A B S T R A C T Parameters of universal form of weight functions having four terms and five terms are derived for edge cracks in finite width of plate. The standard Tada Green's function is taken as the basis for the derivation. The shape of universal form of weight functions considered enables closed form expressions for cohesive toughness of three-point bending test geometry of notched concrete beams due to linear cohesive stress distribution in the fictitious fracture zone. This solution provides a viable method to determine the double-K fracture parameters: the initiation toughness, K ini IC and the unstable toughness K un IC for mode I fracture of concrete beam. A comparison with existing analytical method shows that the weight function method for determination of the double-K fracture parameters yields results without any appreciable error. The use of weight function will not only simplify the calculation to obtain the double-K fracture parameters, K ini IC and K un IC but also it will avoid the need of skilled numerical integration technique due to singularity problem at the integral boundary.

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Due to enormous growth in industrial development, the consumption of cement is substantially increased in the recent times and the cement manufacturing industry produces annually about 1.35 billion tons of the greenhouse gas emissions which are about 7% of the total greenhouse gas emission by man‐made to the atmosphere. At the same time, the thermal power plants have been generating huge quantity of fly‐ash, which is not being recycled properly. This creates huge burden on solid waste management. Hence, to minimize the emission of CO2 from cement industry and to increase the utilization of fly‐ash, a geopolymer technology is one of the viable solutions. In terms of global warming, the geopolymer technology‐based fly‐ash activated by an alkaline activators not only have potential to significantly reduce carbon footprint of ordinary portland cement concrete, but also shows considerable promise for applications in concrete industry as an alternative binder to the Portland cement. This paper provides a brief status of fly‐ash based geopolymer paste and concrete, encapsulates, and analyses critically the most significant research findings on various properties of geopolymer concrete (GPC) over the past two decades. Also, it identifies the important factors to be considered in improving the performance of GPC at elevated temperatures as well as at ambient temperatures. Collation and analysis of more than 100 research papers in this area may provide a valuable stating document for further research.

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Comparative study on analytical method, simplified method and weight function approach for determination the double-K fracture parameters using three-point bend and compact tension tests specimen geometries is presented in the paper. The input data required for numerical calculations are obtained using Fictitious Crack Model. The study reports that the double-K fracture parameters computed depends on factors such as initial-notch length/depth ratios, specimen geometry and size-effect. In addition, it is demonstrated that the use of weight function will further improve the computational efficiency without loss of accuracy.Keywords Three-point bend test · Compact tension test · Concrete fracture · Mode-I fracture · Double-K fracture parameters · Weight function · Cohesive stress Abbreviations LEFM Linear elastic fracture mechanics FCM Fictitious crack model TPBT Three-point bending test CT Compact tension WST