In this study, uniaxial and biaxial compression tests were simulated to assess the impact of sample scale - both dimensions and shape - along with the rate and nature of loading on the strength behavior and deformability of a limestone rock specimen. For this end, the finite difference method (FDM) using FLAC code was employed. The compression test simulations utilized an innovative technique based on the model's equilibrium principle during loading, mimicking static loading conditions in reality. This approach facilitated systematic control of axial and lateral loads on the model, effectively preventing abrupt violent failure. A series of two-dimensional (2D) models were subjected to varying loading conditions to appraise the stress-strain behavior of the computational models. Numerical results show that changes in the model's shape and dimensions affected the compressive strength of rock models. Here, an increment in the width-to-length ratio of the model led to enhanced compressive strength. Similarly, an increase in the loading rate also increased the uniaxial compressive strength of the model. Also, by applying and augmentation of lateral pressure in the biaxial compression test further increased the rock model's compressive strength. Hence, rocks under pressure demonstrate scale-dependent behaviors, exhibiting varying strengths under different loading conditions.
Bieniawski, Z. T. (1974). Geomechanics Classification of Rock Masses and Its Application in Tunneling. Proceedings of 3rd Congress of the International Society of Rock Mechanics, Denever National Academy of Sciences, Denver, United States.
Cargill, J. S., & Shakoor, A. (1990). Evaluation of empirical methods for measuring the uniaxial compressive strength of rock. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 27(6), 495–503. doi:10.1016/0148-9062(90)91001-N.
Kanji, M., He, M., & Ribeiro e Sousa, L. (Eds.). (2020). Soft Rock Mechanics and Engineering. Springer, Cham, Switzerland. doi:10.1007/978-3-030-29477-9.
Ulusay, R. (Ed.). (2015). The ISRM Suggested Methods for Rock Characterization, Testing and Monitoring: 2007-2014. Springer, Cham, Switzerland. doi:10.1007/978-3-319-07713-0.
Zhang, L. (2016). Engineering properties of rocks. Butterworth-Heinemann, Waltham, United States.
Hawkins, A. B., & Oivert, J. A. G. (1986). Point Load Tests: Correlation factors and contractual use. An example from the Corallian at Weymouth. Geological Society Engineering Geology Special Publication, 2(1), 269–271. doi:10.1144/GSL.1986.002.01.48.
Romana, M. (1999). Correlation between uniaxial compressive and point-load (Franklin test) strengths for different rock classes. 9th ISRM Congress, 25 August, 1999 Paris, France.
Rusnak, J., & Mark, C. (2000). Using the point load test to determine the uniaxial compressive strength of coal measure rock. Proceedings of the 19th International Conference on Ground Control in Mining, August 8-10, 2000, Morgantown, United States.
Tsiambaos, G., & Sabatakakis, N. (2004). Considerations on strength of intact sedimentary rocks. Engineering Geology, 72(3–4), 261–273. doi:10.1016/j.enggeo.2003.10.001.
Singh, T. N., Kainthola, A., & Venkatesh, A. (2012). Correlation between point load index and uniaxial compressive strength for different rock types. Rock Mechanics and Rock Engineering, 45(2), 259–264. doi:10.1007/s00603-011-0192-z.
Garrido, M. E., Petnga, F. B., Martínez-Ibáñez, V., Serón, J. B., Hidalgo-Signes, C., & Tomás, R. (2022). Predicting the Uniaxial Compressive Strength of a Limestone Exposed to High Temperatures by Point Load and Leeb Rebound Hardness Testing. Rock Mechanics and Rock Engineering, 55(1), 1–17. doi:10.1007/s00603-021-02647-0.
Sadeghi, E., Nikudel, M. R., Khamehchiyan, M., & Kavussi, A. (2022). Estimation of Unconfined Compressive Strength (UCS) of Carbonate Rocks by Index Mechanical Tests and Specimen Size Properties: Central Alborz Zone of Iran. Rock Mechanics and Rock Engineering, 55(1), 125–145. doi:10.1007/s00603-021-02532-w.
Sachpazis, C. I. (1990). Correlating schmidt hardness with compressive strength and young’s modulus of carbonate rocks. Bulletin of the International Association of Engineering Geology, 42(1), 75–83. doi:10.1007/BF02592622.
Katz, O., Reches, Z., & Roegiers, J. C. (2000). Evaluation of mechanical rock properties using a Schmidt Hammer. International Journal of Rock Mechanics and Mining Sciences, 37(4), 723–728. doi:10.1016/S1365-1609(00)00004-6.
Kahraman, S. (2001). Evaluation of simple methods for assessing the uniaxial compressive strength of rock. International Journal of Rock Mechanics and Mining Sciences, 38(7), 981–994. doi:10.1016/S1365-1609(01)00039-9.
Mostyn, G. R., & Li, K. S. (2020). Probabilistic slope analysis — State-of-play. Probabilistic Methods in Geotechnical Engineering, 89–109. doi:10.1201/9781003077749-6.
Yaşar, E., & Erdoǧan, Y. (2004). Estimation of rock physicomechanical properties using hardness methods. Engineering Geology, 71(3–4), 281–288. doi:10.1016/S0013-7952(03)00141-8.
Shalabi, F. I., Cording, E. J., & Al-Hattamleh, O. H. (2007). Estimation of rock engineering properties using hardness tests. Engineering Geology, 90(3–4), 138–147. doi:10.1016/j.enggeo.2006.12.006.
Aldeeky, H., Al Hattamleh, O., & Rababah, S. (2020). Assessing the uniaxial compressive strength and tangent Young’s modulus of basalt rock using the leeb rebound hardness test. Materiales de Construccion, 70(340), 230– 230. doi:10.3989/MC.2020.15119.
Pappalardo, G. (2015). Correlation Between P-Wave Velocity and Physical–Mechanical Properties of Intensely Jointed Dolostones, Peloritani Mounts, NE Sicily. Rock Mechanics and Rock Engineering, 48(4), 1711–1721. doi:10.1007/s00603-014-0607-8.
Abdelhedi, M., Aloui, M., Mnif, T., & Abbes, C. (2017). Ultrasonic velocity as a tool for mechanical and physical parameters prediction within carbonate rocks. Geomechanics and Engineering, 13(3), 371–384. doi:10.12989/gae.2017.13.3.371.
Gomez-Heras, M., Benavente, D., Pla, C., Martinez-Martinez, J., Fort, R., & Brotons, V. (2020). Ultrasonic pulse velocity as a way of improving uniaxial compressive strength estimations from Leeb hardness measurements. Construction and Building Materials, 261, 119996. doi:10.1016/j.conbuildmat.2020.119996.
Benavente, D., Martinez-Martinez, J., Galiana-Merino, J. J., Pla, C., de Jongh, M., & Garcia-Martinez, N. (2022). Estimation of uniaxial compressive strength and intrinsic permeability from ultrasounds in sedimentary stones used as heritage building materials. Journal of Cultural Heritage, 55, 346–355. doi:10.1016/j.culher.2022.04.010.
Chen, J., Du, C., Jiang, D., Fan, J., & He, Y. (2016). The mechanical properties of rock salt under cyclic loading-unloading experiments. Geomechanics and Engineering, 10(3), 325–334. doi:10.12989/gae.2016.10.3.325.
Komadja, G. C., Stanislas, T. T., Munganyinka, P., Anye, V., Pradhan, S. P., Adebayo, B., & Onwualu, A. P. (2022). New approach for assessing uniaxial compressive strength of rocks using measurement from nanoindentation experiments. Bulletin of Engineering Geology and the Environment, 81(8), 299. doi:10.1007/s10064-022-02801-0.
Deere, D. U., & Miller, R. P. (1966). Engineering Classification and Index Properties for Intact Rock. Defense Technical Information Center, Fort Belvoir, United States. doi:10.21236/ad0646610.
Hawkins, A. B., & McConnell, B. J. (1992). Sensitivity of sandstone strength and deformability to changes in moisture content. Quarterly Journal of Engineering Geology, 25(2), 115–130. doi:10.1144/gsl.qjeg.1992.025.02.05.
Lashkaripour, G. R. (2002). Predicting mechanical properties of mudrock from index parameters. Bulletin of Engineering Geology and the Environment, 61(1), 73–77. doi:10.1007/s100640100116.
Yilmaz, I. (2010). Influence of water content on the strength and deformability of gypsum. International Journal of Rock Mechanics and Mining Sciences, 47(2), 342–347. doi:10.1016/j.ijrmms.2009.09.002.
Jaeger, J. C., Cook, N. G., & Zimmerman, R. (2009). Fundamentals of rock mechanics. John Wiley & Sons, Hoboken, United States.
Bieniawski, Z. T. (1974). Estimating the Strength of Rock Materials. Journal of The South African Institute of Mining and Metallurgy, 74(8), 312–320. doi:10.1016/0148-9062(74)91782-3.
Johnston, I. W. (1985). Strength of intact geomechanical materials. Journal of Geotechnical Engineering, 111(6), 730–749. doi:10.1061/(ASCE)0733-9410(1985)111:6(730).
Ramamurthy, T., Rao, G. V., & Rao, K. S. (1985). A strength criterion for rocks. Proceedings of the Indian Geotechnical Conference, 16-18 December, 1985, Roorkee, India.
Hoek, E., & Brown, E. T. (1980). Empirical Strength Criterion for Rock Masses. Journal of the Geotechnical Engineering Division, 106(9), 1013–1035. doi:10.1061/ajgeb6.0001029.
Veríssimo-Anacleto, J., Ludovico-Marques, M., & Neto, P. (2020). An empirical model for compressive strength of the limestone masonry based on number of courses – An experimental study. Construction and Building Materials, 258, 119508. doi:10.1016/j.conbuildmat.2020.119508.
Mahmoodzadeh, A., Mohammadi, M., Hashim Ibrahim, H., Nariman Abdulhamid, S., Ghafoor Salim, S., Farid Hama Ali, H., & Kamal Majeed, M. (2021). Artificial intelligence forecasting models of uniaxial compressive strength. Transportation Geotechnics, 27, 100499. doi:10.1016/j.trgeo.2020.100499.
Alzabeebee, S., Mohammed, D. A., & Alshkane, Y. M. (2022). Experimental Study and Soft Computing Modeling of the Unconfined Compressive Strength of Limestone Rocks Considering Dry and Saturation Conditions. Rock Mechanics and Rock Engineering, 55(9), 5535–5554. doi:10.1007/s00603-022-02948-y.
Lawal, A. I., Kwon, S., Aladejare, A. E., & Oniyide, G. O. (2022). Prediction of the static and dynamic mechanical properties of sedimentary rock using soft computing methods. Geomechanics and Engineering, 28(3), 313–334. doi:10.12989/gae.2022.28.3.313.
Özdemir, E. (2022). A New Predictive Model for Uniaxial Compressive Strength of Rock Using Machine Learning Method: Artificial Intelligence-Based Age-Layered Population Structure Genetic Programming (ALPS-GP). Arabian Journal for Science and Engineering, 47(1), 629–639. doi:10.1007/s13369-021-05761-x.
Jing, L., & Hudson, J. A. (2002). Numerical methods in rock mechanics. International Journal of Rock Mechanics and Mining Sciences, 39(4), 409–427. doi:10.1016/S1365-1609(02)00065-5.
Fuenkajorn, K., & Serata, S. (1993). Numerical simulation of strain-softening and dilation of rock salt. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 30(7), 1303–1306. doi:10.1016/0148-9062(93)90113-r.
Mohammad, N., Reddish, D. J., & Stace, L. R. (1997). The relation between in situ and laboratory rock properties used in numerical modelling. International Journal of Rock Mechanics and Mining Sciences, 34(2), 289–297. doi:10.1016/S0148-9062(96)00060-5.
Lu, Y. B., Li, Q. M., & Ma, G. W. (2010). Numerical investigation of the dynamic compressive strength of rocks based on split Hopkinson pressure bar tests. International Journal of Rock Mechanics and Mining Sciences, 47(5), 829–838. doi:10.1016/j.ijrmms.2010.03.013.
TOKASHIKI, N., & AYDAN, Ö. (2010). the Stability Assessment of Overhanging Ryukyu Limestone Cliffs With an Emphasis on the Evaluation of Tensile Strength of Rock Mass. Doboku Gakkai Ronbunshuu C, 66(2), 397–406. doi:10.2208/jscejc.66.397.
Bidgoli, M. N., Zhao, Z., & Jing, L. (2013). Numerical evaluation of strength and deformability of fractured rocks. Journal of Rock Mechanics and Geotechnical Engineering, 5(6), 419–430. doi:10.1016/j.jrmge.2013.09.002.
Xu, T., Ranjith, P. G., Wasantha, P. L. P., Zhao, J., Tang, C. A., & Zhu, W. C. (2013). Influence of the geometry of partially-spanning joints on mechanical properties of rock in uniaxial compression. Engineering Geology, 167, 134–147. doi:10.1016/j.enggeo.2013.10.011.
Wang, S. Y., Sloan, S. W., Sheng, D. C., Yang, S. Q., & Tang, C. A. (2014). Numerical study of failure behaviour of pre-cracked rock specimens under conventional triaxial compression. International Journal of Solids and Structures, 51(5), 1132–1148. doi:10.1016/j.ijsolstr.2013.12.012.
Rathnaweera, T. D., Ranjith, P. G., Perera, M. S. A., & De Silva, V. R. S. (2017). Development of a laboratory-scale numerical model to simulate the mechanical behaviour of deep saline reservoir rocks under varying salinity conditions in uniaxial and triaxial test environments. Measurement, 101, 126–137. doi:10.1016/j.measurement.2017.01.015.
Xu, Z. H., Wang, W. Y., Lin, P., Xiong, Y., Liu, Z. Y., & He, S. J. (2020). A parameter calibration method for PFC simulation: Development and a case study of limestone. Geomechanics and Engineering, 22(1), 97–108. doi:10.12989/gae.2020.22.1.097.
Yin, Y., Li, G., Liu, Y., Jiang, X., & Luan, W. (2021). Research on uniaxial compression of jointed rock mass based on numerical simulation. IOP Conference Series: Earth and Environmental Science, 804(2), 22053. doi:10.1088/1755-1315/804/2/022053.
Noorian-Bidgoli, M. (2014). Strength and deformability of fractured rocks. PhD Thesis, KTH Royal Institute of Technology, Stockholm, Sweden.
Itasca, FLAC. (2000). Fast Lagrangian analysis of continua. Itasca Consulting Group Inc., Minneapolis, United States.
Harrison, J. P., & Hudson, J. A. (2000). Introduction. Engineering Rock Mechanics Part II, 3–11, Elsevier, Amsterdam, Netherlands. doi:10.1016/b978-008043010-2/50002-2.
Sano, O., Ito, I., & Terada, M. (1981). Influence of strain rate on dilatancy and strength of Oshima granite under uniaxial compression. Journal of Geophysical Research, 86(B10), 9299–9311. doi:10.1029/JB086iB10p09299.
Mogi, K. (2012). How I developed a true triaxial rock testing machine. True Triaxial Testing of Rocks, 4, 139–157. doi:10.1201/b12705.
Noorian-Bidgoli, M. , & Koochaki, M. (2025). Numerical investigation of the effect of scale, loading rate, and lateral load on the stress-strain behavior of rock under pressure. Contributions of Science and Technology for Engineering, 2(2), 47-55. doi: 10.22080/cste.2025.28773.1018
MLA
Majid Noorian-Bidgoli; Mahboobeh Koochaki. "Numerical investigation of the effect of scale, loading rate, and lateral load on the stress-strain behavior of rock under pressure", Contributions of Science and Technology for Engineering, 2, 2, 2025, 47-55. doi: 10.22080/cste.2025.28773.1018
HARVARD
Noorian-Bidgoli, M., Koochaki, M. (2025). 'Numerical investigation of the effect of scale, loading rate, and lateral load on the stress-strain behavior of rock under pressure', Contributions of Science and Technology for Engineering, 2(2), pp. 47-55. doi: 10.22080/cste.2025.28773.1018
CHICAGO
M. Noorian-Bidgoli and M. Koochaki, "Numerical investigation of the effect of scale, loading rate, and lateral load on the stress-strain behavior of rock under pressure," Contributions of Science and Technology for Engineering, 2 2 (2025): 47-55, doi: 10.22080/cste.2025.28773.1018
VANCOUVER
Noorian-Bidgoli, M., Koochaki, M. Numerical investigation of the effect of scale, loading rate, and lateral load on the stress-strain behavior of rock under pressure. Contributions of Science and Technology for Engineering, 2025; 2(2): 47-55. doi: 10.22080/cste.2025.28773.1018