Determination of the stress-strain demand curve of the sprayed waterproofing membrane interface in composite SCL tunnels

•A conceptual framework is established for the membrane states.•These states start from the construction stage and over the whole design life.•These states can be captured in demand curves through numerical modelling.•The range of water pressure application positions can be bounded by demand curves.•The concept of capacity envelopes and demand curves for the membrane are introduced. Understanding the evolution of the stress-strain states of the sprayed waterproofing membrane within composite sprayed concrete lined (SCL) tunnels from the short-term dry condition to the long-term wet condition is critical to ensure the integrity of the composite SCL tunnels. This paper presents a conceptual framework describing the evolution of the states and demonstrates a methodology that enables the designer to determine the states using a demand curve that bounds all possible stress-strain states of the membrane interface. It firstly presents a conceptual framework for the evolution of the state stress and strain of the membrane interface in typical composite SCL tunnels from short to long term and from ‘dry’ to ‘wet’ membrane saturation. A numerical method to simulate this evolution is presented. A numerical analysis of a full composite SCL tunnel in typical over-consolidated ground was carried out for the range of possible locations of groundwater pressure application in the lining, and the results used to demonstrate the process of obtaining a set of stress-strain demand curves for the tunnel. The research shows that the membrane interface in a composite SCL tunnel is in a state of combined normal and shear stress and strain but that these stresses and strains remain finite and do not become unbounded, due to the statically indeterminate nature of the structure. It is however an interaction problem so that the normal and shear stress and strain need to be checked together. Some insights are given as to the nature of a laboratory testing programme that could be carried out on the membrane interface to obtain capacity envelopes to compare with the demand curves for design.