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An integrated EOS, pore-crush, strength and damage model framework for near-field ground-shock

Kane C. Bennett, Alyson M. Stahl, Thomas R. Canfield, Garrett G. Euler

Abstract

An integrated Equation of State (EOS) and strength/pore-crush/damage model framework is provided for modeling near to source (near-field) ground-shock response, where large deformations and pressures necessitate coupling EOS with pressure-dependent plastic yield and damage. Nonlinear pressure-dependence of strength up to high-pressures is combined with a Modified Cam-Clay-like cap-plasticity model in a way to allow degradation of strength from pore-crush damage, what we call the "Yp-Cap" model. Nonlinear hardening under compaction allows modeling the crush-out of pores in combination with a fully saturated EOS, i.e., for modeling partially saturated ground-shock response, where air-filled voids crush. Attention is given to algorithmic clarity and efficiency of the provided model, and the model is employed in example numerical simulations, including finite element simulations of underground explosions to exemplify its robustness and utility.

An integrated EOS, pore-crush, strength and damage model framework for near-field ground-shock

Abstract

An integrated Equation of State (EOS) and strength/pore-crush/damage model framework is provided for modeling near to source (near-field) ground-shock response, where large deformations and pressures necessitate coupling EOS with pressure-dependent plastic yield and damage. Nonlinear pressure-dependence of strength up to high-pressures is combined with a Modified Cam-Clay-like cap-plasticity model in a way to allow degradation of strength from pore-crush damage, what we call the "Yp-Cap" model. Nonlinear hardening under compaction allows modeling the crush-out of pores in combination with a fully saturated EOS, i.e., for modeling partially saturated ground-shock response, where air-filled voids crush. Attention is given to algorithmic clarity and efficiency of the provided model, and the model is employed in example numerical simulations, including finite element simulations of underground explosions to exemplify its robustness and utility.
Paper Structure (15 sections, 45 equations, 18 figures, 1 table)

This paper contains 15 sections, 45 equations, 18 figures, 1 table.

Table of Contents

  1. Introduction
  2. Assumptions and constitutive setting
  3. Theory
  4. Yield surface
  5. Elastic strain energy and EOS
  6. Saturated EOS with pore-crush
  7. Numerical implementation and algorithms
  8. Algorithm
  9. Considerations for large strain
  10. Example results and discussion
  11. Material point simulations
  12. Finite Element simulation of the NPE
  13. Conclusion
  14. Acknowledgements
  15. Newton Raphson iteration for crush

Figures (18)

  • Figure 1: The two yield surfaces that combine into the Yp-Cap model: (a) The Yp yield surface, showing nonlinear dependence on pressure approaching maximum strength, $\alpha$, at high pressure (strength "cut-off") and tensile apex, $a$; and (b) the classical MCC yield surface and surface-evolution, showing the CSL with slope $M$, preconsolidation stress $p_{c}$ and critical state points $\{p_{cs},q_{cs}$}.
  • Figure 2: Composite Yp-Cap yield surface that is made up of the Yp and MCC surfaces: (a) The intersection of the surfaces at the critical state, and (b) the complete Yp-Cap yield surface.
  • Figure 3: Evolution of Yp-Cap yield surface for different values of the propensity for damage parameter, $X$: (a) $X=0$ and (b) $X=1$.
  • Figure 4: Crush out of ISV $z$ through exponential hardening. Crush is cut-off at $z_{max}$ (a), which corresponds to relatively very-small increments of plastic multiplier (b).
  • Figure 5: Hydrostatic compression using tuff Sesame Table 7221. Loading curves show combined pore-crush and EOS response, and unload curve is EOS response without crush. (a) 20% air-filled porosity crushed out at high pressure vs. specific volume ($=1/\rho$). (b) calibration to crush ($\rho/\rho_0 -1$) curve reported for NPE working point by kamm1995comparison.
  • ...and 13 more figures