TECHNICAL | TUNNELLING IMPACTS


⅓h


½d


½d


½d


½d


⅓d


⅓d


⅓d h


(A)


(B)


(C)


Above, figure 4: Stress distributions across a masonry arch (after Heyman (1982)) with the thrust line acting: (a) at the centre (b) at slightly off-centre (c) at the limit of ‘middle-third’ (d) outside the ‘middle-third’ limit (Note: h/3 is the location of the thrust line measured from the edge of the arch)


egg, circular, horseshoe, arched crown and invert with


vertical sidewall). Analyses of such structures can be analytically more difficult, more uncertain and highly condition dependant. A basic understanding of masonry arch theory (see Heyman (1982 & 1995), Szechy (1970) for further reading) will assist in undertaking analyses for assessment purposes. Transverse stability is usually the primary concern for


masonry arch. Some forms of structural overloading or asymmetrical loading often result in the development of tension in the masonry. This can result in a loss of mortar or bricks within the crown of the arch (see Figure 3) or elsewhere between the springings, which can subsequently result in collapse as the arch is no longer functioning because it becomes kinematically unstable. Arch design seeks to resolve the loads upon the arch


into compressive stresses and thereby eliminate tension. Figure 4 illustrates the stress distributions across a masonry arch with the thrust line acting at various locations. Compressive stress is developed across the whole arch thickness when the thrust line is retained within the ‘middle-third’ of the arch thickness. However, tension is developed when the thrust line is outside the ‘middle-third’ limit. This results in the formation of cracks because masonry is assumed to have negligible tensile strength for assessment purposes. CIRIA C671 (2009) provides useful guidance for a


thrust line analysis of a circular masonry structure and further details are provided in Appendix A. The aim for the thrust line analysis is to confirm if the line of thrust can be developed within an arch ring and equilibrate the given loading. Figure 5 shows an example of a thrust line analysis of a 2m internal diameter and 0.6m thick circular brick sewer located at a depth of 8m under three different horizontal stress to vertical stress ratios (KT


). The location of the thrust line is one of the


determining factors for masonry sewer transverse stability:


16 | February 2022 i


Developed within the intrados-third of the masonry arch thickness (see Figure 5a) – tension will be developed at the extrados of the sewer. However, the stability of the sewer could be maintained if there is sufficient external ground pressure to hold the arch in place.


ii


Developed within the middle-third of the masonry arch thickness (see Figure 5c) – tension will not be developed within the arch and the stability of the sewer is maintained.


iii Developed within the extrados-third of the masonry arch thickness (see Figure 5e) – tension will be developed at the intrados of the sewer and this could result in the loss of mortar and/or bricks around the crown of the sewer.


The ‘ULS envelopes’ shown on Figures 5b, 5d and 5f indicate the minimum depths from the intrados and extrados of the sewer at which the thrust line can be located without exceeding the ULS masonry compressive strength (assuming it to be 2.5MPa in the analysis). For stability, the thrust line should remain within the ‘ULS envelopes’ at all times and also cross the middle axis of the arch at least twice. The development of tension in the masonry can


also be caused by ground movements associated with various construction activities. Given sewer arches are considered to be semi-continuous linear structures, they are potentially vulnerable to the longitudinal ground movement curvatures in a similar way to pipes (see Section 6.3). Further details with regard to transverse strain analysis for masonry structures subject to external ground movements are presented in Section 6.8. Published test results on tensile and compressive


strengths of masonry (see Backes (1985)) indicate that maximum tensile strength can be less than 1% of compressive strength whereas tensile modulus can be significantly less than the compressive modulus. However, there is a common mistake by assessors to


(D)


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