On the kinematics of 2D tunnel collapse in undrained clay

Abstract

Citation for published item:ysmnD eF F nd wirD F tF nd foltonD wF hF @PHHTA 9yn the kinemtis of Ph tunnel ollpse in undrined lyF9D q¡ eotehniqueFD ST @WAF ppF SVSESWSF Further information on publisher's website: httpXGGdxFdoiForgGIHFITVHGgeotFPHHTFSTFWFSVS Publisher's copyright statement:Additional information: Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. A kinematic plastic solution has been developed for ground movements around a shallow, unlined tunnel embedded within an undrained clay layer. In this solution, the pattern of deformation around the tunnel is idealised by a simple plastic deformation mechanism. Within the boundaries of the deformation mechanism, the soil is required to shear compatibly and continuously with no relative sliding at the boundaries. The soil is regarded here as a rigid plastic (Tresca) material. Peck (1969) summarises the most important requirements for successful design and construction in tunnels as stability, control of ground movements, and performance of linings. This paper aims to provide a simple theoretical framework for assessing the first two requirements for tunnels constructed in clays. This paper is concerned only with construction effects in clays that are presumed to remain undrained. The upper and lower bound theorems of plasticity (Drucker et al., 1952) offer a rigorous and powerful technique for estimating the collapse loads. Davis et al. (1980) derived plasticity solutions employing kinematic upper bounds and statically admissible lower bounds for planestrain circular tunnels and for a two-dimensional idealisation of the tunnel heading stability in clays with constant shear strength. To obtain an upper bound to the collapse load, they developed a number of deformation mechanisms in which the soil moves as rigid blocks sliding relative to each other with displacement discontinuities at their boundaries. Davis et al. (1980) found that the three-variable and the fourvariable mechanisms shown in Figs 1(a) and 1(b) give the lowest (i.e. the most critical) upper bounds. Sloan & Assadi (1993) developed extensive sets of upper bound and lower bound solutions for plane-strain tunnels in soils whose undrained strength varies with depth. Significant improvements on the upper bound solutions were achieved by using a more complex seven-variable mechanism ( Fig. 1(c)). Sloan & Assadi (1993) also improved both upper bound and lower bound calculations using numerical limit analysis. In this technique, rigorous upper and lower bound collapse loads are found numerically by linear programm...

Predicting 2D ground movements around tunnels in undrained clay

“…This mechanism does not incorporate slip surfaces. Osman et al (2006) demonstrated that the upper bound theorem applied to distributed shearing mechanism offered a reasonable assessment for collapse, and also matches the displacement field observed in centrifuge tests of tunnel failure in clay (Mair, 1979). It was also demonstrated that the shape of the surface settlement profile remained the same as the magnitude of settlement increased towards failure.…”

“…The vertical displacements in the deformation mechanism ( Fig. 1) proposed by Osman et al (2006) are taken to follow a Gaussian distribution on each successive horizontal plane at depth z below the surface. The distance to the point of inflexion i z is then expressed by…”

“…Finite element analyses of modelling tunnel construction of the Jubilee Line Extension (JLE) beneath St James's Park conducted by Addenbrooke et al (1997) showed that modelling soil as a linear-elastic material leads to inadequate displacement prediction. Osman et al (2006) developed a kinematic plastic solution for ground movements around a shallow, unlined, tunnel embedded within an undrained clay layer. In this solution, the pattern of deformation around the tunnel is idealised by a simple plastic deformation mechanism (Fig.…”

Face Stability Analysis of Circular Tunnels Driven by a Pressurized Shield

“…For the 3D face stability analysis, their numerical results were better than the values published by Davis et al ͑1980͒ for great values of C / D where Cϭtunnel cover and Dϭtunnel diameter. A somewhat similar approach has been undertaken previously by Osman et al ͑2006͒ for the 2D stability analysis of circular tunnels in a cohesive soil. However, the velocity field was based on the empirical Gaussian settlement trough near the ground surface instead of the analytical elasticity equations.…”

Collapsed Shape of Shallow Unlined Tunnels Based on Functional Catastrophe Theory

“…More recently, several kinematical approaches based on continuous velocity fields in limit analysis theory were proposed. Osman et al [12] developed upper-bound calculations of collapse loads in tunnels using a distributed shear deformation mechanism. They assumed that the soil deforms compatibly following a Gaussian distribution within the boundaries of this deformation mechanism and is rigid outside this mechanism.…”