SUPPORT PRESSURE FOR STABILITY OF CIRCULAR TUNNELS UNDER DIFFERENT GROUND CONDITIONS

Abstract

The use of underground space has considerably been increased, nowadays, in the form of tunnels/underground openings for highways and railways to smoothen the traffic, underground canal systems, pipelines and hydropower projects. The soil mass both in the front of tunnel face and around periphery of tunnel tends to deform causing instability of tunnel during the event of excavation. Compressed air or pressurized slurry is used to prevent the face instability; whereas, the installation of support systems in the form of precast concrete segmental lining/steel plate liners restricts the peripheral instability. The peripheral stability of tunnels depends upon the resistance/stiffness of support system. Thus, the required support pressure to be offered by support system must be known prior to its design to maintain stability. A number of research works have been reported on the determination of required support pressure for maintaining stability of tunnel in different types of soils considering as isotropic and homogeneous medium. However, soil deposits encountered in practice are generally not isotropic and homogeneous. Further, in many cases, tunnels are advanced through water bearing stratum, that is, below ground water table and water bodies, where the seepage of water towards the tunnel exerts additional pressure on the support system in excess of the overburden pressure due to self weight of soil and surcharge on the ground surface, if any. Limited studies seem to be available for assessing the stability of tunnels driven in anisotropic and non-homogeneous clay, and in water bearing ground. Solutions are yet to be obtained to determine the support pressure for tunnels taking into account the effect of anisotropy and non-homogeneity of soil, and seepage towards the tunnel. In this thesis, an attempt has been made to obtain the required pressure to be offered by support systems to maintain the stability of circular tunnels advanced in different ground conditions. The different ground conditions consist of (i) undrained clay with an overlay of another clay layer as well as granular soil layer (ii) anisotropic and non-homogeneous undrained clay, and (iii) anisotropic granular soil where tunnel located below groundwater table and water bodies. In this thesis, numerical solutions have been developed based on lower bound theorem of limit analysis in combination with finite elements and second order cone programming. From design point of view, the solutions obtained on the basis of lower bound theorem of limit analysis remain always safe as the limit load computed by this method is smaller than or equal to the true collapse load. The computations have been performed considering iii iv Abstract plane strain condition valid with the assumption that length of the tunnel is very long as compared to its diameter. The soil mass has been modeled as perfectly plastic material following an associated flow rule based on Tresca criterion for clay under undrained condition, Mohr-Coulomb criterion for granular soil under drained condition and Davis Christian yield criterion for anisotropic clay under undrained condition. The support pressure is assumed to be acting uniformly and radially along the periphery of the tunnel. For solving various problems of the present research work, computer programming codes have been written using ‘MATLAB’ and second order conic optimization is performed by employing ‘MOSEK’, an optimization toolbox available for ‘MATLAB’. Three noded triangular elements have been used throughout the thesis for performing the finite element analysis. Each node is involved with three basic unknowns, namely, horizontal normal stress, vertical normal stress, and the shear stress on the horizontal/vertical plane. A line of discontinuity is allowed between the interface of two adjacent elements for allowing stress discontinuity between the edges of adjacent elements; thus, each node is made unique to a particular element so that a number of nodes will have the same coordinates. The lower bound solution becomes close to the true solution due to incorporation of statically admissible stress discontinuities while performing the analysis. The required support pressure for circular tunnels located in undrained clay with an overlay of (i) another udrained clay layer of relatively stiffer and softer than lower layer, and (ii) granular soil layer has been computed. Each layer is assumed to be isotropic in nature. The influence of thickness of lower clay layer above the crown of tunnel, thickness of upper clay and granular soil layer, strength of both the layers in terms of undrained shear strength of clay layers and internal friction angle of granular soil, and unit weight of both layers on required support pressure has been studied. The required support pressure is defined in terms of non-dimensional factor normalized with respect to undrained cohesion of lower clay layer. For a given combination of ratio of thickness and unit weight of both the layers, the magnitude of support pressure has been found to be continuously increasing and decreasing depending upon increase and decrease in the undrained cohesion of upper layer with respect to undrained cohesion of lower clay layer. The magnitude of required support pressure is found to be reducing continuously with an increase in the internal friction angle of the overlying granular soil. The required support pressure for the case tunnel driven in layered soil medium as compared to that driven in homogeneous clay (the properties of lower layer of layered clay remains same as that of homogeneous clay), has been found to be greater and smaller, which depends on the combined influence of 2/1, Abstract v H2/H1, cu2/cu1 and angle of internal friction of upper granular soil layer; where, 1 and 2 refer to unit weight of lower and upper layer, respectively; H1 and H2 denote to thickness of lower layer above tunnel crown and thickness upper layer, respectively; cu1 and cu2 are the undrained cohesion of lower and upper layer, respectively. The support pressure for circular tunnels located in undrained clay considering the anisotropy and non-homogeneity in shear strength has been computed. Two cases have been considered to include the non-homogeneity in the analysis; in the first case the stratum is single layer whose undrained shear strength varies linearly with depth but the unit weight remains same with depth, and in the second case, the strata is a two layered clay medium where the undrained cohesion and unit weight of both the layers are different from each other but remains constant with depth in each layer. The anisotropy in undrained shear strength is defined in terms of two anisotropic coefficients as re = cu90/cu0 and rs = cu45/cu0; where, cu0, cu45 and cu90 are the undrained shear strength of clay when the direction of major principal stress is vertical, inclined an angle of 45 with vertical and horizontal, respectively. The required support pressure is expressed in terms of non-dimensional factors normalized with respect to undrained cohesion at the ground surface and undrained cohesion of lower clay layer for the first and second case, respectively. For different values of anisotropic coefficients, the magnitude of required support pressure has been obtained by varying tunnel cover, rate of linear variation of undrained cohesion with depth, normalized overburden pressure, thickness of lower clay layer above tunnel crown, thickness of upper layer, and undrained cohesion and unit weight of upper layer relative to lower layer. It has been found that the required support pressure continuously reduces with increase in the magnitude of anisotropic coefficients and rate of increase of undrained strength with depth. Support pressure for circular tunnels driven in anisotropic granular soil below groundwater table and water bodies has been obtained. The required support pressure is defined in terms of non-dimensional factors normalized with respect to unit weight of soil and diameter of tunnel. The effect of anisotropy in both strength and hydraulic properties of granular soil on the magnitude of required support pressure has been examined. The variation of support pressure for different combinations of strength and hydraulic parameters of soil, elevation of groundwater table above tunnel crown, height of water level above bed of water bodies, and cover of tunnel has been established. The magnitude of support pressure has been vi Abstract observed to be substantially influenced by strength anisotropy of soil; whereas, the influence of hydraulic anisotropy has been shown to be insignificant on the support pressure. Moreover, the support pressure is found to be increasing with increase in the position of water level and is observed to be higher when the tunnel is driven in water bearing stratum as compared to dry stratum.