A pile driving model applied to the hammering insertion of the MUPUS penetrator

Preliminary results

Norbert Kömle, Günter KarglSpace Research Institute, Austrian Academy of Sciences

Graz, Austria

MUPUS Progress Meeting Graz 24-25 October 2013

Items to be considered

1. Piledriving in geotechnical engineering

2. Scaling to MUPUS-PEN dimensions and mass

3. Modelling method:- Represent pile and hammer by springs and weights- Numerical solution of the 1D wave equation- Compute solutions for various configurations (MUPUS-

PEN, mole, etc.) for 1 stroke!- Make parameter studies by computing solutions for

different values of hammer impact velocity, gravity, and probe and soil material-parameters

Pile driving models (dynamic)Key references:Smith (1951): Pile driving impactLovery et al. (1969): Pile driving analysis – State of the artSalgado and Zhang (2012): Use of pile driving analysis for assessment of axial load capacity profiles

A pile driven into soil by subsequent impacts by a ram from the topside can be described by a sequence of masses connected by springs.

The basic equation to be solved is the one-dimensional wave equation.

Pile driving models

Standard model used for driving a pile from top side

Model adapted to the „mole“ configuration:Hollow tube driven by the impact of an interior ram weight

Ref.:Smith E.A.L. (1962): Pile-driving aanalysis by the wave equation. Transactions ASCE 127, Part I, pp- 1145-1183.

PEN ParametersParameter Value

Hammer impact speed on tube 0.9 – 4.0 m/s

Insertion depth of tube rear end (full insertion) 0 cm

Hammer mass 30 grams

PEN tube mass 20 grams

PEN-tube diameter 1 cm

PEN tube length 30 cm

Young‘s modulus of PEN-tube 17 GPa

Coefficient of restitution between hammer and PEN-tube 1.0

Soil ParametersParameter Value

Young‘s modulus of soil 50 MPa

Poisson‘s ratio of soil 0.25

Yield strength of soil at tip 600 kPa

Shear stress at soil-tube-interface 60 ka

Soil damping constant at tip 0.5 s/m

Soil damping constant at soil-tube interface 0.15 s/m

Ultimate static bearing strength of soil alt PEN tip 2 MPa

Angle of soil internal friction 38°

Soil cohesion (cohesoinless soil) 0 Pa

Soil shear module: G_soil=E_soil/(2*(1+nu_soil))

Soil quake at tip: Q_soil=(1+nu_soil)/(2*E_soil)*yield_soil*rad_tube Soil quake for side friction: Q_tube=shear_soiltube/G_soil*rad_tube*log(rad_disturbed/rad_tube)

Results (1): time evolution of different model variables durng one MUPUS hammer stroke

Results (2): time evolution of different model variables during one MUPUS hammer stroke for small gravity

Results (3): Soil displacement for different power settings of the MUPUS hammer

Further Studies

Influence of coefficient of restitution < 1 (Titan on Titan ?) on the solutions

Effect of different hammer modes (impact velocities) on penetration per stroke

Influence of soil parameters (cohesion, angle of internal friction, shear strength) on penetration per stroke

Include the casing of the hammer and its mass into the model

A model of this type also allows to analyse the tensional an compressional stress along the PEN-tube during a stroke.