Actual mesostructure based three-dimensional numerical modeling method for heterogeneous geomaterials

Abstract

This paper presents a three-dimensional numerical modeling method associated with actual mesostructures for heterogeneous geomaterials. Firstly, digital image techniques are used to extract two-dimensional material heterogeneity from material surface images. Secondly, the 2D square mesostructures are extrapolated to form 3D cuboidal mesostructures with the assumption that the material surface is a representation of the inner material distribution within a very small depth. Thirdly, an iterative milling and scanning system is set up to remove the material surface layer at a very small depth. The newly exposed surface is scanned to form the new digital representation of material heterogeneity. The milling and scanning process is repeated until the entire specimen can be represented by a series of layers of the cuboidal elements. These one-layer-thick 3D mesostructures are connected in series to form the actual 3D mesostructures. Finally, the 3D mesostructures are incorporated into traditional numerical methods to examine the mechanical behavior and fracture patterns of heterogeneous geomaterials under external loadings. A Hong Kong granite specimen is used to demonstrate the procedure of the 3D mesostructure establishment. The granite heterogeneity consists of three minerals: biotite, quartz and feldspar. A 40 × 118 × 10 cuboidal model is established. The actual size of the model is 15.00 mm × 44.25 mm × 3.56 mm. By adopting the commercial finite difference code FLAC, the 3D stress distribution, crack propagation process and failure model of rock under uniaxial compression loadings are simulated. Three homogenous cases and one heterogonous case are studied. The stress distribution and failure patterns associated with the three homogenous cases and a heterogeneous case are different. The load and displacement curves show that the compressive strength of the heterogeneous case is lower than those of the homogenous cases. The numerical results indicate that material heterogeneity can play an important role in the failure behavior as well as fracture patterns of geomaterials under external loading.

提出基于真實細觀結構的巖土工程材料三維數值分析方法。運用數字圖像技術,將巖土工程材料的表面圖像轉換為材料的真實矢量細觀結構。然后通過一種簡單變換,將該矢量結構轉換為單層的三維結構。最后采用研磨及掃描循環系統,逐步掃描并生成每一層材料的表面細觀結構,將這些沿深度方向連續的細觀結構逐層逐層疊加起來,從而形成了整個試件的三維真實細觀結構。該細觀結構可以與傳統數值計算方法耦合來分析非均質巖土工程材料的力學性能。以香港花崗巖為例,采用有限差分法軟件FLAC3D,分析巖石在單軸受壓情況下的三維應力分布及裂紋的產生及擴展過程。計算結果顯示真實細觀結構能顯著影響材料的力學性能及破裂模式。