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Numerical modeling of free-falling spherical penetrometer–clay–water interactions

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Abstract

Large deformation finite element simulations of the dynamic penetration of underwater free-fall spherical penetrometers into clay are carried out using the coupled Eulerian–Lagrangian approach. Two undrained total stress analysis models are constructed and applied to simulate four well-documented centrifuge tests of sphere penetration. Model A is a new model that simulates both the free-fall process in water and the penetration process in clay. Model B, as usual, simulates only the penetration process in clay in the absence of overlying water. The simulation of the free-fall process in water is validated against an analytical solution and calibrated against the measured impact velocities of the tested spheres upon hitting the clay surface. The ability of the two models to predict the dynamic penetration behavior in clay is evaluated by comparing their results with the centrifuge test results. Model A provides a better prediction of the penetration behavior than Model B. Fully open, partially closed, and fully closed cavities formed by the passages of the sphere and water were reproduced by Model A. The water flow in the wake of the penetrating sphere is shown to have an important influence on the deformations of the clay surface and cavity wall.

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Data availability

All data generated or analyzed during the study are available from the leading author by request.

Abbreviations

a g :

Acceleration due to Earth’s gravity or artificial gravity

a z :

Linear acceleration of sphere

α w, β w :

Constants in the CD–Re relation of sphere in water

β :

Shear strain rate parameter for su-op

c 0 :

Speed of sound in water

C D, Re:

Drag coefficient and Reynolds number

d e :

Embedment depth measured from the clay surface to the sphere invert

d w, v z w :

Fall distance and velocity of sphere under water

D, m :

Diameter and mass of sphere

E, ν :

Young’s modulus and Poisson’s ratio of clay

g :

Earth’s gravitational acceleration

γ′ :

Submerged unit weight of clay

\(\dot{\gamma }\), \(\dot{\gamma }_{{{\text{ref}}}}\) :

Operative and reference shear strain rates

Γ0 :

Grüneisen parameter for water under the reference state

h d :

Drop height of sphere relative to the clay surface

h dc :

Precalibrated drop height used in the simulation

k :

Rate of increase in undrained shear strength with depth

K 0 :

Coefficient of at-rest lateral earth pressure of clay

μ w :

Dynamic viscosity of water

ρ 0 :

Mass density of water under the reference state

ρ s, \(\rho^{\prime}_{{\text{s}}}\) :

Total and submerged mass densities of sphere

ρ sat, ρ′ :

Saturated and submerged densities of clay

s :

Slope of the linear shock velocity versus particle velocity relation for water

s u :

Undrained shear strength profile of clay

s u0 :

Undrained shear strength at the clay surface

s u-op, s u-ref :

Undrained shear strengths of clay at operative and reference strain rates

σ z, \(\sigma^{\prime}_{z}\) :

Total and effective vertical stresses

t w, t s :

Elapsed times since the commencements of fall in water and penetration in clay

v i :

Impact velocity of sphere upon hitting the clay surface

v z :

Penetration velocity of sphere

z :

Downward positive vertical coordinate with the origin at the clay surface

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Acknowledgements

The authors gratefully appreciate the financial support of the National Natural Science Foundation of China (grant numbers 52178326 and 51578213), the Fundamental Research Funds for the Central Universities of China (grant number B200203091), the Innovation Group Project of Southern Marine Science and Engineering Guangdong Laboratory (Zhuhai) (grant number SML2022014), and the Postgraduate Research & Practice Innovation Program of Jiangsu Province (grant number KYCX20_0446).

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  1. Key Laboratory of Geomechanics and Embankment Engineering of the Ministry of Education, Geotechnical Research Institute, Hohai University, 1 Xikang Road, Nanjing, 210024, Jiangsu, China

    Yaotian Gu & Guo Hui Lei

  2. College of Architectural Engineering, Yangzhou Polytechnic Institute, Yangzhou, 225100, China

    Yaotian Gu

  3. School of Civil Engineering, Sun Yat-Sen University, Guangzhou, 510275, China

    Xiaogang Qin

  4. Southern Marine Science and Engineering Guangdong Laboratory (Zhuhai), Zhuhai, 519082, China

    Xiaogang Qin

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Gu, Y., Lei, G.H. & Qin, X. Numerical modeling of free-falling spherical penetrometer–clay–water interactions. Acta Geotech. 19, 2395–2418 (2024). https://doi.org/10.1007/s11440-024-02290-3

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