This study uses the classical Flügge shell theory and homogenization transformation method to predict the critical pressure of functionally graded material (FGM) cylindrical shells under hydrostatic pressure. The method considers the similarity in physical properties and mechanical behavior between FGM and uniform materials. The vibration equation of the coupled system of an underwater FGM cylindrical shells is derived using the wave method, taking into account the influence of fluids. The natural frequency of the FGM cylindrical shell under hydrostatic pressure is obtained using the Newton iteration method. Based on the linear correlation between critical load and load level with zero natural frequency, the fitting curve method and the formula method after homogenization transformation are used to predict and analyze the critical pressure of FGM cylindrical shells under hydrostatic pressure. The effects of various parameters on the critical pressure are discussed. The results show that the material elastic modulus E, geometric dimensions h/R and L/R of FGM cylindrical shells, and different boundary conditions have a significant impact on the critical pressure. Through multiple comparative analyses of examples, the correctness and effectiveness of the proposed method are verified. The method has high prediction accuracy and low computational cost, providing a new exploration path for the analysis of non-uniform structural mechanical behavior.

Homogenized micro-crack crushing can fully retain the bearing capacity of concrete pavement, but local weak road base needs to be reinforced before being directly overlaid with hot-mixed asphalt. Therefore, indoor tests were conducted to study the mechanical properties of slag-based geopolymer as a grouting material for weak road base, and the morphology and influence of polymerization reactants were observed. Concurrently, on-site grouting tests were conducted to study the grouting effect. The results show that the compressive strength, flexural strength and bonding strength of slag-based geopolymer all increase with age. The maximum compressive strength and flexural strength of the geopolymer at 28 d were 18.88 MPa and 6.50 MPa, respectively. The maximum flexural bonding strength at 14 d was 4.58 MPa. As the ratio between water and slag powder increased, the compressive strength and flexural strength gradually decreased, while the bonding strength first increased and then decreased. In the range of ratios of water to slag powder from 0.26 to 0.28, the above three strengths were relatively high, and the compressive shear bonding strength was the highest when the ratio of water to slag powder was 0.28. The shrinkage of the slag-based geopolymer increases with the increase in ratio of water to slag powder, and the porosity also increases, resulting in a decrease in compactness after consolidation. When the ratio of water to slag powder was 0.28, the reactant was mainly a gel-phase material, and the shrinkage crack of the consolidated geopolymer was relatively small. After grouting the weak road base of the concrete pavement, the voids at the bottom of the concrete pavement slab were effectively filled, and the deflection of the pavement slab was significantly reduced. The average deflections of monitoring line I, monitoring line II and monitoring line III decreased by 49%, 41% and 54%, respectively, after grouting. After solidification, the slag-based geopolymer was distributed in layers, which further compacted the road structure layer and improved the bearing capacity.

As functionally graded material (FGM) plates are widely used in engineering and industrial fields, the fracture strength evaluation of the cracked FGM plate becomes increasingly important. However, due to the gradation of the mechanical properties of FGM, few analytical methods are simple and available. In this paper, a convenient strength evaluation method for the cracked FGM plates under different loadings is proposed in terms of the stress intensity factor (SIF) appearing at a crack tip. This method uses the stable relationship of singular stress fields between FGM and homogeneous material to greatly simplify the complex SIF calculation process of the cracked FGM plate. The results show that the SIFs of FGM plates under tension, bending, and three-point bending (experiment) can be obtained conveniently and accurately by using two simple formulas, and the trends of critical SIF can also be investigated directly even if the SIF solution of the homogeneous plate (reference problem) is unknown. Comparisons with the published theoretical and experimental results indicated that the present method is reliable, precise, and practical to determine SIF and perform strength prediction.

Homogenized micro-crack crushing is a new method of concrete pavement rehabilitation that makes full use of the bearing capacity of the original concrete pavement, whereby the treated pavement can be directly overlaid with hot mixed asphalt concrete. In order to solve the problem of longitudinal crack extension of a cracked core in the weak position of local pavement, the crack propagation mode of concrete slabs under low-velocity impact from different numbers and distributions of impact heads was studied using numerical simulation. Moreover, field tests were also carried out to determine the optimal layout of drop hammer impact heads, and the numerical simulation results were compared with the experimental data. The results show that, when a concrete slab is impacted by a single impact head, the bottom of the slab first cracks and then the crack develops upward until the main crack runs through the concrete slab. However, when the concrete slab is impacted by multiple-impact heads, including three or four impact heads, the concrete slab forms a triangular or quadrilateral fracture core, respectively. The numerical simulation results are in good agreement with the laboratory experiments. Through the optimized arrangement of the hammer’s impact heads, the problem of longitudinal crack extension of a cracked core can be effectively solved, and the probability of reflection cracks can be reduced.