Rock mechanics and rock engineering

Research impacts

  • Stochastic representation of fracture networks, flow through such networks and thermal performance
  • Fracture process caused by external and hydraulic pressure (experiments and analysis/theory)
  • Modeling of fracture system performance
  • Fracture aperture geometry and effects on flow

Research areas

Related publications

Einstein, H.H. (2024). Physical Modelling in Rock Mechanics and Rock Engineering. Rock Mechanics and Rock Engineering, 57, 10187–10204. doi:10.1007/s00603-024-04106-y

Einstein, H.H. (2021). Fractures: Tension and Shear. Rock Mechanics and Rock Engineering, 54, 3389–3408 (2021). doi:10.1007/s00603-020-02243-8

Li, B.Q., Gonçalves da Silva, B.M., and Einstein, H.H. (2019). Laboratory hydraulic fracturing of granite: Acoustic emission observations and interpretation. Engineering Fracture Mechanics, 209, 200-220. doi:10.1016/j.engfracmech.2019.01.034

Li, B.Q., and Einstein, H.H. (2019). Normalized radiated seismic energy from laboratory fracture experiments on Opalinus Clayshale and Barre Granite. Submitted to Journal of Geophysical Research: Solid Earth.

Li, B.Q., and Einstein, H.H. (2019). Direct and microseismic observations of hydraulic fracturing in Barre Granite and Opalinus Clayshale. Journal of Geophysical Research: Solid Earth, 124. doi:10.1029/2019JB018376

Li, B.Q., and Einstein, H.H. (2019). Direct and microseismic observations of hydraulic fracturing in Barre Granite and Opalinus Clayshale. In: Geophysical Research Abstracts, Vol. 21, EGU General Assembly 2019. EGU2019-431

Al Dajani, O.A., Germaine, J.T., and Einstein, H.H. (2019). Isotropic versus anisotropic stress field effects on hydraulic fracture mechanisms in Opalinus Shale. In: Proceedings of the 53rd U.S. Rock Mechanics / Geomechanics Symposium, 23-26 June, New York City, NY. ARMA-2019-1552

Gonçalves da Silva, B., and Einstein, H.H. (2018). Physical processes involved in the laboratory hydraulic fracturing of granite: Visual observations and interpretation. Engineering Fracture Mechanics, 191, 125-142. doi:10.1016/j.engfracmech.2018.01.011

Al Dajani, O.A., Germaine, J.T., and Einstein, H.H. (2018). Hydraulic fracture of Opalinus Shale under uniaxial stress: Experiment design and preliminary results. In: Proceedings of the 52nd U.S. Rock Mechanics/Geomechanics Symposium, 17-20 June, Seattle, Washington. ARMA-2018-1221

Morgan, S.P., Li, B.Q., and Einstein, H.H. (2017). Effect of injection rate on hydraulic fracturing of Opalinus Clay Shale. In: Proceedings of the 51st U.S. Rock Mechanics / Geomechanics Symposium, 25-28 June, San Francisco, California. ARMA-2017-0873

Li, B.Q., and Einstein, H.H. (2017). Comparison of visual and acoustic emission observations in a four point bending experiment on Barre Granite. Rock Mechanics and Rock Engineering, 50 (9), 2277–2296. doi:10.1007/s00603-017-1233-z

Gonçalves da Silva, B., and Einstein, H.H. (2017). Comparison between numerical and experimental observations made in hydraulic fracturing tests. In: Proceedings of the 51st U.S. Rock Mechanics/Geomechanics Symposium, 25-28 June, San Francisco, California. ARMA-2017-0655

AlDajani, O.A., Morgan, S.P., Germaine, J.T., and Einstein, H.H. (2017). Vaca Muerta Shale – Basic properties, specimen preparation, and fracture processes. In: Proceedings of the 51st U.S. Rock Mechanics/Geomechanics Symposium, 25-28 June, San Francisco, California. ARMA-2017-0784

Seiphoori, A., Moradian, Z., Einstein, H.H., and Whittle, A.J. (2016). Microstructural characterization of Opalinus shale. In: Proceedings of the 50th U.S. Rock Mechanics/Geomechanics Symposium, 26-29 June, Houston, Texas. ARMA-2016-783

Moradian, Z., Einstein, H.H., and Ballivy, G. (2016). Detection of cracking levels in brittle rocks by parametric analysis of the acoustic emission signals. Rock Mechanics and Rock Engineering, 49 (3), 785–800. doi:10.1007/s00603-015-0775-1

Moradian, Z., Li, Q.B., Morgan, S., Gonçalves da Silva, B., Germaine, G.T., and Einstein, H.H. (2015). Accoustic emission characteristics of shale. In: Proceedings of the 13th ISRM International Congress of Rock Mechanics, 10-13 May, Montreal, Canada. ISRM-13CONGRESS-2015-366

Gonçalves da Silva, B., Li, B.Q., Moradian, Z., Germaine, G.T., and Einstein, H.H. (2015). Development of a test setup capable of hydraulic fracturing tests in the laboratory with image and acoustic emission monitoring. In: Proceedings of the 48th U.S. Rock Mechanics Symposium, San Francisco, CA. ARMA-2015-141

Morgan, S.P., and Einstein, H.H. (2014). The effect of bedding plane orientation on crack propagation and coalescence in shale. In: Proceedings of the 48th U.S. Rock Mechanics/Geomechanics Symposium, 1-4 June, Minneapolis, Minnesota. ARMA-2014-7727

Moradian, Z., and Einstein, H.H. (2014). Monitoring cracking process of gypsum by means of acoustic emission and high speed camera imaging. In: Proceedings of the 48th U.S. Rock Mechanics/Geomechanics Symposium, 1-4 June, Minneapolis, Minnesota. ARMA-2014-7528

Li, W., and Einstein, H.H. (2014). Numerical and Analytical Modeling of Heat Transfer between Fluid and Fractured Rocks. Final report (121 pages), Massachusetts Institute of Technology. Prepared for USDOE Office of Energy Efficiency and Renewable Energy, Geothermal Technologies Office under Contract no. EE0002743, Recovery Act – Decision Aids for Geothermal Systems, May 2014. doi:10.2172/1236455

Gonçalves da Silva, and Einstein, H.H. (2014). Finite Element study of fracture initiation in flaws subject to internal fluid pressure and vertical stress. International Journal of Solids and Structures, 51 (23-24), 4122–4136. doi:10.1016/j.ijsolstr.2014.08.006

Einstein, H.H., and Vecchiarelli, A. (2014). Further Development and Application of GEOFRAC-FLOW to a Geothermal Reservoir. Final report, Massachusetts Institute of Technology (131 pages). Prepared for USDOE Office of Energy Efficiency and Renewable Energy, Geothermal Technologies Office under Contract no. EE0002743, Recovery Act – Decision Aids for Geothermal Systems, May 2014. doi:10.2172/1236455

Morgan, S.P., Johnson, C.A., and Einstein, H.H. (2013). Cracking processes in Barre granite: fracture process zones and crack coalescence. International Journal of Fracture, 180 (2), 177-204. doi:10.1007/s10704-013-9810-y

Gonçalves da Silva, B., and Einstein, H.H. (2013). Modeling of crack initiation, propagation and coalescence in rocks. International Journal of Fracture, 182 (2), 167-186. doi:10.1007/s10704-013-9866-8

Brooks, Z., Ulm, F.-J., and Einstein, H.H. (2013). Environmental scanning electron microscopy (ESEM) and nanoindentation investigation of the crack tip process zone in marble. Acta Geotechnica, 8 (3), 223-245. doi:10.1007/s11440-013-0213-z

Morgan, S.P., and Einstein, H.H. (2011). Complex inclusion geometry pairs in brittle material. In: Proceedings of the 45th U.S. Rock Mechanics / Geomechanics Symposium, 26-29 June, San Francisco, California. ARMA-11-449

Brooks, Z., Ulm, F.-J., Einstein, H.H., and Abousleiman, Y. (2010). A nanomechanical investigation of the crack tip process zone. In: Proceedings of the 44th U.S. Rock Mechanics Symposium and 5th U.S.-Canada Rock Mechanics Symposium, 27-30 June, Salt Lake City, Utah. ARMA-10-309

Wong, L.N.Y., and Einstein, H.H. (2009). Crack coalescence in molded gypsum and Carrara marble: Part 2. Macroscopic observations and interpretation. Rock Mechanics and Rock Engineering, 42 (3), 513-545. doi:10.1007/s00603-008-0003-3

Wong, L.N.Y., and Einstein, H.H. (2009). Crack coalescence in molded gypsum and Carrara marble: Part 1. Macroscopic observations and interpretation. Rock Mechanics and Rock Engineering, 42 (3), 475-511. doi:10.1007/s00603-008-0002-4

Wong, L.N.Y., and Einstein, H.H. (2009). Process zone development associated with cracking processes in Carrara marble. In G. Ma & Y. Zhou (eds): Proceedings of the 9th International Conference on Analysis of Discontinuous Deformation: New Developments and Applications, 25-27 November 2009, Singapore. doi:10.3850/9789810844554-0076

Wong, L.N.Y., and Einstein, H.H. (2009). Using high speed video imaging in the study of cracking processes in rock. Geotechnical Testing Journal, 32 (2), 164-180. doi:10.1520/GTJ101631

Wong, L.N.Y., and Einstein, H.H. (2009). Systematic evaluation of cracking behavior in specimens containing single flaws under uniaxial compression. International Journal of Rock Mechanics and Mining Sciences, 46 (2), 239-249. doi:10.1016/j.ijrmms.2008.03.006

Miller, J.T., and Einstein, H.H. (2008). Crack coalescence tests on granite. In: Proceedings of the 42nd U.S. Rock Mechanics Symposium (USRMS), 29 June-2 July, San Francisco, California. ARMA-08-162

Wong, L.N.Y., and Einstein, H.H. (2007). Crack coalescence in molded gypsum and Carrara marble. Poster-paper presented at the American Geophysical Union Fall Meeting, 10-14 December 2007, San Francisco, California, USA. Abstract only: T11A-0342.

Wong, L.N.Y., and Einstein, H.H. (2007). Coalescence behavior in Carrara marble and molded gypsum containing artificial flaw pairs under uniaxial compression. In: Proceedings of the 1st Canada – U.S. Rock Mechanics Symposium, 27-31 May, Vancouver, Canada. ARMA-07-071

Wong, L.N.Y., and Einstein, H.H. (2006). Fracturing behavior of prismatic specimens containing single flaws. In: Proceedings of Golden Rocks 2006, the 41st U.S. Symposium on Rock Mechanics (USRMS), 17-21 June, Golden, Colorado. ARMA-06-899

Ko, T.Y., Einstein, H.H., and Kemeny, J. (2006). Crack coalescence in brittle material under cyclic loading. In: Proceedings of the 41st U.S. Symposium on Rock Mechanics (USRMS), Golden Rocks, 17-21 June, Golden, Colorado. ARMA-06-930

Bobet, A., and Einstein, H.H. (2004). Crack coalescence in brittle materials – overview of current knowledge. In W. Schubert (ed.): Rock Engineering – Theory and Practice. Proceedings of the ISRM regional symposium EUROCK 2004 and the 53rd Geomechanics Colloquy, Salzburg, Austria, 7-9 October (pp. 475-478). Essen: Verlag Glückauf. ISBN 978-3773959959

Zhang, L., and Einstein, H.H. (2000). Estimating the intensity of rock discontinuities. International Journal of Rock Mechanics and Mining Sciences, 37 (5), 819-837. doi:10.1016/S1365-1609(00)00022-8

Bobet, A., and Einstein, H.H. (1996). Fracture coalescence in rock material under uniaxial and biaxial loading. In: Proceedings of the 2nd North American Rock Mechanics Symposium, 19-21 June, Montreal, Quebec, Canada. ARMA-96-1603

Shen, B., Stephansson, O., Einstein, H.H., and Ghahreman, B. (1995). Coalescence of fractures under shear stresses in experiments. Journal of Geophysical Research, 100 (B4), 5975-5990. doi:10.1029/95JB00040

Reyes, O., and Einstein, H.H. (1991). Failure mechanisms of fractured rock – a fracture coalescence model. In: Proceedings of the 7th ISRM Congress, 16-20 September, Aachen, Germany. ISRM-7CONGRESS-1991-066

Dershowitz, W.S., and Einstein, H.H. (1990). Tensile and shear fracturing in predominantly compressive stress fields—a review. Engineering Geology, 29 (2), 149-172. doi:10.1016/0013-7952(90)90004-K

Chan, H.C.M., Li, V., and Einstein, H.H. (1990). A hybridized displacement discontinuity and indirect boundary element method to model fracture propagation. International Journal of Fracture, 45 (4), 263-282. doi:10.1007/BF00036271

Li, V.C., Chong, K.P., and Einstein, H.H. (1989). Tension softening and size effects on the fracture determination of geomaterials. In S.P. Shah, S.E. Swartz (eds.): Proceedings of the SEM-RILEM International Conference on Fracture in Concrete and Rock, Houston, Texas, 17-19 June 1987, pp. 255-264. Springer New York 1989. ISBN: 978-0387968803 (Print) 978-1461235781 (Online) doi:10.1007/978-1-4612-3578-1_25

Chong, K.P., Li, V.C., and Einstein, H.H. (1989). Size effects, process zone and tension softening behavior in fracture of geomaterials. Engineering Fracture Mechanics, 34 (3), 669-678. doi:10.1016/0013-7944(89)90129-X