A pile driving model applied to the hammering insertion of the MUPUS penetrator Preliminary results Norbert Kömle, Günter Kargl Space Research Institute, Austrian Academy of Sciences Graz, Austria MUPUS Progress Meeting Graz 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 impact Lovery et al. (1969): Pile driving analysis – State of the art Salgado 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

PEN Parameters ParameterValue Hammer impact speed on tube0.9 – 4.0 m/s Insertion depth of tube rear end (full insertion)0 cm Hammer mass30 grams PEN tube mass20 grams PEN-tube diameter1 cm PEN tube length30 cm Young‘s modulus of PEN-tube17 GPa Coefficient of restitution between hammer and PEN-tube1.0

Soil Parameters ParameterValue Young‘s modulus of soil50 MPa Poisson‘s ratio of soil0.25 Yield strength of soil at tip600 kPa Shear stress at soil-tube-interface60 ka Soil damping constant at tip0.5 s/m Soil damping constant at soil-tube interface0.15 s/m Ultimate static bearing strength of soil alt PEN tip2 MPa Angle of soil internal friction38° 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.