Movements around a tunnel in two-layer ground
An increasing need for accurate predictions of tunnelling-induced ground movements and potential damage to structures has produced a number of publications over the past 30 years. Few, however, have addressed the problem of tunnelling in ground consisting of more than one soil layer or the associated subsurface movements. The aim of the research was to investigate ground movements in two-layer ground conditions, specifically movements above tunnels driven in clay overlain by coarse grained materials. The principal methods of investigation were geotechnical centrifuge model testing and finite element analysis using the 3-Surface Kinematic Hardening (3-SKH) model, an elasto-plastic soil model implemented in the finite element program CRISP at City University, London. Both methods use effective stress path modelling to produce soil behaviour representative of prototype situations. Twenty-eight plane strain centrifuge model tests are reported in which the tunnel was represented by a SOmm diameter cylindrical cavity supported by compressed air pressure. The tunnel cavity was located within a layer of overconsolidated kaolin clay and in most cases the clay had an overlying layer of coarse grained material. The main variables in the tests were: the type of overlying strata; the thicknesses of the two strata; and the position of the water table. Tests were conducted at an acceleration of 1 OOg when the cavity then represented a Sm diameter tunnel with a maximum depth to tunnel axis of 22.Sm at prototype scale. After effective stress equilibrium was achieved, ground movements were generated by reducing the tunnel support pressure at a rate which produced essentially undrained behaviour in the clay. Transducers were used to measure pore pressures in the clay near the tunnel and displacements at the ground surface and at the clay/sand interface. Subsurface movements in the clay were obtained from images from a CCD camera, mounted on the centrifuge swing to view the front of the model in-flight, using a new digital image processing system developed at City University to track targets in the vertical face of the clay. Stress path triaxial tests were performed on some of the sands used in the centrifuge experiments, to determine stiffness properties for analysis of centrifuge test results and input for numerical analyses. Values of shear stiffness at very small strains, G'max, were determine dusing the bender element technique. Finite element analyses were conducted at centrifuge model scale with carefully simulated model stress histories. Some were direct simulations of physical model tests and were fully evaluated by comparison with centrifuge test data. Numerical predictions could be used with confidence, therefore, within the known limitations of the analyses. As well as evaluating the numerical model, the main points of investigation were the effects of: modelling conditions such as boundary proximity and stress history; the constitutive model used for the sand: the stiffness and depth of the upper strata on the movements in the clay. The results are applicable to predicting ground movements in the plane perpendicular to single, long tunnels, and the most important findings of the research are as follows. i) Both surface and subsurface settlement troughs are well represented by Gaussian distributions, except within a vertical distance of approximately O.5D of the tunnel cro\\ n when considerably steeper settlement profiles should be anticipated. ii) The form of the settlement profiles is constant until the tunnel begins to collapse (V-20%). iii)The equations of Mair et al (1993) adequately describe the distributioll of vertical movements with depth for tunnels in clay-only soil profiles, although, near a "free" ground surface the distribution of movements may be considerably wider (also see (i) above). iv) F or tunnels in clay with an overlying layer of different material the ratio of the shear stiffnesses at the interface between the materials should be taken into account. v) For undrained (constant volume) conditions, horizontal displacements may be inferred from the vertical displacements as the vectors of movement focus on the point where the tangent to the distribution of i \vith depth intersects the vertical tunnel axis.