This paper presents simplified closed-form analytical solutions that can be used to interpret and predict ground movements caused by shallow tunneling in soft ground conditions. These solutions offer a more comprehensive framework for understanding the distribution of ground movements than widely used empirical functions. Analytical solutions for the displacement field within the ground mass are obtained for two basic modes of deformation corresponding to uniform convergence and ovalization at the wall of a circular tunnel cavity, based on the assumption of linear, elastic soil behavior. Deformation fields based on the superposition of fundamental, singularity solutions are shown to differ only slightly from analyses that consider the physical dimensions of the tunnel cavity, except in the case of very shallow tunnels. The Authors demonstrate a simplified method to account for soil plasticity in the analyses and illustrate closed-form solutions for a three-dimensional tunnel heading. A companion paper describes applications of these analyses to interpret field measurements of ground response to tunneling.

This paper presents a numerical formulation of a three dimensional embedded beam element for the modeling of piles, which incorporates an explicit interaction surface between soil and pile. The formulation is herein implemented for lateral loading of piles but is able to represent soil-pile interaction phenomena in a general manner for different types of loading conditions or ground movements. The model assumes perfect adherence between beam and soil along the interaction surface. The paper presents a comparison of the results obtained by means of the present formulation and by means of a previously formulated embedded pile element without interaction surface, as well as reference semi-analytical solutions and a fully 3D finite element (FE) model. It is seen that the proposed embedded element provides a better convergence behavior than a previously formulated embedded element and is able to reproduce key features of a full 3D FE model.

Summary This paper presents a numerical formulation for a three dimensional elasto‐plastic interface, which can be coupled with an embedded beam element in order to model its non‐linear interaction with the surrounding solid medium. The formulation is herein implemented for lateral loading of piles but is able to represent soil‐pile interaction phenomena in a general manner for different types of loading conditions or ground movements. The interface is formulated in order to capture localized material plasticity in the soil surrounding the pile within the range of small to moderate lateral displacements. The interface is formulated following two different approaches: (i) in terms of beam degrees of freedoms; and (ii) considering the displacement field of the solid domain. Each of these alternatives has its own advantages and shortcomings, which are discussed in this paper. The paper presents a comparison of the results obtained by means of the present formulation and by other well‐established analysis methods and test results published in the literature. Copyright © 2016 John Wiley & Sons, Ltd.