Virtual Shake Robot: Simulating Dynamics of Precariously Balanced Rocks for Overturning and Large-displacement Processes




Precariously balanced rocks, seismic hazard analysis, physics engine, robotics, rockfall, dynamics simulation, ground motions, fragile geological features, automated geoscience


 Understanding the dynamics of precariously balanced rocks (PBRs) is important for seismic hazard analysis and rockfall prediction. Utilizing a physics engine and robotic tools, we develop a virtual shake robot (VSR) to simulate the dynamics of PBRs during overturning and large-displacement processes. We present the background of physics engines and technical details of the VSR, including software architecture, mechanical structure, control system, and implementation procedures. Validation experiments show the median fragility contour from VSR simulation is within the 95% prediction intervals from previous physical experiments, when PGV/PGA is greater than 0.08 s. Using a physical mini shake robot, we validate the qualitative consistency of fragility anisotropy between the VSR and physical experiments. By overturning cuboids on flat terrain, the VSR reveals the relationship between fragility and geometric dimensions (e.g., aspect and scaling ratios). The ground motion orientation and lateral pedestal support affect PBR fragility. Large-displacement experiments estimate rock trajectories for different ground motions, which is useful for understanding the fate of toppled PBRs. Ground motions positively correlate with large displacement statistics such as mean trajectory length, mean largest velocity, and mean terminal distance. The overturning and large displacement processes of PBRs provide complementary methods of ground motion estimation.


Agliardi, F., & Crosta, G. B. (2003). High resolution three-dimensional numerical modelling of rockfalls. International Journal of Rock Mechanics and Mining Sciences, 40(4), 455–471.

Alian, M., Ein-Mozaffari, F., & Upreti, S. R. (2015). Analysis of the mixing of solid particles in a plowshare mixer via discrete element method (DEM). Powder Technology, 274, 77–87.

Anderson, J. G., Biasi, G. P., & Brune, J. N. (2014). Chapter 14 - Precarious Rocks: Providing Upper Limits on Past Ground Shaking from Earthquakes. In J. F. Shroder & M. Wyss (Eds.), Earthquake Hazard, Risk and Disasters (pp. 377–403). Elsevier.

Anooshehpoor, A., Brune, J. N., & Zeng, Y. (2004). Methodology for obtaining constraints on ground motion from precariously balanced rocks. Bulletin of the Seismological Society of America, 94(1), 285–303.

Asaf, Z., Rubinstein, D., & Shmulevich, I. (2007). Determination of discrete element model parameters required for soil tillage. Soil and Tillage Research, 92(1–2), 227–242.

Azzoni, A., La Barbera, G., & Zaninetti, A. (1995). Analysis and prediction of rockfalls using a mathematical model. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 32(7), 709–724.

Baker, J., Bradley, B., & Stafford, P. (2021). Seismic Hazard and Risk Analysis. Cambridge University Press.

Bao, Y., & Konstantinidis, D. (2020). Dynamics of a sliding‐rocking block considering impact with an adjacent wall. Earthquake Engineering & Structural Dynamics, 49(5), 498–523.

Bell, J. W., Brune, J. N., Liu, T., Zreda, M., & Yount, J. C. (1998). Dating precariously balanced rocks in seismically active parts of California and Nevada. Geology, 26(6), 495.<0495:dpbris>;2

Bender, J., Erleben, K., & Trinkle, J. (2013). Interactive Simulation of Rigid Body Dynamics in Computer Graphics. Computer Graphics Forum, 33(1), 246–270.

Beverloo, W. A., Leniger, H. A., & van de Velde, J. (1961). The flow of granular solids through orifices. Chemical Engineering Science, 15(3–4), 260–269.

Bozzolo, D., & Pamini, R. (1986). Simulation of rock falls down a valley side. Acta Mechanica, 63(1–4), 113–130.

Brune, J. N. (1996). Precariously balanced rocks and ground-motion maps for Southern California. Bulletin of the Seismological Society of America, 86(1A), 43–54.

Brune, J. N., Anooshehpoor, A., Purvance, M. D., & Brune, R. J. (2006). Band of precariously balanced rocks between the Elsinore and San Jacinto, California, fault zones: Constraints on ground motion for large earthquakes. Geology, 34(3), 137.

Byerlee, J. (1978). Friction of Rocks. In Rock Friction and Earthquake Prediction (pp. 615–626). Birkhäuser Basel.

Çaktı, E., Saygılı, Ö., Lemos, J. V., & Oliveira, C. S. (2016). Discrete element modeling of a scaled masonry structure and its validation. Engineering Structures, 126, 224–236.

Catanoso, D., Stucky, T., Case, J., & Rogg, A. (2020, March). Analysis of Sample Acquisition Dynamics Using Discrete Element Method. 2020 IEEE Aerospace Conference.

Caviezel, A., Lu, G., Demmel, S., Ringenbach, A., Bühler, Y., Christen, M., & Bartelt, P. (2019). RAMMS:: ROCKFALL-a modern 3-dimensional simulation tool calibrated on real world data. 53rd US Rock Mechanics/Geomechanics Symposium.

Chen, Z. (2022). Automated Geoscience with Robotics and Machine Learning: A New Hammer of Rock Detection, Mapping, and Dynamics Analysis [PhD Dissertation]. Arizona State University.

Chen, Z. (2023). Virtual Shake Robot Software. Zenodo.

Chen, Z., Arrowsmith, J. R., & Das, J. (2024, in prep). Target-oriented UAV Mapping of Precariously Balanced Rocks for Seismic Studies. Journal of Field Robotics.

Chen, Z., Keating, D., Shethwala, Y., Saravanakumaran, A. A. P., Arrowsmith, R., Madugo, C., Kottke, A., & Das, J. (2022). Shakebot: A Low-cost, Open-source Shake Table for Ground Motion Seismic Studies. ArXiv Preprint ArXiv:2212.10763.

Chiama, K., Chauvin, B., Plesch, A., Moss, R., & Shaw, J. H. (2023). Geomechanical Modeling of Ground Surface Deformation Associated with Thrust and Reverse-Fault Earthquakes: A Distinct Element Approach. Bulletin of the Seismological Society of America, 113(4), 1702–1723.

Chuhan, Z., Pekau, O. A., Feng, J., & Guanglun, W. (1997). Application of distinct element method in dynamic analysis of high rock slopes and blocky structures. Soil Dynamics and Earthquake Engineering, 16(6), 385–394.

Cleary, P. W. (2015). A multiscale method for including fine particle effects in DEM models of grinding mills. Minerals Engineering, 84, 88–99.

Coetzee, C. J., & Lombard, S. G. (2011). Discrete element method modelling of a centrifugal fertiliser spreader. Biosystems Engineering, 109(4), 308–325.

Coumans, E., & Bai, Y. (2016). PyBullet, a Python module for physics simulation for games, robotics and machine learning.

Cundall, P. A. (1988). Formulation of a three-dimensional distinct element model—Part I. A scheme to detect and represent contacts in a system composed of many polyhedral blocks. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 25(3), 107–116.

Cundall, P. A., & Strack, O. D. L. (1979). A discrete numerical model for granular assemblies. Géotechnique, 29(1), 47–65.

Dorren, L. K. A. (2003). A review of rockfall mechanics and modelling approaches. Progress in Physical Geography: Earth and Environment, 27(1), 69–87.

Drumwright, E., Hsu, J., Koenig, N., & Shell, D. (2010). Extending Open Dynamics Engine for Robotics Simulation. In Lecture Notes in Computer Science (pp. 38–50). Springer Berlin Heidelberg.

Erez, T., Tassa, Y., & Todorov, E. (2015, May). Simulation tools for model-based robotics: Comparison of Bullet, Havok, MuJoCo, ODE and PhysX. 2015 IEEE International Conference on Robotics and Automation (ICRA).

Erleben, K., Sporring, J., Henriksen, K., & Dohlmann, H. (2005). Physics-based animation. Charles River Media Hingham.

Garcia, F. E., & Bray, J. D. (2018). Distinct element simulations of earthquake fault rupture through materials of varying density. Soils and Foundations, 58(4), 986–1000.

Garcia, F. E., & Bray, J. D. (2022). Discrete element analysis of earthquake surface fault rupture through layered media. Soil Dynamics and Earthquake Engineering, 152, 107021.

Garcia-Hernandez, A., Wan, L., Dopazo-Hilario, S., Chiarelli, A., & Dawson, A. (2021). Generation of virtual asphalt concrete in a physics engine. Construction and Building Materials, 286, 122972.

Gascuel, J.-D., Cani-Gascuel, M.-P., Desbrun, M., Leroi, E., & Mirgon, C. (1999). Simulating Landslides for Natural Disaster Prevention. In Computer Animation and Simulation ’98 (pp. 1–12). Springer Vienna.

Guzzetti, F., Crosta, G., Detti, R., & Agliardi, F. (2002). STONE: a computer program for the three-dimensional simulation of rock-falls. Computers & Geosciences, 28(9), 1079–1093.

Haddad, D. E., Zielke, O., Arrowsmith, J. R., Purvance, M. D., Haddad, A. G., & Landgraf, A. (2012). Estimating two-dimensional static stabilities and geomorphic settings of precariously balanced rocks from unconstrained digital photographs. Geosphere, 8(5), 1042–1053.

Hao, W., Jian, H., Xiang, H., Jingqing, Y., Zicheng, H., & Ying, H. (2021). A New Rockfall Simulation Tool based on Unity 3D. IOP Conference Series: Earth and Environmental Science, 861(3), 32059.

Haron, A., & Ismail, K. A. (2012). Coefficient of restitution of sports balls: A normal drop test. IOP Conference Series: Materials Science and Engineering, 36, 12038.

He, H., Zheng, J., Chen, Y., & Ning, Y. (2021). Physics engine based simulation of shear behavior of granular soils using hard and soft contact models. Journal of Computational Science, 56, 101504.

He, H., Zheng, J., & Li, Z. (2020, February). Comparing Realistic Particle Simulation Using Discrete Element Method and Physics Engine. Geo-Congress 2020.

Housner, G. W. (1963). The behavior of inverted pendulum structures during earthquakes. Bulletin of the Seismological Society of America, 53(2), 403–417.

Ishiyama, Y. (1982). Motions of rigid bodies and criteria for overturning by earthquake excitations. Earthquake Engineering & Structural Dynamics, 10(5), 635–650.

Itasca Consulting Group, Inc. (2020). 3DEC — Three-Dimensional Distinct Element Code.

Izadi, E., & Bezuijen, A. (2014). Simulation of granular soil behaviour using the Bullet physics library. In Geomechanics from Micro to Macro (pp. 1565–1570). CRC Press.

Kim, J.-C., Jung, H., Kim, S., & Chung, K. (2015). Slope Based Intelligent 3D Disaster Simulation Using Physics Engine. Wireless Personal Communications, 86(1), 183–199.

Kirkpatrick, P. (1927). Seismic measurements by the overthrow of columns. Bulletin of the Seismological Society of America, 17(2), 95–109.

Kobayashi, Y., Harp, E. L., & Kagawa, T. (1990). Simulation of rockfalls triggered by earthquakes. Rock Mechanics and Rock Engineering, 23(1), 1–20.

Koenig, N., & Howard, A. (n.d.). Design and use paradigms for gazebo, an open-source multi-robot simulator. 2004 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) (IEEE Cat. No.04CH37566).

Komaragiri, S., Gigliotti, A., & Bhasin, A. (2021). Calibration and extended validation of a virtual asphalt mixture compaction model using bullet physics engine. Construction and Building Materials, 311, 125257.

Konstantinidis, D. A. (2008). Experimental and analytical studies on the seismic response of freestanding and anchored building contents [PhD Dissertation]. University of California, Berkeley.

Lan, H., Derek Martin, C., & Lim, C. H. (2007). RockFall analyst: A GIS extension for three-dimensional and spatially distributed rockfall hazard modeling. Computers & Geosciences, 33(2), 262–279.

Leine, R. I., Schweizer, A., Christen, M., Glover, J., Bartelt, P., & Gerber, W. (2013). Simulation of rockfall trajectories with consideration of rock shape. Multibody System Dynamics, 32(2), 241–271.

Lozos, J. C., Harris, R. A., Murray, J. R., & Lienkaemper, J. J. (2015). Dynamic rupture models of earthquakes on the Bartlett Springs Fault, Northern California. Geophysical Research Letters, 42(11), 4343–4349.

Lu, G., Third, J. R., & Müller, C. R. (2015). Discrete element models for non-spherical particle systems: From theoretical developments to applications. Chemical Engineering Science, 127, 425–465.

Ma, Q. T., Parshttam, S., & Montalla, M. (2018, June 25). Modelling rocking behaviour using physics engine simulation. Eleventh U.S. National Conference on Earthquake Engineering.

Martin, C. L., Bouvard, D., & Shima, S. (2003). Study of particle rearrangement during powder compaction by the Discrete Element Method. Journal of the Mechanics and Physics of Solids, 51(4), 667–693.

Mehrotra, A., & DeJong, M. (2017). The Performance of Slender Monuments during the 2015 Gorkha, Nepal, Earthquake. Earthquake Spectra, 33, 321–343.

Millington, I. (2007). Game Physics Engine Development. CRC Press.

Milne, J., & Omori, F. (1893). On the overturning and fracturing of Brick and other Columns by horizontally applied Motion. Seismological Journal of Japan, 17(2), 95–109.

Mirtich, B., & Canny, J. (1995). Impulse-based simulation of rigid bodies. Proceedings of the 1995 Symposium on Interactive 3D Graphics - SI3D ’95.

Papantonopoulos, C., Psycharis, I. N., Papastamatiou, D. Y., Lemos, J. V., & Mouzakis, H. P. (2002). Numerical prediction of the earthquake response of classical columns using the distinct element method. Earthquake Engineering & Structural Dynamics, 31(9), 1699–1717.

Pezo, L., Jovanović, A., Pezo, M., Čolović, R., & Lončar, B. (2015). Modified screw conveyor-mixers – Discrete element modeling approach. Advanced Powder Technology, 26(5), 1391–1399.

Pompei, A., Scalia, A., & Sumbatyan, M. A. (1998). Dynamics of Rigid Block due to Horizontal Ground Motion. Journal of Engineering Mechanics, 124(7), 713–717.

Purvance, M. D. (2005). Overturning of slender blocks: Numerical investigation and application to precariously balanced rocks in southern California [PhD Dissertation]. University of Nevada, Reno.

Purvance, M. D., Anooshehpoor, A., & Brune, J. N. (2008). Freestanding block overturning fragilities: Numerical simulation and experimental validation. Earthquake Engineering & Structural Dynamics, 37(5), 791–808.

Purvance, M. D., Anooshehpoor, A., & Brune, J. N. (2012). Fragilities for Precarious Rocks at Yucca Mountain (p. PEER Report 2012-06) [Techreport]. Pacific Earthquake Engineering Research Center.

Pytlos, M., Gilbert, M., & Smith, C. C. (2015). Modelling granular soil behaviour using a physics engine. Géotechnique Letters, 5(4), 243–249.

Rood, A. H., Rood, D. H., Stirling, M. W., Madugo, C. M., Abrahamson, N. A., Wilcken, K. M., Gonzalez, T., Kottke, A., Whittaker, A. C., Page, W. D., & Stafford, P. J. (2020). Earthquake Hazard Uncertainties Improved Using Precariously Balanced Rocks. AGU Advances, 1(4).

Rood, Anna H., Rood, D. H., Balco, G., Stafford, P. J., Ludwig, L. G., Kendrick, K. J., & Wilcken, K. M. (2022). Validation of earthquake ground-motion models in southern California, USA, using precariously balanced rocks. GSA Bulletin.

Saifullah, M. K., & Wittich, C. E. (2021). Seismic Response of Two Freestanding Statue-Pedestal Systems during the 2014 South Napa Earthquake. Journal of Earthquake Engineering, 26(10), 5086–5108.

Saifullah, M., & Wittich, C. (2022). Fragility of Precariously Balanced Rocks: Shake Table Testing and Numerical Modeling for a Sample Granitic Rock. 12th National Conference on Earthquake Engineering.

Scalia, A., & Sumbatyan, M. A. (1996). Slide Rotation of Rigid Bodies Subjected to a Horizontal Ground Motion. Earthquake Engineering & Structural Dynamics, 25(10), 1139–1149.<1139::aid-eqe606>;2-s

SCEC researchers. (2022). SCEC Precariously Balanced Rocks Project: PBR Data Archive.

Shenton, I., & Harry, W. (1996). Criteria for Initiation of Slide, Rock, and Slide-Rock Rigid-Body Modes. Journal of Engineering Mechanics, 122(7), 690–693.

Shi, B., Anooshehpoor, A., Zeng, Y., & Brune, J. N. (1996). Rocking and overturning of precariously balanced rocks by earthquakes. Bulletin of the Seismological Society of America, 86(5), 1364–1371.

Stanford Artificial Intelligence Laboratory. (2018). Robotic Operating System (ROS Melodic Morenia) [Computer software].

Sun, C., Nakashima, H., Shimizu, H., Miyasaka, J., & Ohdoi, K. (2019). Physics engine application to overturning dynamics analysis on banks and uniform slopes for an agricultural tractor with a rollover protective structure. Biosystems Engineering, 185, 150–160.

Toson, P., & Khinast, J. G. (2017). Impulse-based dynamics for studying quasi-static granular flows: Application to hopper emptying of non-spherical particles. Powder Technology, 313, 353–360.

van den Bergen, G. (2003). Collision Detection in Interactive 3D Environments. CRC Press.

Veeraraghavan, S. (2015). Toppling analysis of precariously balanced rocks [PhD Dissertation]. California Institute of Technology.

Veeraraghavan, Swetha, Hall, J. F., & Krishnan, S. (2020). Modeling the Rocking and Sliding of Free-Standing Objects Using Rigid Body Dynamics. Journal of Engineering Mechanics, 146(6).

Veeraraghavan, Swetha, Hudnut, K. W., & Krishnan, S. (2016). Toppling Analysis of the Echo Cliffs Precariously Balanced Rock. Bulletin of the Seismological Society of America, 107(1), 72–84.

Williams, J., Lu, Y., & Trinkle, J. C. (2014, August). A Complementarity Based Contact Model for Geometrically Accurate Treatment of Polytopes in Simulation. Volume 6: 10th International Conference on Multibody Systems, Nonlinear Dynamics, and Control.

Wittich, C. E., & Hutchinson, T. C. (2017). Rocking bodies with arbitrary interface defects: Analytical development and experimental verification. Earthquake Engineering & Structural Dynamics, 47(1), 69–85.

Xu, Z., Lu, X., Guan, H., Han, B., & Ren, A. (2013). Seismic damage simulation in urban areas based on a high-fidelity structural model and a physics engine. Natural Hazards, 71(3), 1679–1693.

Yim, C., Chopra, A. K., & Penzien, J. (1980). Rocking response of rigid blocks to earthquakes. Earthquake Engineering & Structural Dynamics, 8(6), 565–587.

Zhu, F., & Zhao, J. (2019). Modeling continuous grain crushing in granular media: A hybrid peridynamics and physics engine approach. Computer Methods in Applied Mechanics and Engineering, 348, 334–355.

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How to Cite

Chen, Z., Arrowsmith, R., Das, J., Wittich, C., Madugo, C., & Kottke, A. (2024). Virtual Shake Robot: Simulating Dynamics of Precariously Balanced Rocks for Overturning and Large-displacement Processes. Seismica, 3(1).