International Journal of Frontiers in Engineering Technology, 2021, 3(9); doi: 10.25236/IJFET.2021.030910.
Zhe Liu, Jiajing Li, Wei Wang
School of Petroleum Engineering, Guangdong University of Petrochemical Technology, Maoming 525000, Guangdong, China
This paper studies the stress-strain relationship of rock in the process of loading and unloading. Taking sandstone as an example, conventional triaxial loading and unloading experiments are carried out. The non-linear characteristics of rock during the post-peak unloading stage are analyzed, and the damage variable of rock is defined. An elastic modulus model for describing the stress-strain relationship during post-peak unloading is presented. The relationship between the axial strain and the radial strain in the loading-unloading process is analyzed; the Poisson's ratio model in unloading process is obtained. The D-P plastic model is introduced to modify the hardening function according to the plastic hardening characteristics of sandstone; a damage model associated with equivalent plastic strain is established. The computational model is matrixed and then calculated numerically. In the process, the following conclusions are drawn: (1) The porous rock shows obvious non-linear characteristics during loading. With the increase of body stress, the elastic modulus of rock increases gradually. (2) When the axial stress is greater than the confining pressure in the process of unloading rock after peak load, Stress-strain can be described by multiplying the elastic modulus model of the pre-peak elastic stage by the continuity factor. (3) With the increase of equivalent plastic strain, Poisson's ratio increases first, then decreases, and finally tends to be stable. In the post-peak unloading process, the equivalent plastic strain does not change, while the Poisson's ratio remains unchanged. The results show that the proposed model can reflect the stress-strain law of rock during post-peak unloading.
Rock Mechanics, Stress-Strain Relationship, Modulus of Elasticity
Zhe Liu, Jiajing Li, Wei Wang. Loading-Unloading Mechanical Characteristics and Constitutive Model of Porous Rock. International Journal of Frontiers in Engineering Technology (2021), Vol. 3, Issue 9: 56-65. https://doi.org/10.25236/IJFET.2021.030910.
[1] Wang, X. X., Ma, W. J., Huang, J. W., & Liao, Z. Y. (2014) “Mechanical Properties of Sandstone under Loading and Unloading Conditions”, Advanced Materials Research, 852(1), pp. 441-446.
[2] Imole, O. I., Wojtkowski, M., Magnanimo, V., & Luding, S. (2014) “Micro-macro Correlations and Anisotropy in Granular Assemblies under Uniaxial Loading and Unloading”, Physical Review E Statistical Nonlinear & Soft Matter Physics, 89(4), pp.042210.
[3] Koniorczyk, M., Gawin, D., & Schrefler, B. A. (2015) “Modeling Evolution of Frost Damage in Fully Saturated Porous Materials Exposed to Variable Hygro-thermal Conditions”, Computer Methods in Applied Mechanics & Engineering, 297(3), pp. 38-61.
[4] Zeng, Z., & Tan, J. C. (2017) “Afm Nanoindentation to Quantify the Mechanical Properties of Nano- and Micron-sized Crystals of A Metal-organic Framework Material”, Acs Appl Mater Interfaces, 9(45), pp.39839-39854.
[5] Bi, L., & Pan, G. (2014) “Facile and Green Fabrication of Multiple Magnetite Nano-cores@void@porous Shell Microspheres for Delivery Vehicles”, Journal of Materials Chemistry A, 2(11), pp.3715-3718.
[6] Liu, X. R., Liu, J., Dong-Liang, L. I., Chun-Mei, H. E., Wang, Z. J., & Xie, Y. K. (2017) “Experimental Research on the Effect of Different Initial Unloading Levels on Mechanical Properties of Deep-buried Sandstone”, Rock & Soil Mechanics, 38(11), pp. 3081-3088.
[7] Mehdizadeh, S. (2014) “Profiles and Projections of Ohio's 60 Population: County-By-County”, Journal of Materials Science, 49(1), pp. 163-179.
[8] Liang, Y., Li, Q. , Gu, Y. , & Zou, Q. . (2017) “Mechanical and Acoustic Emission Characteristics of Rock: Effect of Loading and Unloading Confining Pressure at the Postpeak Stage”, Journal of Natural Gas Science and Engineering, 44(3), pp. 54-64.
[9] Dong, X., Tian-Hong, Y. , Pei-Tao, W. , Peng-Hai, Z. , & Yong-Chuan, Z. . (2014) “Experimental Study of Acoustic Emission Characteristics of Dry and Saturated Rocks during Cyclic Loading and Unloading Process”, Journal of China Coal Society, 39(7), pp.1243-1247.
[10] Therefore. (2018) “Mechanical Behavior of Shale Rock under Uniaxial Cyclic Loading and Unloading Condition”, Advances in Civil Engineering, 2018(3), pp.1-8.
[11] Huo, L., Zhou, Y., Yang, C. H., Mao, H. J., Liu, J. X., & Chen, X. L. (2017) “Experimental Study of Unloading Mechanical Behaviour of Mudstone in Different Geological Era”, Rock & Soil Mechanics, 38(3), pp. 714-722.