Uniaxial compression failure and energy dissipation of marble specimens with flaws at the end surface
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摘要: 對含端部雙裂隙?50 mm×50 mm的圓柱體大理巖試樣進行單軸壓縮試驗，并利用高速攝影儀實時記錄試樣破壞過程，研究了端部裂隙長度和傾角對大理巖力學特性及裂紋擴展規律的影響。研究表明，當裂隙長度達到門檻值前，試樣的單軸抗壓強度的弱化程度較低，彈性模量、峰值應變的變化較小。相對垂直裂隙，相同長度的傾斜裂隙對大理巖的影響更加顯著。試驗結果與理論分析均表明，裂紋一般不從端部垂直裂隙尖端起裂，試樣的起裂裂紋大多發展為主裂紋，擴展過程中較少產生分支與分叉，試樣表面會產生局部剝落，傾斜裂隙試樣宏觀上呈剪切或拉剪復合破壞，垂直裂隙試樣呈劈裂拉伸破壞。試樣能耗參數與單軸抗壓強度的變化趨勢一致，試樣總應變能和其單軸抗壓強度有較好的正相關關系。最后，比較了動、靜載荷作用下含端部裂隙大理巖力學響應與裂紋擴展過程的差異。Abstract: It is a fact that a large number of defects such as cracks, voids, inclusions, weak planes, and joint sets are generated within the rock mass during the process of rock formation because of geological-tectonic evolution. The existence of these preexisting natural defects poses potential threats to the stability and safety of structures built on the rock mass. Therefore, it is highly significant to better understand the effects of the preexisting defects on the rock mechanical and fracture behaviors for the stability and safety assessment of rock structures. Uniaxial compression tests were carried out by using ?50 mm × 50 mm cylindrical marble specimens with double parallel flaws at end surfaces. When tests were performed, a high speed camera was used to capture the failure processes of the marble specimens. The effects of the flaw length and inclination angle on the mechanical properties and crack propagation of marble specimens were investigated. Further, the experimental results indicate that the uniaxial compressive strength, elastic modulus, and peak strain of the specimen decrease slightly before the flaw length reaches the threshold value. Compared to flaws at vertical angle 90°, flaws at inclined angles (0°<α<90°) of the same length have larger effect on the mechanical properties of marble. It is found from both the experimental and theoretical analysis that cracks usually do not start from the tip of vertical end flaws and most of initiation cracks are developed into dominant cracks. In addition, there are few branches and bifurcations in the crack propagation process, and further, local spalling also occurs at the surface of the specimen. The specimens with inclined flaws exhibit shear failure or combined shear and tensile failure and the ones with vertical end flaws show axial splitting tensile failure. The variation trend of energy consumption parameters is consistent with that of uniaxial compressive strength. It is found that total strain energy of the specimen is positively correlated with its uniaxial compressive strength. Finally, the difference between mechanical and crack propagation processes of marble specimens with end flaws under dynamic and static loads were compared.
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Key words:
- rock mechanics /
- marble /
- flaws at the end surfaces /
- strength /
- crack propagation /
- energy evolution
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圖 1 含雙裂隙大理巖試樣示意圖
Figure 1. Sketch of marble specimens containing two flaws at the end surfaces
圖 3 單軸壓縮下標準試樣的應力–應變曲線
Figure 3. Stress?strain curve of standard marble specimens under uniaxial compression
圖 4 單軸壓縮下含裂隙試樣的應力–應變曲線。（a）不同裂隙長度；（b）不同裂隙傾角
Figure 4. Stress?strain curves of flawed marble specimens under uniaxial compression: (a) different flaw lengths; (b) different flaw angles
圖 5 單軸壓縮下含裂隙試樣的裂紋擴展過程。（a）完整試樣；(b) 5 mm, 90°；（c）10 mm，90°；（d）15 mm，90°；（e）15 mm，30°；（f）15 mm, 60°
Figure 5. Crack propagation of flawed specimens under uniaxial compression: (a) intact; (b) 5 mm, 90°; (c) 10 mm, 90°; (d) 15 mm, 90°; (e) 15 mm, 30°; (f) 15 mm, 60°
圖 7 能量耗散與裂隙參數的關系。（a）不同裂隙長度；（b）不同裂隙傾角
Figure 7. Relationship between energy parameters and flaw geometries: (a) different flaw lengths; (b) different flaw angles
圖 8 輸入能和單軸抗壓強度的關系。（a）不同裂隙長度；（b）不同裂隙傾角
Figure 8. Relationship between input energy and uniaxial compressive strength: (a) different flaw lengths; (b) different flaw angles
圖 9 能量利用率與裂隙參數的關系。（a）不同裂隙長度；（b）不同裂隙傾角
Figure 9. Relationship between energy efficiency and flaw geometries: (a) different flaw lengths; (b) different flaw angles
表 1 動、靜態加載下含裂隙大理巖的力學參數均值[3]
Table 1. Mechanical parameters of flawed marble specimens under dynamic and static loads
Loading type Specimen Peak strength/
MPaElastic modulus/
GPaPeak strain/
10?2Static uniaxial compression Intact 133.40 5.94 1.95 SM–5–90 109.29 5.87 1.83 SM–10–90 123.27 5.42 2.01 SM–15–30 91.82 5.93 1.41 SM–15–60 105.04 5.76 1.55 SM–15–90 122.36 5.88 1.84 Dynamic loading DM–15–30 97.0 32.8 0.40 DM–15–60 129.0 32.8 0.52 DM–15–90 204.0 45.7 0.46 Note：S represents the static uniaxial compression test，D represents the dynamic unconfined compression test，M represents marble，5/10/15 is the flaw length，and 30/60/90 is the flaw angle. 
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