深埋花岗岩细观力学特性纳米压痕试验及参数均质化研究

Meso-mechanical properties of deep granite using nanoindentation test and homogenization approach

采用纳米压痕试验研究双江口地下厂房花岗岩主要矿物石英、钾长石、斜长石以及云母的细观力学特性。为研究纳米压头压入峰值荷载与力学参数之间的关系,石英、钾长石和斜长石纳米压痕试验的峰值荷载取2×10^(-3),3×10^(-3),4×10^(-3),5×10^(-3),6×10^(-3),7×10^(-3)和8×10^(-3) N,云母的纳米压痕试验的峰值荷载取1×10^(-3),2×10^(-3),3×10^(-3),4×10^(-3)和5×10^(-3)N。基于细观力学参数结果,采用稀疏(Dilute)法、Mori-Tanaka法和自洽(Self-consistent)法3种均质化方法求解花岗岩的等效弹性模量和泊松比,并与三轴压缩试验测定的宏观弹性模量和泊松比进行对比。研究结果表明:石英力学性质良好,钾长石次之,斜长石较差,云母最差且其测试参数最为离散;石英、钾长石和斜长石的弹性模量和硬度随峰值荷载的增大呈减小趋势,当峰值荷载达到5×10^(-3) N时,弹性模量和硬度测试结果趋于稳定,其弹性模量均值分别为105.5,100.8和68.1 GPa,硬度均值分别为14.8,11.7和3.1 GPa;云母受其片状层理结构和内部孔洞的影响,弹性模量和硬度随峰值荷载的变化趋势不明显,其弹性模量和硬度分别为44.2~47.8 GPa和1.57~2.01 GPa。均质化方法获得的等效泊松比与三轴压缩试验测得的宏观泊松比基本相同;均质化方法获得的等效弹性模量均大于三轴压缩试验测得的结果,其中Self-consistent法所得等效弹性模量偏差最大,Mori-Tanaka法次之,Dilute法最小;均质化方法获得的等效弹性模量更接近于高围压下的宏观弹性模量。

The meso-mechanical properties of quartz, K-feldspar, plagioclase and mica were studied by nanoindentation tests. To study the relationships between the meso-mechanical parameters of granite minerals and peak loads, nanoindentation tests were designed for quartz, potash feldspar and plagioclase under peak loads of2×10^(-3), 3×10^(-3), 4×10^(-3), 5×10^(-3), 6×10^(-3), 7×10^(-3) and 8×10^(-3) N, and for mica under peak loads of 1×10^(-3), 2×10^(-3),3×10^(-3), 4×10^(-3) and 5×10^(-3) N. The equivalent elastic moduli and Poisson’s ratios of granite were obtained by three homogenization approaches, i.e., Dilute, Mori-Tanaka, and Self-consistent approaches, based on the tested mesomechanical parameters of the primary minerals of granite. The equivalent elastic moduli and Poisson’s ratios obtained by three homogenization approaches were compared with those from triaxial compression tests. The results show that quartz has the best mechanical properties, followed by K-feldspar and plagioclase, and mica has the worst mechanical properties and the most discrete test parameters. The elastic moduli and hardness of quartz,potassium feldspar, and plagioclase decrease with the increase of the peak load of indentation. When the peak load reaches 5×10^(-3) N, the tested elastic moduli and hardness tend to be stable, and the average elastic moduli of quartz,potassium feldspar and plagioclase are 105.5, 100.8 and 68.1 GPa, respectively, and the average hardness is 14.8,11.7 and 3.1 GPa, respectively. The trend of elastic moduli and hardness of mica with peak load is not obvious due to the influence of lamellar bedding and microporous of mica, and the tested elastic moduli and hardness are 44.2-47.8 GPa and 1.57-2.01 GPa, respectively. The equivalent Poisson’s ratios from the homogenization approaches are basically the same as the macroscopic Poisson’s ratios from the triaxial compressive tests. The equivalent elastic moduli from the homogenization approaches are greater than the macroscopic elastic moduli from the triaxial tests. There exist differences between the equivalent elastic moduli from Self-consistent approach those from the triaxial tests. Among them, the predictions from self-consistent approach has the largest deviation, the predictions from Mori-Tanaka approach has the second deviation, and the predictions from dilute approach has the smallest deviation. The equivalent elastic moduli from the homogenization approaches are generally closer to the tested macroscopic elastic modulus under high confining pressure.