Jointed rock masses – Herbert H. Einstein Research Group

Research scope

Jointed (fractured) rock masses have been studied in the context of rock slope stability, tunnel deformability and stability, and energy related problems such as Engineered Geothermal Systems (EGS) and the extraction of hydrocarbons (both oil and gas). The performance of rock masses in all of the above applications is related to the geometry of fracture networks in the rock mass and to the mechanical and hydraulic interaction among fractures; consequently, all these aspects have been studied. Research topics on jointed rock masses range from geometric, stochastic, fracture network models, an important part of which has been the development of sampling procedures for relating observations on outcrops and in boreholes to three-dimensional fracture network geometry; to experimental and analytical studies of fracture initiation, propagation, and coalescence, including that in relation to hydraulic fracturing; to models of flow and thermal transfer through rock fracture networks.

Related publications:

Fracture mechanics of jointed rock masses

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 53^rd 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 52^nd 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 51^st 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 51^st 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 51^st 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 50^th 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 13^th 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 48^th 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 48^th 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 48^th 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 45^th 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 44^th U.S. Rock Mechanics Symposium and 5^th 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 9^th 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 42^nd 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 1^st 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 41^st 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 41^st 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 53^rd 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 2^nd 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 7^th 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

Fracture geometry of jointed rock masses

Li, W., Ivanova, V.M., Einstein, H.H., Sousa, R.L., and Vecchiarelli, A. (2017). GEOFRAC and its applications. ARMA e-Newsletters, Spring 2017 issue, 2-11. ARMA Letters

Ivanova, V.M., Sousa, R., Murrihy, B., and Einstein, H.H. (2014). Mathematical algorithm development and parametric studies with the GEOFRAC three-dimensional stochastic model of natural rock fracture systems. Computers & Geosciences, 67, 100-109. doi:10.1016/j.cageo.2013.12.004

Vecchiarelli, A., Sousa, R., and Einstein, H.H. (2013). Parametric study with GEOFRAC: A three-dimensional stochastic fracture flow model. In: Proceedings of the 38^th Workshop on Geothermal Reservoir Engineering, 11-13 February 2013, Stanford University, Stanford, California, pp. 637-645.

Umilli, G., Ferrero, A., and Einstein, H.H. (2013). A new method for automatic discontinuity traces sampling on rock mass 3D model. Computers & Geosciences, 51, 182-192. doi:10.1016/j.cageo.2012.07.026

Sousa, R., Ivanova, V.M., Murrihy, B., and Einstein, H.H. (2012). Decision Aids for Engineered Geothermal Systems: Fracture Pattern Modeling. Research Report, Massachusetts Institute of Technology, Cambridge, MA. Prepared for USDOE Office of Energy Efficiency and Renewable Energy, Geothermal Technologies Office under Contract no. EE0002743, Recovery Act – Decision Aids for Geothermal Systems, 2012.

Einstein, H.H., and Locsin, J.-L. Z. (2012). Modeling rock fracture intersections and application to the Boston area. Geotechnical and Geoenvironmental Engineering, 138 (11), 1415-1421. doi:10.1061/(ASCE)GT.1943-5606.0000699

Zhang, L., and Einstein, H.H. (2009). The planar shape of rock joints. Rock Mechanics and Rock Engineering, 43 (1), 55-68. doi:10.1007/s00603-009-0054-0

Ivanova, V.M., and Einstein, H.H. (2004). Three dimensional hierarchical stochastic modeling of rock fracture systems: an example from the Yates field. In: Proceedings of the Gulf Rocks 2004, the 6^th North America Rock Mechanics Symposium (NARMS), 5-9 June, Houston, Texas. ARMA-04-479

Zhang, L., Einstein, H.H., and Dershowitz, W.S. (2002). Stereological relationships between trace length distribution and size distribution of elliptical discontinuities. Geotechnique, 52 (6), 419-433. doi:10.1680/geot.2002.52.6.419

Meyer, T., and Einstein, H.H. (2002). Geologic stochastic modeling and connectivity assessment of fracture systems in the Boston area. Rock Mechanics and Rock Engineering, 35 (1), 23-44. doi:10.1007/s006030200007

Dershowitz, W.S., Curran, B., Einstein, H.H., LaPointe, P.R., Shuttle, D., and Klise, K. (2002). Discrete Feature Approach for Heterogeneous Reservoir Production Enhancement. Technical report, 1 October 1998 – 30 September 2001, National Petroleum Technology Office. Prepared for US Department of Energy, Assistant Secretary for Fossil Energy, Washington, D.C., under Contract no. AC26-98BC15101, July 2002. doi:10.2172/797644

Meyer, T., Einstein, H.H., and Ivanova, V.M. (1999). Geologic stochastic modeling of fracture systems related to crustal faults. In: Proceedings of the 9^th Congress of the International Society for Rock Mechanics, 25-28 August, Paris, France. ISRM-9CONGRESS-1999-101

Zhang, L., and Einstein, H.H. (1998). Estimating the Mean Trace Length of Rock Discontinuities. Rock Mechanics and Rock Engineering, 31 (4), 217-235. doi:10.1007/s006030050022

Dershowitz, W.S., LaPointe, P.R., Einstein, H.H., and Ivanova, V. (1998). Fractured Reservoir Discrete Feature Network Technologies. Annual report, 7 March 1996 – 28 February 1997, BDM Oklahoma, Inc. Prepared for US Department of Energy, Assistant Secretary for Fossil Energy, Washington, D.C., under Contract no. AC22-94PC91008, January 1998. doi:10.2172/570115

Dershowitz, W.S., Einstein, H.H., LaPointe, P.R., Eiben, T., Wadleigh, E., and Ivanova, V. (1998). Fractured Reservoir Discrete Feature Network Technologies. Final technical research report, 7 March 1996 – 30 September 1998, Golder Associates, Inc. Prepared for US Department of Energy, Assistant Secretary for Fossil Energy under Contract no. AC22-94PC91008, December 1998. doi:10.2172/757228

Ivanova, V.M., Veneziano, D., Yu, X., and Einstein, H.H. (1995). Development of stochastic models for fracture systems. In: Proceedings of the 35^th U.S. Symposium on Rock Mechanics (USRMS), 5-7 June, Reno, Nevada. ARMA-95-0725

Herda, H.H.W., Einstein, H.H., and Dershowitz, W.S. (1991). Problems with representation of rock‐fracture clusters. Geotechnical Engineering, 117 (11), 1754-1771. doi:10.1061/0733-9410(1991)117:11(1754)

Lee, J.-S., Veneziano, D., and Einstein, H.H. (1990). Hierarchical fracture trace model. In: Proceedings of the 31^st U.S. Symposium on Rock Mechanics (USRMS), 18-20 June, Golden, Colorado. ARMA-90-0261

Dershowitz, W.S., and Einstein, H.H. (1988). Characterizing rock joint geometry with joint system models. Rock Mechanics and Rock Engineering, 21(1), 21-51. doi:10.1007/BF01019674

Combined fracture mechanics and geometry

Pei, J., and Einstein, H.H., and Whittle, A.J. (2018). The normal stress space and its application to constructing a new failure criterion for cross-anisotropic geomaterials. International Journal of Rock Mechanics and Mining Sciences, 106, 364-373. doi:10.1016/j.ijrmms.2018.03.023

Brooks, Z., Ulm, F.-J., and Einstein (2012). Role of microstructure size in fracture process zone development of marble. In: Proceedings of the 46^th U.S. Rock Mechanics/Geomechanics Symposium, 24-27 June, Chicago, Illinois. ARMA-2012-421

Janeiro, R.P., and Einstein, H.H. (2010). Experimental study of the cracking behavior of specimens containing inclusions (under uniaxial compression). International Journal of Fracture, 164 (1), 83-102. doi:10.1007/s10704-010-9457-x

Einstein, H.H., Miller, J., and Silva, B. (2009). Experimental and Analytical Research on Fracture Processes in Rock. Massachusetts Institute of Technology, Department of Civil Engineering. Final report no. DOE/GO/16061-1, February 2009. Prepared for USDOE Office of Geothermal Technologies under Contract no. FG36-06GO16061. doi:10.2172/948451

Zhang, L., and Einstein, H.H. (2004). Using RQD to estimate the deformation modulus of rock masses. International Journal of Rock Mechanics and Mining Sciences, 41 (2), 337-341. doi:10.1016/S1365-1609(03)00100-X

Zhang, L., and Einstein, H.H. (2000). Estimating the deformation modulus of rock masses. In: Proceedings of the 4^th North American Rock Mechanics Symposium, 31 July-3 August, Seattle, Washington. ARMA-2000-0703

Einstein, H.H., and Stephansson, O. (2000). Fracture systems, fracture propagation and fracture coalescence. In: Proceedings of the ISRM International Symposium, 19-24 November, Melbourne, Australia. ISRM-IS-2000-033

Einstein, H.H. (1998). Fractures, discontinuities, and mechanical breakage of rocks. General report. In: Proceedings of the 3^rd North American Rock Mechanics Symposium, NARMS’98 (J. Orozco, J. Schmitter, eds.), 3-5 June 1998, Cancun, Mexico, vol. 2, pp. 159-168. Elsevier: Amsterdam, Netherlands. ISBN 978-0080433332

Bobet, A., and Einstein, H.H. (1998). Numerical modeling of fracture coalescence in a model rock material. International Journal of Fracture, 92 (3), 221-252. doi:10.1023/A:1007460316400

Bobet, A., and Einstein, H.H. (1998). Fracture coalescence in rock-type materials under uniaxial and biaxial compression. International Journal of Rock Mechanics and Mining Sciences, 35 (7), 863-889. doi:10.1016/S0148-9062(98)00005-9

Einstein, H.H. (1995). Risk and risk analysis in rock engineering. Keynote lecture. In: Proceedings of the Swedish Rock Mechanics Day, Stockholm, Sweden, 1995. Also in: Tunneling and Underground Space Technology, 11 (2), 141-155. doi:10.1016/0886-7798(96)00014-4

Einstein, H.H. (1993). Modern Developments in Discontinuity Analysis – The Persistence–Connectivity Problem. In J.A. Hudson (ed.): Comprehensive Rock Engineering, Volume 3: Rock Testing and Site Characterization: Principles, Practice and Projects, Chapter 9, 193-213. Pergamon Press Ltd., 1993. ISBN: 978-0080420660 doi:10.1016/B978-0-08-042066-0.50016-1

Lee, J.-S., and Einstein, H.H. (1992). Topological slope stability analysis using stochastic fracture geometry model. In: Proceedings of the International Conference on Fractured and Jointed Rock Masses (N.G.W. Cook, et al., eds.), 3-5 June 1992, Lake Tahoe, California. Balkema, Rotterdam. ISBN 978-9054105916

Iglesia, G., Einstein, H.H., Whitman, R.V., Jessberger, H.L., and Güttler, U. (1991). Trapdoor experiments with simulated jointed rock. In: Proceedings of the International Conference Centrifuge 1991 (H.-Y. Ko, F.G. McLean, eds.), 13-14 June, Boulder, Colorado. Balkema, Rotterdam, 1991. ISBN 978-9061911937

Einstein, H.H., Li, V., Whitman, R.V., Veneziano, D., Reyes, O., and Lee, J.S. (1990). Stochastic and Centrifuge Modeling of Jointed Rock. Executive Summary. Massachusetts Institute of Technology, Department of Civil Engineering. Final report, June 1987-May 1990. Executive summary: MIT report R90-22, 95 pages. Prepared for the Air Force Office of Scientific Research and the Air Force Engineering Services Center. Grant No. AFOSR-87-0260. MIT Libraries: 000614099

Reyes, O.M.L., and Einstein, H.H. (1990). Stochastic and Centrifuge Modeling of Jointed Rock. Part I: Fracturing of Fractured Rock. Massachusetts Institute of Technology, Department of Civil Engineering. Final report, June 1987-May 1990. Part 1: MIT report R90-23, 211 pages. Prepared for the Air Force Office of Scientific Research and the Air Force Engineering Services Center. Grant No. AFOSR-87-0260. MIT Libraries: 000614067

Iglesia, G.R., Einstein, H.H., and Whitman, R.V. (1990). Stochastic and Centrifuge Modeling of Jointed Rock. Part II: Centrifuge Modelling of Jointed Rock.. Massachusetts Institute of Technology, Department of Civil Engineering. Final report, June 1987-May 1990. Part 2: MIT report R90-24, 281 pages. Prepared for the Air Force Office of Scientific Research and the Air Force Engineering Services Center. Grant No. AFOSR-87-0260. MIT Libraries: 000614100

Suk, J.-S., Einstein, H.H., and Veneziano, D. (1990). Stochastic and Centrifuge Modeling of Jointed Rock. Part III: Stochastic and Topological Fracture Geometry Model. Massachusetts Institute of Technology, Department of Civil Engineering. Final report, June 1987-May 1990. Part 3: MIT report R90-25, 306 pages. Prepared for the Air Force Office of Scientific Research and the Air Force Engineering Services Center. Grant No. AFOSR-87-0260. MIT Libraries: 000651871

Joseph, P.J., Einstein, H.H., and Whitman, R.V. (1988). A Literature Review of Geotechnical Centrifuge Modeling with Particular Emphasis on Rock Mechanics. Massachusetts Institute of Technology, Department of Civil Engineering. Final report, April-December 1986, 119 pages. Prepared for Air Force Engineering & Services Center, Tyndall Air Force Base, under Contract no. DACA88-86-D-0013, June 1988.

Joseph, P.J., and Einstein, H.H. (1988). Rock Modeling Using the Centrifuge. Massachusetts Institute of Technology, Department of Civil Engineering. Final report, April-December 1986, 50 pages. Prepared for Air Force Engineering & Services Center, Tyndall Air Force Base, under Contract no. DACA88-86-D-0013, June 1988.

Kafritsas, J., and Einstein, H.H. (1987). Coupled flow/deformation analysis of a dam foundation with the distinct element method. In: Proceedings of the 28^th U.S. Symposium on Rock Mechanics (USRMS), 29 June-1 July, Tucson, Arizona. ARMA-87-0481

Dershowtiz, W.S., and Einstein, H.H. (1987). Three-dimensional flow modeling in jointed rock masses. In: Proceedings of the Sixth Congress of the International Society for Rock Mechanics, 30 August-3 September, Montreal, Canada. ISRM-6CONGRESS-1987-016

Einstein, H.H., et al. (1986). Rock Mass Persistence: Final Technical Report and Executive Summary. Massachusetts Institute of Technology, Department of Civil Engineering. MIT report, 95 pages, February 1986. Prepared for U.S. Army Research Office, Grant no. DAAG-29-83-K-0016. MIT Libraries: 000713272

Kafritsas, J., and Einstein, H.H. (1984). Coupled deformation/flow analysis with the distinct element method. In: Proceedings of the 25^th U.S. Symposium on Rock Mechanics (USRMS), 25-27 June, Evanston, Illinois. ARMA-84-0239

Einstein, H.H., Veneziano, D., Baecher, G.B., and O’Reilly, K.J. (1983). The effect of discontinuity persistence on rock slope stability. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 20 (5), 227-236. doi:10.1016/0148-9062(83)90003-7

Einstein, H.H., Baecher, G.B., and Veneziano, D. (1982). Risk analysis for rock slopes in open pit mines (in 8 parts): Einstein, H H; Baecher, G B; Veneziano, D. US Bureau of Mines reports OFR 46(1-8)-81, Nov 1979, 1954P. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 19 (3), 67. doi:10.1016/0148-9062(82)91320-1

Einstein, H.H., Baecher, G.B., Veneziano, D., et al. (1980). Risk Analysis for Rock Slopes in Open Pit Mines. Massachusetts Institute of Technology, Department of Civil Engineering. MIT reports prepared for the U.S. Bureau of Mines. Six volumes, MIT series R80-18-R80-23. Executive summary. Part 1 – Distributions of rock mass properties. Part 2 – Limit equilibrium analysis for rock wedge stability. Part 3 – Reliability analysis of rock slope stability. Part 4 – Field exploration to determine rock mass properties. Part 5 – Probabilistic models of jointed rock mass deformation and their implications. Appendices A through M – Detailed geologic data underlying developments. MIT Libraries: 000660195

Glynn, E.F., and Einstein, H.H. (1979). Probability of kinematic instability in rock slopes – a numerical approach. In: Proceedings of the 20^th U.S. Symposium on Rock Mechanics (USRMS), 4-6 June, Austin, Texas. ARMA-79-0317

Dershowitz, W.S., Baecher, G.B., and Einstein, H.H. (1979). Prediction of rock mass deformability. In: Proceedings of the 4^th ISRM Congress, 2-8 September, Montreux, Switzerland. ISRM-4CONGRESS-1979-082

Glynn, E.F., Veneziano, D., and Einstein, H.H. (1978). The probabilistic model for shearing resistance of jointed rock. In: Proceedings of the 19^th U.S. Symposium on Rock Mechanics (USRMS), 1-3 May, Reno, Nevada. ARMA-78-0090

Einstein, H.H., Baecher, G.B., Glynn, E., Dershowitz, W.S., Lanney, N., and Maloney, G. (1978). Risk Analysis for Rock Slopes in Open Pit Mines: Annual Technical Report. Massachusetts Institute of Technology, Department of Civil Engineering. MIT report no. R78-7, Volumes I and II, 1978. Prepared for the U.S. Bureau of Mines under Contract no. J0275015. MIT Libraries: 000369020

Baecher, G.B., Lanney, N.A., and Einstein, H.H. (1977). Statistical description of rock properties and sampling. In: Proceedings of the 18^th U.S. Symposium on Rock Mechanics (USRMS), 22-24 June, Golden, Colorado. ARMA-77-0400

Einstein, H.H., and Hirschfeld, R.C. (1973). Model studies on mechanics of jointed rock. Journal of the ASCE Soil Mechanics and Foundations Division, 99 (3), 229-248. doi:10.1061/JSFEAQ.0001859

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