Soil—pipe interaction due to tunnelling: comparison between Winkler and elastic continuum solutions

Abstract

An elastic continuum solution and a Winkler solution of the problem of tunnelling effects on existing pipelines are given. A comparison is made between an elastic continuum solution and a closed-form Winkler solution with Vesic subgrade modulus. Although applying the Vesic expression results in the same moments and displacements under external loading in a Winkler system and the elastic continuum, it is found that its use is not necessarily adequate for the problem of tunnelling effects on pipelines and may not be conservative owing to possible underestimation of bending moments. An alternative expression for the subgrade modulus is provided, resulting in similar maximum bending moments in the Winkler and elastic continuum systems.

Tunnelling close beneath an existing tunnel in clay – perpendicular undercrossing

“…Longitudinal bending moment. The centrifuge tests carried out validated the method proposed by Klar et al (2005) for tunnels in clay with shear stiffness degradation based on the NLEPP model (see Fig. 18).…”

“…A fitted K value back-calculated from the bending strains provided a better fit for PP_CYG_C03 (1·5D clear distance), reducing the difference from a factor of 5·1 to 1·2. It should be noted that, although the resultant curve fit was poor, the objective of the exercise was to illustrate the applicability of the method proposed by Klar et al (2005) when the tunnel deformation profile conforms to a Gaussian curve, a trend that is generally observed from field instrumentations (Standing & Selman, 2001;Gue et al, 2015). Two possible explanations are proposed for the wider settlement trough measured in PP_CYG_C03.…”

“…Klar et al (2005) presented a closed-form Winkler spring solution (equation (1)) method for pipeline bending moment assessments, which was derived from typical transverse Gaussian settlements and considered the soilpipe relative stiffness. Klar et al (2005) proposed an alternative subgrade modulus analogue, K s , in place of the method proposed by Vesic (1961), which suffered from disparity between elastic continuum and the Winkler solution for i x /R , 10. …”

“…Taking this into account along with the alternative subgrade modulus analogue proposed by Klar et al (2005), overestimations of maximum bending moments were reduced by approximately 5-7 times for a volume loss of up to 4% as opposed to up to 20 times if the pipelines were forced to conform to greenfield settlement profiles.…”

Analysis of Forces and Deformation Rule of Existing Shield Tunnel Caused by Ground-heaped Load

“…During the completion and operation periods, the existing tunnel is often influenced by foundation pit excavation [1], [2], [3], tunnel excavation [4], [5], [6], pile foundation construction [7], [8], [9], and ground-heaped load [10], [11], [12]. Movement and destruction in the adjacent tunnel would occur during excavation of a foundation pit [13], [14].…”