On the use of moment thrust envelopes at segment joints
Most modern approaches to segmental lining design explicitly consider the behaviour and capacity of the joints. There are however a lot of different approaches to incorporating the joints into the analysis.
One common approach in the UK is to calculate the rotation of the segments at a longitudinal joint based on the as built tolerance and the ground induced deformations of the ring. Given the rotation of the segment and the hoop force it is then possible to derive a size and pressure distribution of the compressive contact patch between the two segments at the joint. The problem is, given this pressure distribution, what checks need to be undertaken.
Typically checks might include compressive bearing stress checks at the joint and tensile bursting stress checks. These are reasonable, code compliant and consistent with past experience of the types of failures that occur at segment joints. There is however also a trend for undertaking bending capacity checks using a moment thrust envelope based on the magnitude of the hoop thrust and the eccentricity of the centre of force in the contact patch. My view is this check is both not necessary and is not representative of the behaviour of the forces either around the joint or in the ring.
The key issue is that there is a critical assumption in the derivation of the moment thrust envelope, ’plane sections remain plane’. This can be practically considered in a few different ways but for the purposes of this discussion I’m going to consider it as meaning that the flow lines of stress in the structure being assessed are parallel to each other and the neutral axis. This is typically a reasonable assumption in the middle section of a segment away from the joints. At the joints however it clearly is not the case; the whole reason for the bursting stress check is the divergence of the compressive stress flow lines around the joint. This means that any check on the moment capacity in the region of the joint using a moment thrust envelope is invalid. Individual checks as a minimum on bearing and bursting should be undertaken at joints and in appropriate cases on other potential failures such as indirect tensile stresses around the joint.
There is an argument that bending checks based on the eccentricity of the forces at the joint are still reasonably valid for the mid-point of a segment, however this approach can also be problematic. Joint rotations will not be the same at either end of the segment and so the moments will also not be the same. The change in force eccentricity from the region near the joint to the region where the compressive flow lines are parallel can be very significant.
Whilst in some cases the approach of checking moment capacity at the joints is a common approach, I believe that it is a flawed and checking effort at the joints should focus on the checks that are reasonable and valid.