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Crack Coalescence in Molded Gypsum and Carrara Marble: Part 1. Macroscopic Observations and Interpretation


Cracking and coalescence behavior has been studied experimentally with prismatic laboratory-molded gypsum and Carrara marble specimens containing two parallel pre-existing open flaws. This was done at both the macroscopic and the microscopic scales, and the results are presented in two separate papers. This paper (the first of two) summarizes the macroscopic experimental results and investigates the influence of the different flaw geometries and material, on the cracking processes. In the companion paper (also in this issue), most of the macroscopic deformation and cracking processes shown in this present paper will be related to the underlying microscopic changes. In the present study, a high speed video system was used, which allowed us to precisely observe the cracking mechanisms. Nine crack coalescence categories with different crack types and trajectories were identified. The flaw inclination angle (β), the ligament length (L), that is, intact rock length between the flaws, and the bridging angle (α), that is, the inclination of a line linking up the inner flaw tips, between two flaws, had different effects on the coalescence patterns. One of the pronounced differences observed between marble and gypsum during the compression loading test was the development of macroscopic white patches prior to the initiation of macroscopic cracks in marble, but not in gypsum. Comparing the cracking and coalescence behaviors in the two tested materials, tensile cracking generally occurred more often in marble than in gypsum for the same flaw pair geometries.

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  1. These cracks are found to consist of individual discontinuous crack segments when examined under ESEM (environmental scanning electron microscope). See the companion paper by the same authors in this issue.


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The project is sponsored by the NSF Geomechanics and Geotechnical Systems Program under grant CMMI-0555053 and the US Department of Energy Geothermal Program under grant DE-FG36-06GO16061. The first author is also thankful to the support by the Croucher Foundation Scholarship (Hong Kong) and the Sir Edward Youde Memorial Fellowship (Hong Kong).

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Correspondence to H. H. Einstein.



This Appendix shows the detailed analysis of cracking processes of the marble specimen with flaw pair geometry 4a-30-120. Figure 30a shows the view of the front face of the specimen before the start of the uniaxial compression loading test. In response to the applied loading, a number of elongated white patches emanated from the flaw tips (Fig. 30b). The subsequent cracking processes are shown in Fig. 31, which consists of a number of high speed images and a final schematic cracking sketch. In Fig. 31, the left column contains individual high speed images which were captured at a rate of 6,600 frames/second, and the right column contains the corresponding descriptions of cracking processes and/or other deformations observed from the video. Each description is preceded by two numbers at the top, for example, the numbers corresponding to the first image in Fig. 31 are:

$$ \begin{gathered} (54.78\;{\text{Mpa}}) \hfill \\ {\text{HS Image}}\# - 6147 \hfill \\ \end{gathered} $$
Fig. 30
figure 30

a View of the specimen (CM 4a-30-120-C) before the start of the uniaxial compression loading test. b A high speed video image and its corresponding sketch showing the development of white patches from the flaw tips in response to the early applied loading increased

Fig. 31
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Cracking processes recorded at a frame rate of 6,600 frames per second in marble specimen CM 4a-30-120-C

The first number corresponds to the applied stress value at which the image is taken. The second number refers to the image number of the particular image (shown in the left column of Fig. 31) captured from the high speed (HS) video. The time interval between any two images can be calculated from the frame rate at which the high speed video was captured. For example, the image numbers of the first image and the second image shown in Fig. 31 are 6,147 and 4,273, respectively. The time interval is given by dividing the difference of 6,147 and 4,273 by 6,600 (frame rate), that is, 0.283 s.

On each high speed image shown in the left column, all the identifiable new cracks (thin solid lines) and the white patches developed in response to loading are identified by reference letters, for example, B, C, etc. Each letter is then followed by a letter T or S in parentheses, which refers to either the tensile mode or the shear mode of crack initiation, respectively. Letters without T, S refer to white patches. The sequence of crack initiation is indicated by numbers shown as subscripts at the end. The first crack to initiate is designated as 1, the second crack as 2, etc. The same number will be assigned to multiple cracks which are observed to initiate simultaneously in the videos. Take crack F’(T)3 as an example. This crack is identified to initiate in a tensile mode from the right tip of the top flaw following the initiation of other cracks with numbers 1 and 2. A pair of arrows and the letter S in parentheses over its trace indicates the sense of shearing which occurred along it after its initiation as a tensile crack. In addition to the observable cracks, the traces of multiple white patches (e.g., A, B, C in the first images), which are free of any observable macroscopic cracks, and develop in response to the applied loading, are also identified. These white patches are represented by thick grey lines in the sketch at the end of Fig. 31.

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Wong, L.N.Y., Einstein, H.H. Crack Coalescence in Molded Gypsum and Carrara Marble: Part 1. Macroscopic Observations and Interpretation. Rock Mech Rock Eng 42, 475–511 (2009).

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  • Uniaxial compressive loading test
  • High speed camera
  • Tensile cracks
  • Shear cracks
  • Crack type classification scheme