Rock block is the key research object of underground cavern and slope as well as foundation engineering. Block theory is one of the critical methods of stability analysis in rock mechanics. Based on the classical block theory, in this study the essential concepts of block is extended firstly to include both intersections and unions of half-spaces. After that, a unified and generalized symbolic representation method was proposed based on three classical methods of representation for convex blocks. A symbol i in the middle of two notations of face half-spaces suggests intersection of the two half-spaces while a symbol u suggests union of the two half-spaces. After that, the algorithm of successive cutting of remaining block is proposed. A non-convex block can be cut into a number of convex blocks connected only by the cutting planes. The shape and size of the non-convex block can therefore be obtained. Comparative study was carried out on a practical example. Compared to the conventional method, the efficiency of the proposed method is improved significantly.
The effect of alteration on the geochemistry and mechanical properties of granite from Pingjiang, Hunan Province, China was investigated. Six weathered and 14 hydrothermally altered samples in three footrills (PD2, PD3, and PD4) were collected for mechanical tests and major and trace element analysis. The results show that the relationship between mechanical strength and the degree of alteration, irrespective of whether this is due to weathering or hydrothermal alteration, can be described by an exponential equation. This implies that the mechanical strength decreases rapidly even at low degrees of alteration. Granite Na 2 O, CaO, K 2 O, and SiO 2 contents were lowered due to weathering, whereas Fe 2 O 3 T contents increased signi cantly due to Fe 2+ oxidation. Based on the hypothesis that Al and Zr are immobile during the hydrothermal alteration, the mobility indexes of various elements were calculated for the hydrothermally altered samples. In general, TiO 2 , K 2 O, Fe 2 O 3 T , Th, Hf, Co, Ni, and V contents were unaffected by hydrothermal alteration; Na 2 O, Sr, Nd, Sm, and Pb contents were lowered by hydrothermal alteration; and SiO 2 , Rb, Cr, U, Zn, Mn, and Cs contents were increased due to reactions with the hydrothermal uids. Even immobile elements, such as Sm, Nd, V, and Cr, were mobilized by high-temperature hydrothermal uids. To assess the degree of hydrothermal alteration, a new model is required that can account for the effects of the different mineral components.
The combination of free planes in the corner of an underground chamber is complex. If the fractures cross the roof and walls, or floor and walls at the same time, a complex key block may exist. The theorem of finiteness in the classical block theory applies only to the convex block, and not to the non-convex. Based on the analysis of the system of spatial planes and the system of blocks, the operations of intersection and union between the half-spaces of surface planes are represented explicitly with two symbols. All the possible finite convex blocks can be analysed by enumeration at first. Then according to the theory of united blocks and the principles that the codes of fractures keep the same all the time, a complete combination of a non-convex block is determined. Further, cutting along the free planes which include concave intersections, the new combination, in which the convex blocks are connected only at the cutting planes, is optimized. Finally, the identification of complex block in the corner of an underground chamber is implemented. The case of practical engineering shows that, the method is correct and effective, and lay a solid theoretical foundation for the further study on the cases of edges or intersecting tunnel. The method also have some practical values to guarantee the safety of underground engineering.
A granite mass in Xinyang, China, was studied to better understand the features of the link between permeability and resistivity. The permeability coefficient of subsurface media has a certain correlation with electrical conductivity. The following steps are conducted in this method; first, water pressure tests were conducted on the borehole to determine the permeability of the granite mass at different depths; next, the electrical resistivity values of the borehole rock were determined using geophysical logging techniques; finally, three mathematical models were chosen to construct the relationship between the two, and their applicability in the study area was confirmed. The method has some applicability and can serve as a guide for the design of reservoir impermeability. It was discovered that the calibration permeability obtained by inverting the power function model has the greatest applicability and can be applied to the permeability zoning of two high-density logging lines to obtain the characteristic dividing line of 0.5 Lu and 1.0 Lu more clearly and that this method has certain applicability and can serve as a reference for the design of reservoir impermeability.
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