Interaction between a long pile and the multilayered soil body with account for elastic and rheological properties as well as soil stabilization

Introduction. When the footing is embedded in loose clayey soils, buildings may settle down for a long period of time. The projected settlement period is of great importance for the design of foundations designated for such soils. Therefore, the approach to describing the process of foundation settlement must be considered as rheological. This article addresses the setting of and a solution to the problem of interaction between a long pile and surrounding multilayered and underlying soils with account taken of the rheological properties of the surrounding soil body. The creep process is considered with account taken of stabilization. Materials and methods. Linear problem setting is considered. The analytical method is employed to present a solution. The rheological stabilization parameter is used to describe the creep process. Results. An expression is derived to determine the reduced shear modulus for the multilayered soil body. The relationship between the value of the force applied to the pile toe and the time is derived with regard for the rheological stabilization parameter. Analytical solutions are enforced by graphs in the article. Graphs describing the relationship between pile settlement, the force applied to the toe of the pile, passing through alternating soil layers, and the time are provided for various values of viscosity and the variable parameter of stabilization. Conclusion. Solutions, obtained by the co-authors, are used to perform the preliminary identification of displacement of long piles and surrounding multilayered underlying soils. The rate of stress changing underneath the pile toe depends on soil viscosity. The rheological coefficient of stabilization has a major effect on the time of pressure stabilization underneath the pile toe, as well as the time of the pile settlement stabilization. Dependencies, derived in this article, make it possible to project the future settlement pattern.

Extended enthalpy formulations in the ice flow model ISSM version 4.17: discontinuous conductivity and anisotropic SUPG

The thermal state of an ice sheet is an important control on its past and future evolution. Some parts of the ice sheets may be polythermal, leading to discontinuous properties at the cold–temperate transition surface (CTS). These discontinuities require a careful treatment in ice sheet models (ISMs). Additionally, the highly anisotropic geometry of the 3D elements in ice sheet modelling poses a problem for stabilization approaches in advection dominated problems. Here, we present extended enthalpy formulations within the finite-element Ice Sheet System Model (ISSM) that show a better performance to earlier implementations. In a first polythermal-slab experiment, we found that the treatment of the discontinuous conductivities at the CTS with a geometric mean produce more accurate results compared to the arithmetic or harmonic mean. This improvement is particularly efficient when applied to coarse vertical resolutions. In a second ice dome experiment, we find that the numerical solution is sensitive to the choice of stabilization parameters in the well-established Streamline Upwind Petrov–Galerkin (SUPG) method. As standard literature values for the SUPG stabilization parameter are not accounting for the highly anisotropic geometry of the 3D elements in ice sheet modelling, we propose a novel Anisotropic SUPG (ASUPG) formulation. This formulation circumvents the problem of high aspect-ratio by treating the horizontal and vertical directions separately in the stabilization coefficients. The ASUPG method provides accurate results for the thermodynamic equation on geometries with very small aspect ratios like ice sheets.

A Robust Discontinuous Galerkin High-Order Finite Element Method for Elasticity Problems with Interfaces

A robust discontinuous Galerkin (DG) finite element method is proposed for elasticity problems with interfaces, where the continuity across the interfaces is weakly enforced by using Nitsche’s method. We employ a weighting for the interfacial consistency terms arising in the Nitsche variational form and present a detailed finite element formulation of this DG method. The stabilization parameter is evaluated by solving element level generalized eigenvalue problem for higher-order elements. Consequently, we give the choice of the weighting parameter that results in an estimate for the stabilization parameter such that the method remains well behaved in the pathological cases. The accuracy and robustness of the proposed method are then demonstrated through several numerical examples.

Sensitivity analysis of the grad-div stabilization parameter in finite element simulations of incompressible flow

We present a numerical study of the sensitivity of the grad-div stabilization parameter for mixed finite element discretizations of incompressible flow problems. For incompressible isothermal and non-isothermal Stokes equations and Navier-Stokes equations, we develop the associated sensitivity equations for changes in the grad-div parameter. Finite element schemes are devised for computing solutions to the sensitivity systems, analyzed for stability and accuracy, and finally tested on several benchmark problems. Our results reveal that solutions are most sensitive for small values of the parameter, near obstacles and corners, when the pressure is large, and when the viscosity is small.

STABILIZED FINITE DIFFERENCE METHODS FOR THE FULLY DYNAMIC BIOT'S PROBLEM

This paper deals with the stabilization of the poroelasticity system, in the incompressible fully dynamic case. The stabilization term is a perturbation of the equilibrium equation that allows us to use central difference schemes to approximate the first order spatial derivatives, yielding numerical solutions without oscillations independently of the chosen discretization parameters. The perturbation term is a discrete Laplacian of the forward time difference, affected by a stabilization parameter depending on the mesh size and the properties of the porous medium. In the one dimensional case, this parameter is shown to be optimal. Some numerical experiments are presented to show the efficiency of the proposed stabilization technique.

Electromagnetic interferometry in wavenumber and space domains in a layered earth

With interferometry applied to controlled-source electromagnetic data, the direct field and the airwave and all other effects related to the air-water interface can be suppressed in a data-driven way. Interferometry allows for retreival of the scattered field Green’s function of the subsurface or, in other words, the subsurface reflection response. This reflection response can then be further used to invert for the subsurface conductivity distribution. To perform interferometry in 3D, measurements on an areal grid are necessary. We discuss 3D interferometry by multidimensional deconvolution in the frequency-wavenumber and in the frequency-space domains and provide examples for a layered earth model. We use the synthetic aperture source concept to damp the signal at high wavenumbers to allow large receiver sampling distances. Interferometry indeed increases the detectability of a subsurface reservoir. Finally, we discuss the dependency of the accuracy of the retrieved reflection response on the two crucial parameters: the conductivity of the seabed at the receiver location and the stabilization parameter of the least-squares inversion.