Abstract
Simulation of fracture initiation, propagation, and arrest is a problem of interest for many applications in the scientific community. There are a number of numerical methods used for this purpose, and among the most widely accepted is the combined finite-discrete element method (FDEM). To model fracture with FDEM, material behavior is described by specifying a combination of elastic properties, strengths (in the normal and tangential directions), and energy dissipated in failure modes I and II, which are modeled by incorporating a parameterized softening curve defining a post-peak stress-displacement relationship unique to each material. In this work, we implement a data assimilation method to estimate key model parameter values with the objective of improving the calibration processes for FDEM fracture simulations. Specifically, we implement the ensemble Kalman filter assimilation method to the Hybrid Optimization Software Suite (HOSS), a FDEM-based code which was developed for the simulation of fracture and fragmentation behavior. We present a set of assimilation experiments to match the numerical results obtained for a Split Hopkinson Pressure Bar (SHPB) model with experimental observations for granite. We achieved this by calibrating a subset of model parameters. The results show a steady convergence of the assimilated parameter values towards observed time/stress curves from the SHPB observations. In particular, both tensile and shear strengths seem to be converging faster than the other parameters considered.
Highlights
The accurate simulation of fracture initiation, propagation, and arrest in materials is an important problem for a number of applications, ranging from the study of microscale behavior of materials to the analysis of large-scale fracture initiation and propagation.Many numerical solutions have been proposed to simulate fractures; one of the most widely accepted is the Combined Finite-Discrete Element Method (FDEM) [1,2]
The results show a good convergence for σtmax, where the assimilation provides a parameter value of around 0.15
Given that no strong suggestion of convergence is seen in this parameter value, it is difficult to conclude that the final value provided in the third iteration of the assimilation is the most likely parameter value for this Split Hopkinson Pressure Bar (SHPB) observations
Summary
The accurate simulation of fracture initiation, propagation, and arrest in materials is an important problem for a number of applications, ranging from the study of microscale behavior of materials to the analysis of large-scale fracture initiation and propagation. The problem itself is complex enough, and the uncertainty on the parameter determination can be quite high This is the case for the simulation of underground processes, such as hydraulic fracturing and earthquake ruptures, where knowledge about material properties is limited to areas where core sampling can be extracted and analyzed. This provides a starting point for analysts to populate their models, but in many cases this is not sufficient, and further calibration is needed. This work presents the implementation of the ensemble Kalman filter to estimate key model parameters of a dynamic Combined Finite Discrete Element model, which simulates the evolution of fractures and cracks in different geomaterials. Sci. 2021, 11, 2898 and the results of the assimilation are presented in Section 5; and Section 6 provides the conclusions and discussion of the results
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
