This paper presents the mechanical and hydraulic behaviour of passively prestressed concrete-lined pressure tunnels embedded in elastic transversely isotropic rocks subjected to non-uniform in situ stresses. Two cases are distinguished based on whether the in situ vertical stress in the rock mass is higher, or lower than the in situ horizontal stress. A two-dimensional finite element model was used to study the influence of dip angle, α, and horizontal-to-vertical stress ratio, k, on the bearing capacity of prestressed concrete-lined pressure tunnels. The study reveals that the in situ stress ratio and the orientation of stratifications in the rock mass significantly affect the load sharing between the rock mass and the lining. The distribution of stresses and deformations as a result of tunnel construction processes exhibits a symmetrical pattern for tunnels embedded in a rock mass with either horizontal or vertical stratification planes, whereas it demonstrates an unsymmetrical pattern for tunnels embedded in a rock mass with inclined stratification planes. The results obtained for a specific value α with coefficient k are identical to that for α + 90° with coefficient 1/k by rotating the tunnel axis by 90°. The maximum internal water pressure was determined by offsetting the prestress-induced hoop strains at the final lining intrados against the seepage-induced hoop strains. As well as assessing the internal water pressure, this approach is capable of identifying potential locations where longitudinal cracks may occur in the final lining.

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Pressure tunnels for hydropower plants are relatively expensive constructions, particularly when steel linings are used. Concrete linings can be economically attractive; however, their applicability is limited by the low tensile strength of concrete. Techniques to improve the bearing capacity of concrete tunnel linings have become one of the interesting topics in hydropower research. One of the techniques available is through prestressing the cast-in-place concrete lining by grouting the circumferential gap between the concrete lining and the rock mass with cement-based grout at high pressure. As a consequence, compressive stresses are induced in the lining. This is meant to offset tensile stresses and avoid tendency for longitudinal cracks to occur in the lining due to radial expansion during tunnel operation. Moreover, as the grout fills discontinuities in the rock mass and hardens, the permeability of the rock mass is reduced. This is favourable in view of reducing seepage. In order to maintain the prestressing effects in the concrete lining, the rock mass has to be firm enough to take the grouting pressure. The grouting pressure, taking into account a certain safety factor, should remain below the smallest principal stress in the rock mass. Since the prestress in the concrete lining is produced by the support from the rock mass, this technique is also called the passive prestressing technique. The overall objective of this research is to investigate the mechanical and hydraulic behaviour of pressure tunnels. By means of a two-dimensional finite element model, the load sharing between the rock mass and the concrete lining is explored. This research deals with the effects of seepage on the bearing capacity of pre-stressed concrete-lined pressure tunnels. A new concept to assess the maximum internal water pressure is introduced. The second innovative aspect in this research is to explore the effects of the in-situ stress ratio in the rock mass on the concrete lining performance. In the final part, this research focuses on the cracking of concrete tunnel linings. A step-by-step calculation procedure is proposed so as to quickly quantify seepage and seepage pressure associated with longitudinal cracks, which is useful for taking measures regarding tunnel stability. If the assumption of elastic isotropic rock mass is acceptable, this research suggests that the load-line diagram method should only be used if it can be guaranteed that no seepage flows into the rock mass. Otherwise, seepage cannot be neglected when determining the bearing capacity of prestressed concrete-lined pressure tunnels. It is evident that the load sharing between the rock mass and the lining determines the bearing capacity of prestressed concrete-lined pressure tunnels. Particularly in the lining, longitudinal cracks can occur along the weakest surface that is submitted to the smallest total stress in the rock mass. When pressure tunnels embedded in elasto-plastic isotropic rock mass, longitudinal cracks may occur at the sidewalls if the in-situ vertical stress is greater than the horizontal. If the in-situ horizontal stress is greater than the vertical, cracks will occur at the roof and invert. When pressure tunnels are embedded in transversely isotropic rocks and the in-situ stresses are uniform, the locations of longitudinal cracks in the lining are influenced by the orientation of stratification planes. If the stratification planes are horizontal and the in-situ vertical stress is greater than the horizontal, cracks can occur at the sidewalls; whereas if the stratification planes are vertical and the in-situ horizontal stress is greater than the vertical, cracks can occur at the roof and invert. When the stratification planes are inclined and the in-situ stresses are non-uniform, longitudinal cracks will take place at the arcs of the lining, and their locations are influenced by the combined effects of the in-situ stress ratio and the orientation of stratification planes in the rock mass. Since crack openings in the lining are difficult to control with the passive prestressing technique, it is essential to maintain the lining in a compressive state of stress during tunnel operation. The attractive design criteria for prestressed concrete-lined pressure tunnels are therefore: avoiding longitudinal cracks in the lining, limiting seepage into the rock mass, and ensuring the bearing capacity of the rock mass supporting the tunnel. All in all, this research demonstrates the applicability of a two-dimensional finite element model to investigate the mechanical and hydraulic behaviour of pressure tunnels. Remaining challenges are identified for further improvement of pressure tunnel modelling tools and techniques in the future.@en

Based on the non-linear finite element analysis, the maximum bearing capacity of a plain circular concrete lining subjected to external and internal pressure is investigated. Numerical results regarding elastic stresses and deformations are compared with those calculated using the classical thick-walled cylinder theory. Referring to the discrete cracking concept and assuming that the concrete behaves as a brittle material, the redistribution of stresses after cracks have occurred is further investigated. The normal tensile strength in the lining will reduce to zero as soon as the joint element is cracked. These analyses confirm that the proposed modelling method may be used satisfactorily, to model the cracking process of passive pre-stressed circular concrete linings.@en