Bulletin of Engineering Geology and the Environment

, Volume 77, Issue 4, pp 1647–1662 | Cite as

Predicting the shear strength parameters of sandstone using genetic programming

  • Jiayi ShenEmail author
  • Rafael Jimenez
Original Paper


The strength of intact rock is, together with the rock mass structure, probably the most important properties for rock engineering. To accurately estimate the Mohr–Coulomb (MC) strength parameters—cohesion c and angle of friction ϕ—of a rock, triaxial tests must be carried out at different stress levels so that a failure envelope can be obtained to be linearized. However, this involves a higher budget and time requirements that are often not available at the early stages of a project; thus faster and cheaper indirect methods have been developed as an alternative. In this paper, we use genetic programming (GP) to develop a predictive model to estimate the MC shear strength parameters of intact sandstone using other strength measures (the uniaxial compressive strength, UCS, and uniaxial tensile strength, UTS) under different stress conditions which shear failure takes place. The reliability of the proposed GP model is evaluated and compared with alternative linear regression models based on UCS or UTS only, and with the traditional triaxial-based approach. Results show that, although the triaxial method provides the better estimations, the proposed GP model has the best prediction performance in the absence of triaxial data, so that it can be used for practical strength estimations for intact sandstone at the early stage of projects or when triaxial test data are not available.


Shear strength parameters Uniaxial compressive strength Tensile strength Confining stress Genetic programming Sandstone 



This research is supported by the Scientific Research Foundation of State Key Laboratory of Coal Mine Disaster Dynamics and Control (No. 2011DA105287-FW201209) and the National Natural Science Foundation of China (No. 51504218).


  1. Armaghani DJ, Hajihassani M, Bejarbaneh BY, Marto A, Mohamad ET (2014) Indirect measure of shale shear strength parameters by means of rock index tests through an optimized artificial neural network. Measurement 55(9):487–498CrossRefGoogle Scholar
  2. Balmer G (1952) A general analytical solution for Mohr’s envelope. Am Soc Test Mater 52:1269–1271Google Scholar
  3. Beyhan S (2008) The determination of G.L.I and E.L.I marl rock material properties depending on triaxial compressive strength. PhD thesis, Osman Gazi University, p 224Google Scholar
  4. Bieniawski ZT (1974) Estimating the strength of intact rock. J S Afr Inst Min Metall 74:312–320Google Scholar
  5. Broch E, Franklin JA (1972) The point-load strength index. Int J Rock Mech Min Sci 9(6):669–697CrossRefGoogle Scholar
  6. Cabalar AF, Cevik A (2009) Genetic programming-based attenuation relationship: an application of recent earthquakes in turkey. Comput Geosci 35(9):1884–1896CrossRefGoogle Scholar
  7. Cai M (2010) Practical estimates of tensile strength and Hoek–Brown parameter m i of brittle rocks. Rock Mech Rock Eng 43(2):167–184CrossRefGoogle Scholar
  8. Cargill J, Shakoor A (1990) Evaluation of empirical-methods for measuring the uniaxial compressive strength of rock. Int J Rock Mech Min Sci 27(6):495–503CrossRefGoogle Scholar
  9. Cobanoglu I, Celik SB (2008) Estimation of uniaxial compressive strength from point load strength, Schmidt hardness and P-wave velocity. Bull Eng Geol Environ 7(4):491–498CrossRefGoogle Scholar
  10. Farah R (2011) Correlations between index properties and unconfined compressive strength of weathered Ocala Limestone. MSc thesis, University of North Florida School of Engineering, p 83Google Scholar
  11. Hoek E, Brown ET (1997) Practical estimates of rock mass strength. Int J Rock Mech Min Sci 34(8):1165–1186CrossRefGoogle Scholar
  12. Jimenez R, Serrano A, Olalla C (2008) Linearization of the Hoek and Brown rock failure criterion for tunnelling in elasto-plastic rock masses. Int J Rock Mech Min Sci 45(7):1153–1163CrossRefGoogle Scholar
  13. Kahraman S (2001) Evaluation of simple methods for assessing the uniaxial compressive strength of rock. Int J Rock Mech Min Sci 38(7):981–994CrossRefGoogle Scholar
  14. Karakus M (2011) Function identification for the intrinsic strength and elastic properties of granitic rocks via genetic programming (GP). Comput Geosci 37:1318–1323CrossRefGoogle Scholar
  15. Karaman K, Cihangir F, Ercikdi B, Kesimal A, Demirel S (2015) Utilization of the brazilian test for estimating the uniaxial compressive strength and shear strength parameters. J S Afr Inst Min Metall 115:185–192CrossRefGoogle Scholar
  16. Koza JR (1992) Genetic programming: on the programming of computers by means of natural selection. MIT press, Cambridge, p 819Google Scholar
  17. Labuz JF, Zang A (2012) Mohr-Coulomb failure criterion. Rock Mech Rock Eng 45(6):975–979CrossRefGoogle Scholar
  18. Li X, Zhou Z, Lok TS, Hong L, Yin T (2008) Innovative testing technique of rock subjected to coupled static and dynamic loads. Int J Rock Mech Min Sci 45:739–748CrossRefGoogle Scholar
  19. Li X, Tao M, Wu C, Du K, Wu Q (2016) Spalling strength of rock under different static pre-confining pressures. Int J Impact Eng 99:69–74CrossRefGoogle Scholar
  20. Lim J, Karakus M, Ozbakkaloglu T (2016) Evaluation of ultimate conditions of FRP-confined concrete columns using genetic programming. Comput Struct 162:28–37CrossRefGoogle Scholar
  21. Lok TS, Li X, Liu D, Zhao P (2002) Testing and response of large diameter brittle materials subjected to high strain rate. J Mater Civ Eng 14:262–269CrossRefGoogle Scholar
  22. Rocscience (2012) “RocData”. Accessed 10 Sept 2016
  23. Sarkar K, Tiwary A, Singh TN (2010) Estimation of strength parameters of rock using artificial neural networks. Bull Eng Geol Environ 69:599–606CrossRefGoogle Scholar
  24. Shen J, Karakus M (2014) Simplified method for estimating the Hoek-Brown constant for intact rocks. J Geotech Geoenviron Eng ASCE 140(6):04014025CrossRefGoogle Scholar
  25. Shen J, Karakus M, Xu C (2012) Direct expressions for linearization of shear strength envelopes given by the generalized Hoek–Brown criterion using genetic programming. Comput Geotech 44:139–146CrossRefGoogle Scholar
  26. Shen J, Jimenez R, Karakus M, Xu C (2014) A Simplified failure criterion for intact rocks based on rock type and uniaxial compressive strength. Rock Mech Rock Eng 47(2):357–369CrossRefGoogle Scholar
  27. Silva S (2007) A genetic programming toolbox for MATLAB: version 3, 2007. Accessed 10 Sept 2016
  28. Tao M, Li X, Li D (2013) Rock failure induced by dynamic unloading under 3D stress state. Theor Appl Fract Mech 65:47–54CrossRefGoogle Scholar
  29. Vásárhelyi B, Kovács L, Ákos Török (2016) Analysing the modified Hoek-Brown failure criteria using Hungarian granitic rocks. Geomech Geophys Geo-Energy Geo-Resour 2(2):131–136CrossRefGoogle Scholar
  30. Zhou Z, Li X, Ye Z, Liu K (2010) Obtaining constitutive relationship for rate-dependent rock in SHPB tests. Rock Mech Rock Eng 43:697–706CrossRefGoogle Scholar
  31. Zuo J, Liu H, Li H (2015) A theoretical derivation of the Hoek–Brown failure criterion for rock materials. J Rock Mech Geotech Eng 7:361–366CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.State Key Laboratory of Coal Mine Disaster Dynamics and ControlChongqing UniversityChongqingChina
  2. 2.Institute of Port, Coastal and Offshore EngineeringZhejiang UniversityHangzhouChina
  3. 3.E.T.S.I. Caminos, Canales y PuertosTechnical University of MadridMadridSpain

Personalised recommendations