Buckling Analysis of Piles in Multi-Layered Soils

Pile buckling is infrequent, but sometimes it can occur in slender piles (i.e., micropiles) driven into soils with soft layers and/or voids. Buckling analysis of piles becomes more complex if the pile is surrounded by multi-layered soil. In this case, the well-known Timoshenko’s solution for pile buckling is of no use because it refers to single-layered soils. A variational approach for buckling analysis of piles in multi-layered soils is herein proposed. The proposed method allows for the estimation of the critical buckling load of piles in any multi-layered soil and for any boundary condition, provided that the distribution of the soil coefficient of the subgrade reaction is available. An eigenvalue-eigenvector problem is defined, where each eigenvector is the set of coefficients of a Fourier series describing the second-order displaced shape of the pile, and the related buckling load is the eigenvalue, thus obtaining the effective buckling load as the minimum eigenvalue. Besides the pile deformed shape, the stiffness distribution in the multi-layered soil is also described through a Fourier series. The Rayleigh–Ritz direct method is used to identify the Fourier development coefficients describing the pile deformation. For validation, buckling analysis results were compared with those obtained from an experimental test and a finite element analysis available in the literature, which confirmed this method’s reliability.

The Analytical Solution of the Grouting Migration Height for the Post-Grouted Drilled Shaft Based on the Herschel-Bulkley Model

The traditional bored pile technology has some arduous problems, such as the sediment at the pile tip, the mud skin along the pile shaft, and the stress release due to borehole construction. The post-grouted technology at the pile tip of bored pile has emerged because of demand. The grouting migration height (GMH) is of great significance to the strengthen and reinforcement of the pile foundation. This paper derives the calculation formula of the GMH based on the theory of the column hole expansion and Herschel-Bulkley model. The influence of relevant parameters on the GMH is discussed. Aiming at the problem of the grouting migration along the pile shaft in layered soils, the iterative calculation method of the GMH is proposed. The correctness of the GMH is verified by an engineering case, which can guide the engineering practice. The result shows that the GMH increases with the increase of the grouting pressure, the pile diameter and the thickness of the mud skin, and the grouting pressure is positively correlated with the GMH. The GMH decreases with the increase of the buried depth, the consistency coefficient and the rheological index. On this basis, the correctness of the GMH is verified by an engineering case.

Development and Validation of a Box and Flux Model to Describe Major, Trace and Potentially Toxic Elements (PTEs) in Scottish Soils

The box and flux model is a mathematical tool used to describe and forecast the major and trace elements perturbations of the Earth biogeochemical cycles. This mathematical tool describes the biogeochemical cycles, using kinetics of first, second and even third order. The theory and history of the box and flux modeling are shortly revised and discussed within the framework of Jim Lovelok’s Gaia theory. The objectives of the investigation were to evaluate the natural versus anthropic load of Potentially Toxic Elements (PTEs) of the Scottish soils, investigate the soil components adsorbing and retaining the PTEs in non-mobile species, evaluate the aging factor of the anthropic PTEs and develop a model which describes the leaching of PTEs in layered soils. In the Scottish land, the soil-to-rock enrichment factorinversely correlates with the boiling point of the PTEs. The same is observed in NW Italy and USA soils, suggesting the common source of the PTEs. The residence time in soils of the measured PTEs linearly correlates with the Soil Organic Matter (SOM). The element property which mostly explains the adsorption capacity for PTEs’ is the ionic potential (IP). The downward migration rates of the PTEs inversely correlate with SOM, and in Scottish soil, they range from 0.5 to 2.0 cm·year−1. Organic Bentoniteis the most important soil phase adsorbing cation bivalent PTEs. The self-remediation time of the polluted soil examined ranged from 50 to 100 years. The aging factor, the adsorption of PTEs’ into non-mobile species, and occlusion into the soil mineral lattice was not effective. The box and flux model developed, tested and validatedhere does not describe the leaching of PTEs following the typical Gaussian shape distribution of the physical diffusion models. Indeed, the mathematical model proposed is sensitive to the inhomogeneity of the layered soils.