Nonlinear elastoplastic formulation for tunneling effects on superstructures

Abstract

The paper presents a formulation for evaluating the effect of tunneling on existing buildings. The formulation involves the matrix condensation method to represent the response of a linear elastic building and macroelements to represent the nonlinear elastoplastic soil behavior. The formulation includes new features that allow interaction between macroelements, both through the soil continuum and the structure, to result in the final displacements of the foundations due to tunneling. One of the advantages of the formulation is its ability to incorporate a general input of a greenfield field displacement for the interaction analysis, allowing consideration of various tunneling scenarios. The formulation is evaluated by a comparison with a continuum-based solution obtained using the finite difference method. The formulation is then used to conduct a parametric analysis of tunneling–soil–superstructure interaction, considering three different approaches: (i) the suggested elastoplastic formulation, (ii) purely elastic analysis, and (iii) simplified analysis in which the foundations are forced to displace as a greenfield. It is shown that the vertical settlements of the foundations, due to tunneling, are the greatest when the first approach is considered. This is an outcome of the combined vertical and horizontal yielding, depicted in the formulation by the coupled yield function and plastic flow potential. Yet damage, which relates to differential settlement, appears to be smaller in the elastoplastic formulation.

Response of Framed Buildings on Raft Foundations to Tunneling

“…Importantly, these approaches for estimating average bay (Son and Cording, 2005;Cook, 1994) and local panel (Boone, 1996;Elkayam and Klar, 2019) shear deformations are comparable in terms of tensile strain max and, thus, categories of damage in Table 1. For the considered framed buildings on raft foundations, the high axial stiffness of horizontal elements (slabs) results in…”

“…Finally, several studies have distinguished between the shear deformations within a bay (averaged along the full-height of the building, as in Son and Cording (2005) and Cook (1994)), and the panel distortions (Boone, 1996;Elkayam and Klar, 2019). For example, for evaluating the distortions of panels, Elkayam and Klar (2019) estimated axial and diagonal strains using the displacements at the four corners of a panel.…”

“…Finally, several studies have distinguished between the shear deformations within a bay (averaged along the full-height of the building, as in Son and Cording (2005) and Cook (1994)), and the panel distortions (Boone, 1996;Elkayam and Klar, 2019). For example, for evaluating the distortions of panels, Elkayam and Klar (2019) estimated axial and diagonal strains using the displacements at the four corners of a panel. On the other hand, for framed buildings with infill walls, to account for the beam/slab to column/wall connections, Boone (1996) suggested that the shear strain γ could be estimated directly from the maximum slope of the beam/slab with respect to the bay tilt w. As illustrated in Figure 2, beams/slabs within the superstructure may undergo either a uniform shear strain (γ 1 in Figure 2(a)) or a varying profile of shear strain along the beam/slab with a maximum around the mid-point (γ 1 in Figure 2(b)).…”

“…x x ≈ 0. Consequently, Equation (2) simplifies to max = xz = γ/2, which can be computed using (i) β from Son and Cording (2005), considering that β ≈ γ, (ii) γ from Cook (1994) and Elkayam and Klar (2019), or (iii) γ 0 or γ 1 from Boone (1996).…”

Assessment of the Posttunneling Safety Factor of Piles under Drained Soil Conditions

“…Tunneling is an important construction activity that enables the use of underground space for essential infrastructure. Many aspects of tunneling have received considerable attention from researchers, for example the shape of tunneling induced settlement troughs (Mair et al, 1993;Marshall et al, 2012; and the effect of tunneling on pipelines (Attewell et al, 1986;Vorster et al, 2005;Marshall et al, 2010;Klar and Marshall, 2015;Klar et al, 2016), foundations (Devriendt and Williamson, 2011;Marshall and Mair, 2011;Basile, 2014;Dias and Bezuijen, 2015), and buildings (Potts and Addenbrooke, 1997;Franzius et al, 2006;Elkayam and Klar, 2018). The level of research conducted on these topics is an indication of the global importance of the subject.…”