A crucial aspect of physical geotechnical model tests (under both 1-g and n-g conditions) is the evaluation of the initial (low-strain) stiffness of the soil layers of the sample test deposit, especially in the case of coarse materials. While for uniform soil deposits this issue can be addressed in a straightforward manner, e.g. by determining the fundamental frequency through the transfer function of an applied white-noise excitation, the problem becomes cumbersome for multi-layered deposits. After reviewing a number of available theoretical solutions, this paper illustrates a simplified yet reliable analytical procedure for determining the shear wave velocity profile (Vs) in a single or bi-layer deposit, taking into account the inhomogeneity of the individual soil layers, under the hypothesis of vanishing shear modulus at ground surface. The fundamental natural frequency of the inhomogeneous bi-layer deposit is analysed using the Rayleigh quotient procedure. The associated shape function is evaluated by considering the equilibrium of the soil column under a pseudo-static lateral inertial excitation imposed at its base, accounting for both layering and inhomogeneity. A validation of the proposed method is provided by comparing numerical results obtained from both time-and frequency-domain analyses against experimental data on Leighton Buzzard sand, from a recently-completed research project conducted on the shaking table facility at BLADE Laboratory, University of Bristol (UK).
Available analytical methodologies for the stress analysis of buried pipelines against large permanent ground displacements (PGDs) apply only to straight pipeline segments. Hence, a new methodology is proposed herein for the analytical computation of pipeline strains in bends of arbitrary angle and radius of curvature, located outside the PGD high-curvature zone, but within the pipeline’s unanchored length. The methodology is based on the equivalent-linear analysis of the bend, assuming that it will perform as an elastic arched beam subjected to uniformly distributed ultimate axial and transverse horizontal soil reactions. The end of the bend towards the PGD zone is subjected to an axial displacement, calculated on the basis of overall displacement compatibility along the pipeline, while the other end is restrained by the unanchored pipeline segment beyond the bend. Using this approach, the maximum axial force at the vicinity of the PGD zone can also be calculated and consequently used for the estimation of corresponding pipeline strains with any of the available numerical or analytical methodologies for straight pipeline segments. Parametric nonlinear finite element analyses are performed to verify the analytical methodology and also derive conclusions of practical interest regarding the effect of bends on pipeline design.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.