Calculation Method of Underground Cavern Loosening Pressure Based on Limit Analysis Using Upper-Bound Theory and Its Engineering Application
Table 3
The relaxation pressures of Jiangxi Road metro station.
Calculation method
q/kPa
e1/kPa
e2/kPa
e0/kPa
e0/q
Remark
Weighted Terzaghi’s formula
181.80
90.12
175.76
135.96
0.75
q is the vertical load of the tunnel; e1 is the load at the top of the sidewall; e2 is the load at the bottom of the sidewall; e0 is the mean value of the top and bottom loads of the sidewall, e0=(e1 + e2)/2。
Modified Terzaghi’s formula
162.84
98.41
211.23
130.63
0.80
Weighted Bierbäumer’s formula
198.03
101.26
186.66
149.65
0.76
Modified Bierbäumer’s formula
168.37
119.53
233.81
143.95
0.85
Weighted Jiaxiao Xie’s formula
174.63
72.51
157.68
123.57
0.71
Modified Jiaxiao Xie’s formula
153.19
76.32
189.40
114.76
0.75
Field measured data
135.65
78.12
192.01
106.89
0.79
Upper-bound theorem of limit analysis
k = 0.40
269.41
107.76
0.40
The upper-bound theorem of limit analysis assumes that the sidewall load is a uniform load e1 = e2 = e0, where k is the ratio of the horizontal support reaction force to the vertical support reaction force, k = e0/q.
