A comprehensive study of the mechanical properties of rock-like materials for inelastic deformation model establishment
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摘要:
文章旨在通过一系列标准化试验研究人造材料样品的不可逆变形行为，探究其力学特性。研究的主要思路在于制备具有既定本构行为模型的人造材料样品。借助该材料特性明确的优势，未来有望利用其对类岩石材料开展各类机械过程的可控试验，为岩石力学领域理论模型的进一步发展与验证提供有力支撑。研究制备了1组人工样品，对其进行加载试验和细致评估，以确定三轴压缩试验和单轴拉伸条件下样品的流变特性。对其中9 个样品进行了不同径向应力水平（0~5 MPa）的三轴加载试验，在控制径向应变和体积应变的情况下，将样品加载至屈服点。基于Drucker-Prager屈服面理论，系统分析了轴向−径向应力应变关系实验数据，并采用非关联塑性流动规律和盖帽模型考虑材料硬化效应。利用有限差分法对样品加载进行数值建模，为确定模型参数设置了一系列试验，通过调整数学模型参数，尽量减少模拟结果与试验数据之间的差异。试验结果显示，所建数学模型能够可靠复现所研究材料的非弹性行为，并可用于解决连续介质力学中的各类实际问题，特别是弹塑性介质中水力裂缝扩展的数值模拟。研究结果表明，在0~5 MPa的侧向荷载作用下，材料弹性极限为2~4 MPa，超出此范围即进入塑性变形阶段；当侧向荷载≥3 MPa时，材料在屈服点后会出现压密现象。从1.4 MPa侧向荷载作用的体积应变变化规律可以推断，材料在3 MPa以下的侧向荷载作用下即应开始产生压密效应。因此，在对此类材料的水力压裂过程进行建模时，必须考虑其塑性行为特征。由此得出的模型材料塑性参数可用于模拟研究岩体的弹塑性变形，包括多孔弹塑性介质中的水力裂缝扩展等过程。 文章提出的试验数据解释方法，可用于开展岩体非弹性应变累积过程的数值模拟研究。该技术途径将有效提升油气田开发优化中所用地质力学模型的可靠性。
Abstract:Objective The work is devoted to the study of irreversible deformation of artificial samples subjected to a set of standard experiments, with an aim to study their mechanical properties. The principal idea of the study is related to the preparation of an artificial material with an established constitutive behavior model. The existence of such a well-described material provides future opportunities to conduct controllable experiments on various mechanical processes in rock-like material for further development and validation of theoretical models used in rock mechanics.
Methods A set of artificial samples was prepared for careful assessment through a number of loading tests. Experimental work was carried out to determine the rheological properties under conditions of triaxial compression tests and uniaxial tension. Triaxial loading tests are completed for 9 samples with varying radial stress levels (0–5 MPa). The samples are loaded up to the yield point with control of radial and volumetric strain. The experimental results, which contain the obtained interrelationships between axial and radial stresses and strains, are analyzed using the Drucker-Prager yield surface. Material hardening is taken into account through the non-associated plastic flow law with the cap model. Numerical modeling of sample loading is performed through the finite difference method. Mathematical model parameters are adjusted to minimize the discrepancy between numerical modeling results and experimental data. The design of a series of experimental studies necessary to determine all the parameters of the model has been studied.
Results It is shown that the formulated mathematical model allows to reliably reproduce the inelastic behavior of the studied material, and it can be used to solve a set of applied problems in continuum mechanics, the problem of numerical simulation of hydraulic fracture growth in an elastoplastic medium in particular. It was found that for the entire range of applied lateral loads (0 – 5 MPa), the elastic limit varied from 2 to 4 MPa, after which the material began to behave plastically. It was also determined that at lateral loads ≥ 3 MPa, compaction began to appear in the material beyond the yield point. Judging by the dependence of volumetric strains under a lateral load equal to 1.4 MPa, compaction should begin to appear even at lateral loads lower than 3 MPa.
Conclusion Taking the plastic behavior of the material into account is necessary when moving on to modeling the hydraulic fracturing process in such a material, and the resultant plasticity parameters for the model material can be used for numerical modeling of elastoplastic deformation of the rock under consideration, including processes such as hydraulic fracture growth in a poroelastoplastic medium. [Significance] The suggested procedure to interpret results of experimental studies can be used for further numerical modeling of mechanical processes in rock masses with inelastic strain accumulation. This opportunity can increase the reliability of geomechanical models used for the optimization of hydrocarbon fields development.
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Key words:
- plastic deformation /
- internal friction /
- shear strength /
- triaxial compression /
- “Brazilian” test /
- loading diagrams
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表 1 试验约束条件
Table 1. Confining conditions in a series of experiments
Test set
conditions1 2 3 4 5 6 7 8 9 Radial stress/MPa 0.1 0.1 0.1 0.1 0.7 1.0 1.4 3.0 5.0 Peak axial stress/MPa 4.4 4.5 4.6 5.5 6.1 5.9 6.4 6.3 5.4 Volumetric strain after complete unloading/% −1.0 −0.9 −2.2 −1.3 −0.1 −0.3 0.0 0.5 1.7 
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表 2 “巴西劈裂法”测试结果
Table 2. Results of the “”Brazilian” test
Sample
numberBreaking force
P/ kNUniaxial tensile
strength UTS/MPa1 1.7 0.6 2 2.6 1.0 3 2.0 0.8 4 2.1 0.8 5 1.8 0.7 6 2.3 0.9
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表 3 特定材料特性
Table 3. Specific material properties
Calculation
numberDensity/
(g/cm3)Shear modulus/
MPaCompression
modulus/MPaInitial cohesion/
MPaHardening
coefficientDilation
coefficientCritical
strainInternal friction
coefficientσ0, MPa ε* 1 1.66 1276 2586 1.028 1.34 0.09 0.0029 0.46 2 1.66 1517 1980 0.775 1.48 0.09 0.0028 0.68 5.5 0.5
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AMOUR F, HAJIABADI M R, NICK H M, 2023. Impact of uncertainties associated with the choice of the yield stress on the prediction of subsurface reservoir compaction: a field study[J]. International Journal of Rock Mechanics and Mining Sciences, 161: 105280. doi: 10.1016/j.ijrmms.2022.105280
BÉSUELLE P, DESRUES J, RAYNAUD S, 2000. Experimental characterisation of the localisation phenomenon inside a Vosges sandstone in a triaxial cell[J]. International Journal of Rock Mechanics and Mining Sciences, 37(8): 1223-1237. doi: 10.1016/S1365-1609(00)00057-5
BIENIAWSKI Z T, 1967. Mechanism of brittle fracture of rock: part I—theory of the fracture process[J]. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 4(4): 395-406.
CASSIANI G, BROVELLI A, HUECKEL T, 2017. A strain-rate-dependent modified Cam-Clay model for the simulation of soil/rock compaction[J]. Geomechanics for Energy and the Environment, 11: 42-51. doi: 10.1016/j.gete.2017.07.001
CHEN Z L, SHI H Z, XIONG C, et al., 2023. Effects of mineralogical composition on uniaxial compressive strengths of sedimentary rocks[J]. Petroleum Science, 20(5): 3062-3073. doi: 10.1016/j.petsci.2023.03.028
DE PATER C J, CLEARY M P, QUINN T S, et al., 1994. Experimental verification of dimensional analysis for hydraulic fracturing[J]. SPE Production & Facilities, 9(4): 230-238.
DRUCKER D C, PRAGER W, 1952. Soil mechanics and plastic analysis or limit design[J]. Quarterly of Applied Mathematics, 10(2): 157-165. doi: 10.1090/qam/48291
ESCRIBANO D E, NASH D F T, DIAMBRA A, 2019. Local and global volumetric strain comparison in sand specimens subjected to drained cyclic and monotonic triaxial compression loading[J]. Geotechnical Testing Journal, 42(4): 1006-1030. doi: 10.1520/GTJ20170054
FU J W, LABUZ J F, GUO M D, et al., 2022. Experimental and numerical investigations on hydraulic fracture growth using rock-like resin material containing an injecting inner pre-crack[J]. Journal of Petroleum Science and Engineering, 213: 110424. doi: 10.1016/j.petrol.2022.110424
GARAGASH D I, 2019. Cohesive-zone effects in hydraulic fracture propagation[J]. Journal of the Mechanics and Physics of Solids, 133: 103727. doi: 10.1016/j.jmps.2019.103727
GARAGASH I A, DUBINYA N V, RUSINA O A, et al., 2018. Estimation of rock strength properties from triaxial test data[J]. Geophysical Research, 19(3): 57-72.
GARAVAND A, STEFANOV Y P, REBETSKY Y L, et al., 2020. Numerical modeling of plastic deformation and failure around a wellbore in compaction and dilation modes[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 44(6): 823-850. doi: 10.1002/nag.3041
GRUESCHOW E, RUDNICKI J W, 2005. Elliptic yield cap constitutive modeling for high porosity sandstone[J]. International Journal of Solids and Structures, 42(16-17): 4574-4587. doi: 10.1016/j.ijsolstr.2005.02.001
HAJIABADI M R, NICK H M, 2020. A modified strain rate dependent constitutive model for chalk and porous rock[J]. International Journal of Rock Mechanics and Mining Sciences, 134: 104406. doi: 10.1016/j.ijrmms.2020.104406
HE W H, CHEN K Y, HAYATDAVOUDI A, et al., 2019. Effects of clay content, cement and mineral composition characteristics on sandstone rock strength and deformability behaviors[J]. Journal of Petroleum Science and Engineering, 176: 962-969. doi: 10.1016/j.petrol.2019.02.016
JIAO Y, ZUO Y J, WEN Z J, et al., 2024. Crack-tip propagation laws and energy evolution of fractured sandstone[J]. Engineering Failure Analysis, 166: 108832. doi: 10.1016/j.engfailanal.2024.108832
JIN Y J, MENG L D, LYU D Y, et al., 2023. Risk assessment of fault reactivation considering the heterogeneity of friction strength in the BZ34-2 oilfield, Huanghekou Sag, Bohai Bay basin, China[J]. Petroleum Science, 20(5): 2695-2708. doi: 10.1016/j.petsci.2023.06.007
LIU S L, LI P F, HU K, et al., 2023. Constitutive modeling of brittle–ductile transition in porous rocks: formulation, identification and simulation[J]. Acta Mechanica, 234(5): 2103-2121. doi: 10.1007/s00707-023-03489-3
LYAKHOVSKY V, PANTELEEV I, SHALEV E, et al., 2022. A new anisotropic poroelasticity model to describe damage accumulation during cyclic triaxial loading of rock[J]. Geophysical Journal International, 230(1): 179-201. doi: 10.1093/gji/ggac062
MA S, LI G M, ZHANG Y J, et al., 2024. Propagation behavior of coal crack induced by liquid CO2 phase change blasting considering blasting pressure effects[J]. PLoS One, 19(1): e0313360.
MAHETAJI M, BRAHMA J, 2024. A critical review of rock failure criteria: a scope of machine learning approach[J]. Engineering Failure Analysis, 159: 107998 doi: 10.1016/j.engfailanal.2024.107998
NIKOLAEVSKII V N, 1971. Governing equations of plastic deformation of a granular medium: PMM vol. 35, n $\mathop = \limits^ \circ $6, 1971, pp. 1070–1082[J]. Journal of Applied Mathematics and Mechanics, 35(6): 1017-1029. doi: 10.1016/0021-8928(71)90106-7
NOVIKOVA E V, TRIMONOVA M A, DUBINYA N V, et al., 2023. Estimation of breakdown pressure in laboratory experiments on hydraulic fracturing[J]. Materials Physics and Mechanics, 51(5): 52-65.
OMAR T, SADREKARIMI A, 2015. Effect of triaxial specimen size on engineering design and analysis[J]. International Journal of Geo-Engineering, 6(1): 5. doi: 10.1186/s40703-015-0006-3
OMLIN S, RÄSS L, PODLADCHIKOV Y Y, 2018. Simulation of three-dimensional viscoelastic deformation coupled to porous fluid flow[J]. Tectonophysics, 746: 695-701. doi: 10.1016/j.tecto.2017.08.012
RONG G, LIU G, HOU D, et al., 2013. Effect of particle shape on mechanical behaviors of rocks: a numerical study using clumped particle model[J]. The Scientific World Journal, 2013: 589215. doi: 10.1155/2013/589215
SATHAR S, REEVES H J, CUSS R J, et al., 2012. The role of stress history on the flow of fluids through fractures[J]. Mineralogical Magazine, 76(8): 3165-3177. doi: 10.1180/minmag.2012.076.8.30
SCHWAB D R, BIDGOLI T S, TAYLOR M H, 2017. Characterizing the potential for injection-induced fault reactivation through subsurface structural mapping and stress field analysis, Wellington Field, Sumner County, Kansas[J]. Journal of Geophysical Research: Solid Earth, 122(12): 10132-10154.
STEFANOV Y P, CHERTOV M A, AIDAGULOV G R, et al., 2011. Dynamics of inelastic deformation of porous rocks and formation of localized compaction zones studied by numerical modeling[J]. Journal of the Mechanics and Physics of Solids, 59(11): 2323-2340. doi: 10.1016/j.jmps.2011.08.002
STEFANOV Y P, BAKEEV R A, 2015. Formation of flower structures in a geological layer at a strike-slip displacement in the basement[J]. Izvestiya, Physics of the Solid Earth, 51(4): 535-547. doi: 10.1134/S1069351315040114
STEFANOV Y P, 2018. Some nonlinear rock behavior effects[J]. Physical Mesomechanics, 21(3): 234-241. doi: 10.1134/S1029959918030074
STEFANOV Y P, ZHARASBAEVA D K, 2022. Loading diagrams and parameters of the model of elastic-pseudoplastic deformation of black shale rocks of the Bazhenov formation[J]. Russian Journal of Geophysical Technologies(3): 13-24. (in Russian
STEFANOV Y P, 2023. Constitutive model of rock, nonlinearity and localization[J]. Reviews on Advanced Materials and Technologies, 5(3): 30-38. doi: 10.17586/2687-0568-2023-5-3-30-38
SUN C, BORGOMANO J V M, FORTIN J, et al., 2020. Effect of pore collapse and grain crushing on the frequency dependence of elastic wave velocities in a porous sandstone[J]. Rock Mechanics and Rock Engineering, 53(11): 5081-5093. doi: 10.1007/s00603-020-02213-0
SUN W J, WANG L B, WANG Y Q, 2017. Mechanical properties of rock materials with related to mineralogical characteristics and grain size through experimental investigation: a comprehensive review[J]. Frontiers of Structural and Civil Engineering, 11(3): 322-328. doi: 10.1007/s11709-017-0387-9
TAN X, KONIETZKY H, FRÜHWIRT T, 2015. Numerical simulation of triaxial compression test for brittle rock sample using a modified constitutive law considering degradation and dilation behavior[J]. Journal of Central South University, 22(8): 3097-3107. doi: 10.1007/s11771-015-2846-6
TANG Y L, LI J C, WANG D P, et al., 2024. An energy-driven crushing-plasticity coupling model for grain crushing in porous rocks[J]. International Journal of Rock Mechanics and Mining Sciences, 183: 105931. doi: 10.1016/j.ijrmms.2024.105931
TRIMONOVA M, BARYSHNIKOV N, ZENCHENKO E, et al. , 2017. The study of the unstable fracure propagation in the injection well: numerical and laboratory modeling[C]//Proceedings of SPE Russian Petroleum Technology Conference. Moscow: SPE: 187822-MS.
VAN DAM D B, PAPANASTASIOU P, DE PATER C J, 2002. Impact of rock plasticity on hydraulic fracture propagation and closure[J]. SPE Production & Facilities, 17(3): 149-159.
VERMEER P A, DE BORST R, 1984. Non-associated plasticity for soils, concrete and rock[J]. Heron, 29(3): 1-64.
VESELOVSKIY R V, DUBINYA N V, PONOMAREV A V, et al., 2022. Shared research facilities "petrophysics, geomechanics and paleomagnetism" of the Schmidt institute of physics of the earth RAS[J]. Geodynamics & Tectonophysics, 13(2): 0579.
WANG D P, LI J C, ZOU C J, et al., 2024. The influence of morphology and the loading-unloading process on discontinuity stress states observed via photoelastic technique and its inspiration to induced seismicity[J]. International Journal of Rock Mechanics and Mining Sciences, 182: 105893. doi: 10.1016/j.ijrmms.2024.105893
WANG J, XIE H P, MATTHAI S K, et al., 2023. The role of natural fracture activation in hydraulic fracturing for deep unconventional geo-energy reservoir stimulation[J]. Petroleum Science, 20(4): 2141-2164. doi: 10.1016/j.petsci.2023.01.007
WENG X W, KRESSE O, CHUPRAKOV D, et al., 2014. Applying complex fracture model and integrated workflow in unconventional reservoirs[J]. Journal of Petroleum Science and Engineering, 124: 468-483. doi: 10.1016/j.petrol.2014.09.021
WILKINS M L, 1999. Computer simulation of dynamic phenomena[M]. Berlin: Springer: 1-260.
WILLIAMS B, HEARD W, GRAHAM S, et al., 2020. Effect of specimen geometry on triaxial compressive response of high-strength concrete[J]. Construction and Building Materials, 244: 118348. doi: 10.1016/j.conbuildmat.2020.118348
WONG T F, BAUD P, 2012. The brittle-ductile transition in porous rock: a review[J]. Journal of Structural Geology, 44: 25-53. doi: 10.1016/j.jsg.2012.07.010
YANG P J, MIAO S J, CAI M F, et al., 2024. Real-time porosity inversion of rock based on the ultrasonic velocity and its compression-damage coupled model under triaxial compression[J]. Scientific Reports, 14(1): 29252 doi: 10.1038/s41598-024-78430-2
YANG S Q, JING H W, WANG S Y, 2012. Experimental investigation on the strength, deformability, failure behavior and acoustic emission locations of red sandstone under triaxial compression[J]. Rock Mechanics and Rock Engineering, 45(4): 583-606. doi: 10.1007/s00603-011-0208-8
YARUSHINA V M, PODLADCHIKOV Y Y, WANG L H, 2020. Model for (de)compaction and porosity waves in porous rocks under shear stresses[J]. Journal of Geophysical Research: Solid Earth, 125(8): e2020JB019683. doi: 10.1029/2020JB019683
YIMSIRI S, SOGA K, 2002. A review of local strain measurement systems for triaxial testing of soils[J]. Journal of the Southeast Asian Geotechnical Society, 33(1): 41-52.
ZHANG B C, LIANG Y N, ZOU Q L, et al., 2024. Damage and hardening evolution characteristics of sandstone under multilevel creep–fatigue loading[J]. Geomechanics and Geophysics for Geo-Energy and Geo-Resources, 10(1): 43. doi: 10.1007/s40948-024-00751-3
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