engineering, as it is relevant to the rotary installation of piles. However, there are limited fundamental explanations of the effect of rotation on the reduction of penetration resistance. In this study, shallow rotational penetration in dry sand is studied using the discrete element method (DEM); the directly available particle-scale data and the derived meso-scale data were analyzed to reveal the underlying mechanism of the rotational effect on penetration. A series of rotational penetration tests with different rotational speeds were conducted. It was confirmed that the penetration resistance at the cone decreases with rotational speed. Analysis of the particle–cone contact data shows that rotation does not only result in the inclination of the contact forces, but also significantly reduces their magnitude and the overall contact number. The force chain network, displacement fields and particle trajectories visualize the rotational effects at the particle-scale; and the evolution of the principal stresses of the soil provides a meso-scale explanation. The new multi-scale data tested the “force chain breakage” hypothesis and challenged the assumptions previously used in developing analytical models. Insights were also provided to power consumption and implications on the design of a self-burrowing robot, which could take advantage of the rotational effect on penetration.

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Abbreviations

\(\alpha\) :

Semi-angle of the cone (°)

\(\alpha_{s}\) :

Shear to normal stiffness ratio

\(\beta\) :

Rolling stiffness coefficient

\(\delta\) :

Angle of soil–penetrator friction (°)

\(\eta\) :

Plastic moment coefficient

\(\theta_{i}\) :

The contact angle between the positive \(z\) axis and the contact force at contact \(i\) (°)

\(\theta_{{\text{r}}}\) :

Rotational angle between two contacting particles (°)

\(\theta\) :

The contact angle between the positive \(z\) axis and the resultant contact force on the cone (°)

\(\vartheta\) :

Rotational angle of the shear stress (°)

\(\omega\) :

Rotational velocity (radian/s)

\(n\) :

Sample initial porosity

\(\sigma\) :

Stress normal to the cone surface (kPa)

\(c_{{\text{a}}}\) :

Soil–penetrator adhesion (kPa)

\({\text{CN}}\) :

Contact number

\(D_{{\text{c}}}\) :

Diameter of the cone (m)

\(D_{{\text{s}}}\) :

Diameter of the shaft (m)

\(F\) :

Total contact force on the penetrator (N)

\(\parallel F_{{\text{n}}} \parallel\) :

Normal value of the normal contact force (N)

\(F_{{\text{z}}}\) :

The vertical component of the total contact force on the penetrator (N)

\(F_{{{\text{zn}}}}\) :

Vertical component of the total contact normal force on the penetrator (N)

\(F_{{{\text{zt}}}}\) :

Vertical component of the total contact shear force on the penetrator (N)

\(F_{{{\text{z}}i}}\) :

Individual contact forces on the penetrator (N)

\(F_{{{\text{zc}}}}\) :

Vertical component of the total contact normal force on the cone (N)

\(F_{{{\text{zs}}}}\) :

Vertical component of the total contact shear force on the shaft (N)

\(F_{{{\text{zn}}i}}\), \(F_{{{\text{zt}}i}}\) :

Vertical components of the individual contact normal forces and that of the contact shear forces (N)

\(F_{{{\text{znc}}}}\), \(F_{{{\text{ztc}}}}\) :

Vertical component of the contact normal force and contact shear force on the cone (N)

\(H_{{\text{s}}}\) :

Height of the shaft (m)

\(k_{{\text{r}}}\) :

Rolling stiffness coefficient

\(k_{{\text{s}}}\) :

Tangential (shear) contact stiffness (kPa)

\(M_{{\text{e}}}\) :

Elastic contact moment (N m)

\(M_{{\text{p}}}\) :

Plastic contact moment (N m)

\(n_{p}\) :

Cone-to-particle diameter ratio

\(P\) :

Power (W)

\(q_{{\text{c}}}\) :

Cone penetration resistance (kPa)

\(q_{{{\text{cmax}}}}\) :

Non-rotational cone penetration resistance at the maximum penetration depth (kPa)

\(q_{{{\text{cRot}}}}\) :

Rotational cone penetration resistance (kPa)

\(Q\) :

Vertical penetration force (N)

\(Q_{{\text{c}}}\), \(Q_{{\text{s}}}\) :

(Vertical components of) the penetration force acting on the cone and shaft (N)

\(r_{{\text{a}}}\), \(r_{{\text{b}}}\) :

Radii for two contacting particles (m)

\(r_{{\text{d}}}\) :

Chamber-to-cone diameter ratio

\(R\) :

Radius of the cone (m)

\(T\) :

Penetration torque or the total contact torque on the penetrator (N m)

\(T_{{\text{p}}}\) :

Rotational period (s)

\(T_{{\text{z}}}\) :

The vertical component of the total contact torque (N m)

\(T_{{{\text{zc}}}}\), \(T_{{{\text{zs}}}}\) :

Vertical components of the torque on the cone and shaft (N m)

\(u\) :

Relative slip velocity

\(v_{{\text{p}}}\) :

Vertical penetration velocity (m/s)

\(v_{{\text{s}}}\) :

Tangential velocity (m/s)

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Acknowledgements

This material is based upon work supported by the National Science Foundation (NSF) under NSF CMMI 1849674 and CMMI 1841574. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect those of the NSF. We also would like to thank the anonymous reviewers whose constructive comments helped us improve the overall quality of the paper.

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Tang, Y., Tao, J. Multiscale analysis of rotational penetration in shallow dry sand and implications for self-burrowing robot design. Acta Geotech. 17, 4233–4252 (2022). https://doi.org/10.1007/s11440-022-01492-x

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