This study investigates the size effect on the compressive strength of foamed concrete at the mesoscale level combining X-ray computed tomography (X-CT) and a discrete lattice model. Image segmentation techniques and X-CT were employed to obtain virtual specimens comprising hydrated cement paste and air voids. The lineal-path function and pore size distribution was used to characterise the air void structure. A two-dimensional lattice fracture model of foamed concrete considering different wet densities was established. The model was verified experimentally at a wet density of 700 kg/m³ and then used to predict the strengths of specimens with wet densities of 600 and 800 kg/m³. Square and rectangular specimens (slenderness ratio = 2) with widths of 10, 20, 40, 70.7, and 100 mm were investigated. Results show that the air void structure significantly influences the observed size effect on the compressive strength in the investigated size range. A random forest regressor was used to predict the compressive strength of the foamed concrete; the regressor yielded satisfactory results. Finally, existing analytical size effect models were used to fit the simulated strength. Although good fitting was achieved, special attention should be given to the applicable range and physical meaning of fitted empirical parameters.

Thanks to the low cost and earth's abundant potassium resources, potassium ion batteries (PIBs) have attracted much interest as alternative energy storage devices. However, there is still a great challenge to develop suitable anode materials for PIBs with high specific capacity, fast charge/discharge and stable ion storage. Nowadays, conductive metal-organic frameworks (c-MOFs) with excellent physicochemical properties are employed for different electrochemical applications, but the study of their potassium storage performance remains unknown, and the detailed potassium storage mechanism needs to be explored. Herein, nanostructured Co₃(HHTP)₂ c-MOF (Co-CAT MOF, HHTP: 2,3,6,7,10,11-hexahydroxytriphenylene) is synthesized by a liquid-phase method and evaluated as the anode for PIBs. The active sites and open pathways in the conductive Co-CAT MOF promote ion diffusion and electron transfer, exhibiting high reversible specific capacity (332 mA h g⁻¹ at 0.1 A g⁻¹), excellent long-cycle stability (230 mA h g⁻¹ at the current density of 1.0 A g⁻¹ after 700 cycles) and outstanding rate performance (165 mA h g⁻¹ at 4.0 A g⁻¹), which is superior to the typical PIB anodes. Combined with different ex situ characterization techniques, the potassium storage mechanism based on 8-electron transfer is revealed. Furthermore, Co-CAT MOF exhibits excellent Li-ion storage performance. In the half-cell, the Co-CAT MOF electrode displays a high reversible capacity of 800 mA h g⁻¹ at 200 mA g⁻¹. In addition, the Co-CAT//LiCoO₂ full cell cycles for 100 cycles at 200 mA h g⁻¹. It is believed that Co-CAT MOF is a promising electrode material for potassium/lithium storage, and the proposed ion storage mechanism can be used to discover other MOF-based electrodes for energy storage.