This article presents nondimensional solutions for laterally loaded piles in sand considering nonlinear soil–pile interactions. A nonlinear elastoplastic p–y model, termed the H-model, is introduced, and its ability to model the responses of laterally loaded piles in sand is demonstrated. Nondimensional forms of both the H-model and the governing equation for laterally loaded piles are then derived, after which the nondimensional responses of free-head piles subject to lateral forces and moments and that of fixed-head piles subject to lateral forces are evaluated using the finite-element method. It is found that (1) the pile responses are significantly affected by the nondimensional pile length; and (2) using nonlinear soil–pile interaction, the critical length of the pile increases with increasing normalized displacement and is noticeably larger than that utilizing linear soil–pile interaction. The quantitative nondimensional relationship between force and the moment responses of free- and fixed-head long piles is also obtained. Two design curves, normalized force against normalized displacement and normalized force against maximum normalized moment, are presented. Illustrative examples are given to show the step-by-step procedure for how the curves could be used in practice to estimate the behavior of piles.
This study investigates the ultimate bearing capacity and typical failure mechanisms of a rough strip footing constructed above an irregular cavity using the upper bound finite element limit analysis (UBFELA) method. A novel method based on the inverse discrete Fourier transform (IDFT) theory is employed to generate and quantitatively describe the irregular shape of natural cavities. Parametric studies are performed to study the influence of several variables, including the ratio of the cavity size to the strip footing width (D/B), the ratio of the cover depth to the footing width (H/B), the internal friction angle (φ), the direction angle of the long axis of the cavity (θ) and the shape descriptors of the cavity (D2, D3, and D8). Numerical results are presented in the form of dimensionless charts for the bearing capacity numbers (Pu/c). The obtained failure modes present significant asymmetry and a critical region is found to be greatly affected by the size of the cavity (D/B), the cavity depth (H/B) and the internal friction angle (φ).
Abstract Biochar has the potential to be a soil amendment in green roofs owing to its water retention, nutrient supply, and carbon sequestration application. The combined effects of biochar and vegetated soil on hydraulic performance (e.g., saturated hydraulic conductivity, retention and detention, and runoff delay) are the crucial factor for the application of the novel biochar in green roofs. Recent studies investigated soil water potential (i.e., suction) either on vegetated soil or on biochar‐amended soil but rarely focused on their integrated application. With the purpose of investigating the hydraulic performance of green roofs in the application of biochar, the combined effect of biochar and vegetated soil on hydrological processes was explored. Artificial rainfall experiments were conducted on the four types of experimental soil columns, including natural soil, biochar‐amended soil, vegetated natural soil, and vegetated biochar‐amended soil. The surface ponding, bottom drainage and the volumetric water content were measured during the rainfall test. Simulation method by using HYDRUS‐1D was adopted for estimating hydraulic parameters and developing modelling analysis. The results indicated that the saturated hydraulic conductivity of vegetated soil columns were higher than bare soil columns. The addition of biochar decreased the saturated hydraulic conductivity, and the magnitude of decrease was much significant in the case of vegetated soil. The influence of vegetation on permeability is more prominent than biochar. The vegetated biochar‐amended soil has the highest retention and detention capacity, and shows a preferable runoff delay effect under heavy rain among the four soil columns. The results from the present study help to understand the hydrological processes in the green roof in the application of biochar, and imply that biochar can be an alternative soil amendment to improve the hydraulic performance.
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