TECHNICAL | TUNNELLING IMPACTS


2.0 1.5 1.0 0.5 0.0


-0.5 -1.0 -1.5 -2.0


Right:


Calculation results from the thrust line analysis


2.0 1.5 1.0 0.5 0.0


-0.5 -1.0 -1.5 -2.0


2.0 1.5 1.0 0.5 0.0


-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 Intrados Intrados ULS Extrados Extrados ULS


Step 2 (all units in m)


2.0 1.5 1.0 0.5 0.0


-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 Intrados Intrados 1/3 Extrados Extrados 1/3 Thrust line


Step 4 (all units in m)


-0.5 -1.0 -1.5 -2.0


-0.5 -1.0 -1.5 -2.0


-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 Intrados Intrados 1/3 Extrados Extrados 1/3


Step 3 (all units in m)


-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 Intrados Intrados ULS Extrados Extrados ULS Thrust line


Step 5 (all units in m)


HH ⅓h


A3


KT σV


Ratio of external horizontal pressure to external vertical pressure = 0.7


External vertical pressure at axis level = 20kN/m3


). σH × 8m × 1.4 = 224kN/m2 (ULS, load factor


of 1.4 for overburden with soil unit weight of 20kN/m3


External horizontal pressure at axis level = KT


σV = 156.8kN/m2 h (ULS). σm Masonry compressive strength = 2.5MPa (ULS).


Step 2 Calculation of ULS envelopes. Step 3 Calculation of ‘middle-third’ envelopes. Step 4 Calculation of thrust line based on dmin


= t/3.


Step 5 Checking if the thrust line is compatible with the masonry compressive strength. Step 6 Conclusions. The analysis indicates that the thrust line: i


Remains within the ‘middle-third’ of the masonry arch thickness and no tension will be developed within the arch.


ii Remains within the ULS envelopes at all times. iii Crosses the middle of the arch at least twice.


σm Above, figure A3: Stress distribution (after Heyman (1982)) 32 | February 2022


Therefore, the arch ring will not collapse under this loading case in accordance with the lower bound theorem of limit analysis.


Page 1  |  Page 2  |  Page 3  |  Page 4  |  Page 5  |  Page 6  |  Page 7  |  Page 8  |  Page 9  |  Page 10  |  Page 11  |  Page 12  |  Page 13  |  Page 14  |  Page 15  |  Page 16  |  Page 17  |  Page 18  |  Page 19  |  Page 20  |  Page 21  |  Page 22  |  Page 23  |  Page 24  |  Page 25  |  Page 26  |  Page 27  |  Page 28  |  Page 29  |  Page 30  |  Page 31  |  Page 32  |  Page 33  |  Page 34  |  Page 35  |  Page 36  |  Page 37  |  Page 38  |  Page 39  |  Page 40  |  Page 41  |  Page 42  |  Page 43  |  Page 44  |  Page 45  |  Page 46  |  Page 47  |  Page 48  |  Page 49