3 and 5; however, the predicted values of critical bending strain were lower than their experimental counterparts for test cases 1, 2 and 4. Th is suggests that the FE model tends to predict reasonably well the behaviour of the lining in the absence of restraint set- ups, as can be shown from Table 1 (i.e. small percentage error in
Results — Writing Task 127 terms of critical strains and defl ections for BC5). It will be shown later on that a more realistic simulation of the restraint set-ups can improve considerably the numerical predictions of the lining response. 4.3. Channeline lining Th e half-length of the Ch pipe was 1170 mm and, again, its thickness (equal to 8 mm) was doubled for elements located at the joint section. Figures 6 and 7 show a comparison between the experimental results and the FE analysis using a lower range of values of isotropic material properties for reasons similar to those for the previous lining. Th ese were chosen as follows: Eh = El = 6.9 kN mm−2 and vh = vl = 0.33. Unlike the St pipeline, which was made up of one-piece linings, the Ch linings are two-piece segmental. As it is diffi cult to simulate realistically the behaviour of the longitudinal joint(s) in the case of segmental linings, the experimental results are still compared with the FE results using the mesh described earlier, even though such a mesh does not attempt to model the joint. From the outcome of this analysis, it can be shown that the response of the numerical model in terms of inner strains and defl ections follows a similar pattern to that of the experimental results, as indicated in Figs. 6 and 7. At fi rst sight, this would seem to imply that the longitudinal joint did in fact provide full shear and bending-moment continuity, so that the joint could be replaced by an equivalent continuous structure (i.e. stiff er than a hinge but well below fi xity). Th is conclusion, however, need not follow since the shape of the bending-moment diagram is such that it changes sign in the vicinity of the longitudinal joint, so that, for this particular type of loading, the latter location is acted upon by relatively small bending action anyway. Th erefore, on the basis of the bending strains, it is diffi cult to establish what the relative stiff ness of the joint is, and it might seem reasonable to postulate a hinge (whether because of a fl exible joint or simply due to the shape of the bending-moment diagram). On the other hand, it is shown from Table 1 that the numerical model predicts reasonably well the behaviour of the lining in terms of values of critical inner
128 Science Research Writing strains, but that it is not so good in terms of values of critical defl ections. Th is fact would now suggest that the presence of the straight longitudinal joint might approach the eff ect of a hinge, thus allowing a larger rotation at the springings, with associated defl ections at the fl at mid-section of the lining, which are bigger than those obtained by the continuous-joint model in which the point of contrafl exure does not occur exactly at the springing locations. 4.4. Celtite lining Th e half-length of the pipe was 1200 mm and its thickness 10 mm (20 mm at the joint section). Similarly to the previous cases, Figs. 8 and 9 show a comparison between the experimental observations and the FE- analysis results. Once again, a lower range of values of material properties is used; these properties are: Eh = 13 kN mm−2, El =