A General Block Stability Analysis Algorithm for Arbitrary Block Shapes

In rock engineering, block theory is a fundamental theory that aims to analyze the finiteness, removability, and mechanical stability of convex blocks under different engineering conditions. In practice, the possible combinations of the fractures and joint sets that may generate key blocks can be identified by stereographic projection graphs of block theory. However, classic key block theory does not provide solutions for nonconvex blocks, which are very common in civil projects, such as those with underground edges, corners, and portals. To enhance the availability of block theory, a general algorithm that can analyze the removability and stability of blocks of arbitrary shapes is proposed in this paper. In the proposed algorithm, the joint pyramid for blocks of arbitrary shapes can be computed, and the faces of the blocks are grouped according to their normal vectors such that parallel or nonadjacent sliding faces with the same normal vector can be immediately identified when the sliding mode is determined. With this algorithm, blocks of arbitrary shapes can be analyzed, and users do not need to have experience interpreting graphs of block theory to take advantage of its accuracy and effectiveness. The proposed algorithm was verified by several benchmarking examples, and it was further applied to investigate the stability of the left bank rock slope of a dam. The results showed that the proposed algorithm is correct, effective, and feasible for use in the design and support of excavation in complex rock masses.

Flexural Performance of FRP-Reinforced Geopolymer Concrete Beam

Fibre-reinforced polymer (FRP) rebar and geopolymer concrete (GPC) are relatively new construction materials that are now been increasingly used in the construction sectors. Both materials exhibit superior structural and durability properties that also make them a sustainable alternative solution. Due to the absence of any design standard for an FRP-reinforced GPC beam, it is important to validate the efficacy of available standards and literature related to other materials, e.g., FRP-reinforced conventional concrete or GPC alone. Four theories/design standards are considered for this comparison—ACI440.1R-15, CAN/CSA S806-12, parabolic stress block theory, and equivalent rectangular stress block theory for GPC under compression. The accuracy of these four approaches is also examined by studying the flexural performance of both the glass FRP (GFRP) and carbon FRP (CFRP). The FRP-reinforced beams are designed against the actual load they will be subjected to in a real-world scenario. It is concluded that parabolic stress block theory over-estimates the capacity, whereas CSA S806-12 yields the most accurate and conservative results. In addition, the flexural performance of the FRP-reinforced beams is evaluated in terms of ultimate, cracking, and service moment capacity, along with serviceable, ultimate, and residual deflection.