Research

Fracture Mechanics Discontinuous Media Autoadaptive Systems Analytical and Numerical Models

Soil-Structure Interaction Tunnels Problem Soils Extreme Events Current Projects

Analytical and Numerical Models

In addition to the experimental work on fracture mechanics, the group has worked on the development of the Displacement Discontinuity Method (DDM) FROCK. In the DDM a crack is discretized into a number of Displacement Discontinuity (DD) Elements. The opposing surfaces of each element can move relative to each other, and thus the displacement field is discontinuous across the element. Displacement Discontinuity elements are well suited to model cracks inside a body but cannot represent very well the boundaries where exterior stresses are applied. This is because of the displacement jump across an element. An alternative approach is to combine the DDM with the Stress Discontinuity Method (SDM) where the stresses are now discontinuous across the element. FROCK follows this hybridized approach which combines both the DD and the SD methods.

The code FROCK has an extensive library of elements which can be used for: tip of a crack, body of a crack, exterior boundary, crack to crack intersection, and crack to boundary intersection. FROCK can model open or closed (frictional) cracks and dynamically adapt the type of element and the state of the element (open or closed) as needed during simulations. It also automatically creates new elements to model fracture propagation. The code is periodically updated and it can now handle mixed mode loading I-II-III, and coupled mechanical and pore fluid flow for short term analysis. In addition to DDM, extensive modeling in geoengineering, soil-structure interaction, and tunneling is conducted with the Finite Element Method (FEM) ABAQUS.

Fracture coalescence modeled with FROCK

• Bobet, A. and Einstein, H.H. (1998). Numerical Modeling of Fracture Coalescence in Rock Materials. International Journal of Fracture, Vol. 92, No. 3, pp. 221-252.


• Vásárhelyi B. and Bobet, A. (2000). Modeling of Crack Coalescence in Uniaxial Compression. Rock Mechanics and Rock Engineering, Vol. 33, No. 2, pp. 119-139.


• Bobet, A. (2000). The Initiation of Secondary Cracks in Compression. Engineering Fracture Mechanics, Vol. 66, No. 2, pp. 187-219.


• Bobet, A. (2001). A Hybridized Displacement Discontinuity Method for Mixed Mode I-II-III Loading. International Journal of Rock Mechanics and Mining Sciences. Vol. 38, pp. 1121-1134.


• Bobet, A. (2001). Numerical solution of initiation of tensile and shear cracks. Proceedings of the 38th U.S. Rock Mechanics Symposium, pp.731-738.


• Fang, C., Haddock, J. and Bobet, A. (2004). 3D Finite Element Study on Contributions of Load Transfer at Concrete Pavement Joint. Computational Mechanics Conference, Tsinghua University Press; Springer-Verlag, 10 pp.


• Bobet, A. and Mutlu, O. (2005). Stress and Displacement Discontinuity Element Method for Undrained Analysis. Engineering Fracture Mechanics Journal, Vol. 72, pp. 1411-1437.


• Bobet, A., Lee, H.S., and Santagata, M.C. (2007). Drained and Undrained Pullout Capacity of a Stiff Inclusion in a Saturated Poroelastic Matrix. International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 31, No. 5, pp. 715-734.


• Park, C.H. and Bobet, A. (2008). Numerical modeling of fracturing in a rock model material with pre-existing flaws. Proceedings of the 42nd US Rock Mechanics Symposium and 2nd U.S.-Canada Rock Mechanics Sympsoium. Paper No. ARMA 08-134, 9 pp.


• Bayoumi, A.M., Bobet, A. and Lee, J. (2008). Pullout capacity of a reinforced soil in drained and undrained conditions. Finite Elements in Analysis and Design, Vol. 44, No. 9-10, pp. 525-536.


• Jung, Ch., Bobet, A. and Fernandez, G. (2010). Analytical Solution for the Response of a Flexible Retaining Structure with an Elastic Backfill. International Journal for Analytical and Numerical Methods in Geomechanics, Vol. 34, pp. 1387-1408.


• Yu, H.-T., Yuan, Y., and Bobet, A. (2013). Multi-scale method for long tunnels subjected to seismic loading. International Journal for Analytical and Numerical Methods in Geomechanics, Vol. 37, No. 4, pp. 374-398.


• Bobet, A., Garcia Marin, V. (2014). A Stress and Displacement Discontinuity Element Method for Elastic Transversely Anisotropic Rock. International Journal of Numerical and Analytical Methods in Geomechanics, Vol. 38, pp. 1898-1922.


• Borela, R., Bobet, A. and Ellett, K. (2016). Numerical Modeling of Desiccation and Tectonic Processes as Driving Mechanisms for Macro-Polygon Formation. The Geological Society of America, North-Central Section - 50th Annual Meeting (18 and 19 April 2016).


• Khasawneh, Y., Bobet, A., and Frosch, R. (2017). A Simple Soil Model for Low Frequency Cyclic Loading. Computers and Geotechnics, Vol. 84, pp. 225-237.


• Wang, Ch., Jiang, K., Bobet, A. and Pyrak-Nolte, L.J. (2020). Numerical Simulation of Rock Fracture Roughness due to Mineral Layering and Texture. American Geophysical Union, 1-17 December, 2020.


• Wang, X., Wu, W., Zhu, H., Zhang, H., Lin, J., Bobet, A. (2020). Improved friction force calculation with an augmented open-close iteration formulation in discontinuous deformation analysis. Computers and Geotechnics, Vol. 130, doi: https://doi.org/10.1016/j.compgeo.2020.103932.


• Wang, X., Wu, W., Zhu, H., Zhang, H., Lin, J.-S. and Bobet, A. (2021). A global direct search method for contact detection between arbitrarily shaped three-dimensional convex polyhedral blocks. Computers and Geotechnics, Vol. 150, https://doi.org/10.1016/j.compgeo.2022.104891.


• Yu, H., Hu, X. and Bobet, A. (2024). A nonlocal hybrid model for elasto-plastic fracture of rock-like materials. Computer Methods in Applied Mechanics and Engineering, Vol. 424, https://doi.org/10.1016/j.cma.2024.116884.


• Yu, H., Xu, H., Bobet, A. and Yang, Q. (2025). A Novel Seismic Input Method for Near-fault Structures with Coupling Effect of Ground Motion and Fault Dislocation. Bulletin of Earthquake Engineering, submitted.