Abstract
In order to investigate mechanical behavior of red sandstone under cyclical compressive and tensile loads, a series of short-term uniaxial constant cyclical compressive and tensile loading tests and uniaxial constant cyclical compressive and tensile loading creep tests were conducted. First, based on the results of short-term uniaxial constant cyclical compressive and tensile loading experimental, the permanent residual strain, strains at peak stress were analyzed. Results show that the specimen shows permanent residual strain after suffering short-term cyclic loads; the residual strains and strains at peak stress show the “decay increase” and “steady-state increase” stages with the cyclic number N; the relationship between the strain at peak stress (tensile or compressive stress) and cyclic number can be well described by a modified Burger model. And then, in accordance with the creep experimental results, the creep behavior of the red sandstone was analyzed. Results show that there is obvious instantaneous strain, decay creep, and steady creep under each stress level of tensile or compressive stress stages; the specimen appears accelerated creep stage under the 5th tensile stress of 1.19 MPa. It was also found that power function can better express the relationship between steady strains and cycle number under tensile or compressive stress levels. In the end, a viscoelastic-plastic creep model was proposed; comparison of the test results with the proposed viscoelastic-plastic creep model predictions indicates that the proposed model is capable of describing the creep behavior of red sandstone subjected to cyclic tensile and compressive stress loading.
Similar content being viewed by others
Abbreviations
- \( {E}_1^N \) :
-
Elastic modulus of the Maxwell body related to short-term cycle number
- \( {\eta}_1^N \) :
-
Viscosity coefficient of the Maxwell body related to short-term cycle number
- \( {E}_2^N \) :
-
Elastic modulus of the Kelvin body related to short-term cycle number
- \( {\eta}_2^N \) :
-
Viscosity coefficient of the Kelvin body related to short-term cycle number
- N :
-
Cycle number
- ε 1 :
-
Axial strain
- ε 3 :
-
Lateral strain
- ε v :
-
Volumetric strain
- η 0 :
-
Initial viscosity coefficient
- t 0 :
-
Unit time, which value is 1
- n :
-
Creep parameter, which related to the cycle number
- E 1 :
-
Elastic modulus of the Maxwell body
- E 2 :
-
Elastic modulus of the Kelvin body
- η 2 :
-
Viscosity coefficient of the Kelvin body
- t :
-
Creep time under each creep stress level
- η(n, t):
-
Viscosity coefficient, which decrease with the cycle number-dependent creep time
References
Arabani M, Kamboozi N (2013) The linear visco-elastic behaviour of glasphalt mixture under dynamic loading conditions. Constr Build Mater 41:594–601
Bagde MN, Petroš V (2005) Fatigue properties of intact sandstone samples subjected to dynamic uniaxial cyclical loading. Int J Rock Mech Min Sci 42(2):237–250
Cao P, Wen YD, Wang YX, Yuan HP, Yuan BX (2016) Study on nonlinear damage creep constitutive model for high-stress soft rock. Environ Earth Sci 75(10):1–8
Erarslan N, Williams D (2012) The damage mechanism of rock fatigue and its relationship to the fracture toughness of rocks. Int J Rock Mech Min Sci 56:15–26
Fairhurst CE, Hudson JA (1993) Draft ISRM suggested method for the complete stress train curve for the intact rock in uniaxial compression. Int J Rock Mech Min Sci 36(3):279–289
Fuenkajorn K, Phueakphum D (2010) Effects of cyclic loading on mechanical properties of Maha Sarakham salt. Eng Geol 112:43–52
Ge X, Jiang Y, Lu Y, Ren J (2003) Testing study on fatigue deformation law of rock under cyclic loading. Chin J Rock Mech Eng 22(10):1581–1585 (in Chinese)
Huang D, Li YR (2014) Conversion of strain energy in Triaxial unloading tests on marble. Int J Rock Mech Min 66:160–168
Khaledi K, Mahmoudi E, Datcheva M, Schanz T (2016) Stability and serviceability of underground energy storage caverns in rock salt subjected to mechanical cyclic loading. Int J Rock Mech Min Sci 86:115–131
Liu JF, Xie HP, Hou ZM, Yang CH, Chen L (2014) Damage evolution of rock salt under cyclic loading in unixial tests. Acta Geotech 9:153–160
Liu XS, Ning JG, Tan YL, Gu QH (2016) Damage constitutive model based on energy dissipation for intact rock subjected to cyclic loading. Int J Rock Mech Min Sci 85:27–32
Liu HZ, Xie HQ, He JD, Xiao ML, Zhuo L (2017) Nonlinear creep damage constitutive model for soft rocks. Mech Time-Depend Mater 21:73–96
Loghman A, Azami M (2016) A novel analytical-numerical solution for nonlinear time-dependent electro-thermo-mechanical creep behavior of rotating disk made of piezoelectric polymer. Appl Math Model 40(7–8):4795–4811
Ma LJ, Liu XY, Wang MY, Xu HF, Hua RP, Fan PX, Jiang SR, Wang GA, Yi QK (2013) Experimental investigation of the mechanical properties of rock salt under triaxial cyclic loading. Int J Rock Mech Min Sci 62:34–41
Oliveira DV, Lourenço PB, Roca P (2006) Cyclic behaviour of stone and brick masonry under uniaxial compressive loading. Mater Struct 39(2):247–257
Roberts LA, Buchholz SA, Mellegard KD, Düsterloh U (2015) Cyclic loading effects on the creep and dilation of salt rock. Rock Mech Rock Eng 48:2581–2590. https://doi.org/10.1007/s00603-015-0845-4
Song HP, Zhang H, Fu DH, Zhang Q (2016) Experimental analysis and characterization of damage evolution in rock under cyclic loading. Int J Rock Mech Min Sci 88:157–164
Wang ZC, Li SC, Qiao LP, Zhao JG (2013) Fatigue behavior of granite subjected to cyclic loading under Triaxial compression condition. Rock Mech Rock Eng 46:1603–1615. https://doi.org/10.1007/s00603-013-0387-6
Wang XG, Hu B, Tang HM, Hu XL, Wang JD, Huang L (2016) A constitutive model of granite shear creep under moisture. J Earth Sci 27(4):677–685
Wu LZ, Li B, Huang RQ, Sun P (2017) Experimental study and modeling of shear rheology in sandstone with non-persistent joints. Eng Geol 222:201–211
Zhang Y, Xu WY, Gu JJ, Wang W (2013) Triaxial creep tests of weak sandstone from fracture zone of high dam foundation. J Cent South Univ 20(9):2528–2536
Zhao BY, Liu DY, Dong Q (2011) Experimental research on creep behaviors of sandstone under uniaxial compressive and tensile stresses. J Rock Mech Geotech Eng 3(Supp):438–444
Zhao BY, Liu W, Xu NC, Li ZY (2016) Development of a rock tensile and compression creep testing machine and its application. J Exp Mech 31(2):238–242 (in Chinese)
Zheng H, Feng XT, Hao XJ (2015) A creep model for weakly consolidated porous sandstone including volumetric creep. Int J Rock Mech Min Sci 78:99–107
Acknowledgments
The authors also thank Prof. YANG Mijia for his valuable suggestions and English improvement of this manuscript, which comes from department of civil and environmental engineering, North Dakota State University.
Funding
This study was partially supported by the National Natural Science Foundation of China (Grant No. (41302223), Science and Technology Plan Projects of Chongqing Administration of Land, Resources and Housing (KJ-2015047), Chongqing No. 3 colleges and universities youth backbone teachers funding plans and Chongqing Research Program of Basic Research and Frontier Technology (cstc2016jcyjA0074, cstc2016jcyjA0933, cstc2015jcyjA90012), Scientific and Technological Research Program of Chongqing Municipal Education Commission (KJ1713327,KJ1600532).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Zhao, B., Liu, D. & Liu, W. Mechanical behavior of sandstone under uniaxial constant cyclical compressive and tensile loading. Arab J Geosci 11, 490 (2018). https://doi.org/10.1007/s12517-018-3845-3
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s12517-018-3845-3