Probing the Effect of Material Model and Geometry Assumptions on Ground Response in the Simulation of Underground Explosions
Authors: Stahl A. , Bennett K. C. , Rougier E. 
Published: September 2022

ABSTRACT:
Numerical modeling of the Earth’s response to underground explosions poses longstanding challenges in relating seismic signal measurements to source yield and emplacement conditions, where complex responses of the earth near to the source affect the propagation of seismic signals. In simulations, assumptions and approximations are necessarily made, e.g., there is often need to make decisions regarding an inherent trade-off between model fidelity and computational expense. It is thus important to be able to justify approximations and understand their limitations. In this work, sequentially more complex constitutive models are introduced into the finite element analysis of underground explosions, starting from simple small-strain elastic models and progressing to elastoplastic models, including large-strain hyper-elastoplasticity. Various model geometry assumptions, such as choices of approximate boundary conditions are also compared. The results show how different modeling assumptions affect the predicted seismic signals and are compared to gauge measurements for a large chemical explosion underground test. Boundary value problems are set up in a variety of configurations in order to assess their effects on model predictions. The outcomes of this work provide insight into the effect of modeling approximations in simulation of underground explosions where decisions pertaining to trade-offs between fidelity and computation speed may be necessary.

1 INTRODUCTION
Numerical modeling of the Earth’s response to Under-Ground explosions (UGX) can be used to estimate the source yield (Bache, 1982) and potentially discriminate whether the source is nuclear or chemical (Kamm and Bos, 1995). However, the Earth exhibits a complex response to the shock in the region immediately surrounding the explosion which affects the propagation of seismic signals through the ground (Johnson and Sammis, 2001a). These complex responses involve a number of processes that occur as the energy density of the shock wave decreases with distance from the explosion. In the immediate vicinity of the explosion, described sometimes as the "hydrodynamic region," the rock behaves as a fluid as it is vaporized and melts (Ford, 2020). Within the hydrodynamic region, the shock front precedes the "temperature front" (cf. Stroujkova and Richards), so inelastic deformation such as dislocation based plasticity and extensive fracture likely occur; however, measurements in this region are sparse because the high stresses and temperatures result in very brief survival of instruments. Outside the hydrodynamic region but still within the so-called "elastic-radius" (where the rock response transitions to purely elastic), inelastic deformation mechanisms are well documented (e.g., Johnson and Sammis, 2001b; Zhang and Zhao, 2014), notably with damage and fracture occurring on a wide range of scales (with cracks ranging from micrometers to many meters in length) (Swanson et al., 2018; Bennett, 2020). The shock wave decays with distance; eventually, the motions are small enough to be described by linear elastic waves (e.g., Harris, 2001).