A comprehensive study of the mechanical properties of rock-like materials for inelastic deformation model establishment
doi: 10.12090/j.issn.1006-6616.2024094
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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. -
Key words:
- plastic deformation /
- internal friction /
- shear strength /
- triaxial compression /
- “Brazilian” test /
- loading diagrams
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图 1 典型试验结果
a—应力、应变与时间的关系; b—轴向应力与轴向、径向和体积应变的关系
Figure 1. Typical experimental results
(a) Dependence of stress and strain on time; (b) Dependence of axial stress on axial, radial, and volumetric strains
图 2 综合试验结果
a—轴向应力与轴向应变的关系; b—轴向应力与体积应变的关系
Figure 2. Combination of experimental results
(a) axial stress dependence on axial strain; (b) axial stress dependence on volumetric strain
图 3 室内试验中获得的应力与应变关系示例
Figure 3. An example of the dependence of stress on strain obtained during a laboratory experiment
图 4 Drucker-Prager屈服面参数的测定
Figure 4. Determination of Drucker-Prager yield surface parameters
图 5 试验过程中塑性变形张量第一不变量的增量与剪切塑性变形强度增量的关系
Figure 5. Dependence of the increment of the first invariant of the plastic deformation tensor on the increment of the intensity of shear plastic deformations for a series of experiments
图 6 “巴西劈裂法 ”测试后破裂试样
Figure 6. Destroyed sample after testing using the “Brazilian” method
图 7 不同围压条件下轴向应力与轴向应变（红线）、径向应变（绿线）和体积应变（蓝线）的关系
实线—试验数据；虚线—1 号数据的计算结果；点虚线—2 号数据的计算结果
Figure 7. Axial stress dependence on axial strain (red line), radial strain (green line), and volumetric strain (blue line) with different radial stresses. solid lines–experimental data; dashed lines–calculation with data No. 1; dotted lines–calculation with data No. 2
表 1 Confining conditions in a series of experiments
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 Results of the “”Brazilian” test
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 Specific material properties
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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