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FracProp: Stochastic Fracture Propagation Model

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Abstract

This paper presents a geometric, mechanics-based, stochastic model—FracProp—that was developed to predict fracture initiation and propagation in rock. FracProp is capable of quantifying uncertainties associated with the point of fracture initiation and direction of fracture propagation. The current version of FracProp uses compounded probability distributions that are continuously fitted based on mechanical principles (stress distribution and material properties). The model assumes that fracture initiation and propagation depend on the stress profiles around the fracture (flaw) tip in a rock block subjected to vertical, horizontal, and internal loading. To develop the model, we studied the mechanics of a rock block containing one single flaw (pre-existing opening) with the Finite Element (FE) software ABAQUS. Stress profiles obtained in the modeling were used with the model’s probabilistic processes to dynamically simulate (model) crack/fracture propagation. FracProp was validated with the results of experiments under various loading conditions done at the Massachusetts Institute of Technology (MIT) geomechanics laboratory.

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Notes

  1. The center of the tip of the ith propagation step is \({c}_{i}\). Any point on the semicircular path is mathematically described based on the center coordinates (\({c}_{i}\)), radius (\({r}_{i}\)) and angle (\({\widehat{\psi }}_{i}\)) as in Eq. (8). This equation is used extensively in FracProp to transform polar coordinates to Cartesian coordinates (See Fig. 16).

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Authors and Affiliations

  1. Siemens Industries, Abu Dhabi, UAE

    Mohammad Abdulla

  2. Stevens Institute of Technology, Hoboken, NJ, USA

    Rita L. Sousa

  3. Massachusetts Institute of Technology, Cambridge, MA, USA

    Ignazio Arzuaga, Omar AlDajani & Herbert H. Einstein

  4. New Jersey Institute of Technology, Newark, NJ, USA

    Bruno Goncalves da Silva

Authors
  1. Mohammad Abdulla
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  2. Rita L. Sousa
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  3. Ignazio Arzuaga
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  4. Omar AlDajani
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  5. Bruno Goncalves da Silva
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  6. Herbert H. Einstein
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Correspondence to Rita L. Sousa.

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Abdulla, M., Sousa, R.L., Arzuaga, I. et al. FracProp: Stochastic Fracture Propagation Model. Rock Mech Rock Eng 54, 2513–2531 (2021). https://doi.org/10.1007/s00603-021-02377-3

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  • DOI: https://doi.org/10.1007/s00603-021-02377-3

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