Calculation Method of Underground Cavern Loosening Pressure Based on Limit Analysis Using Upper-Bound Theory and Its Engineering Application
Table 4
The relaxation pressures of Zhifang tunnel when the depth of the tunnel is 65 m.
Calculation method
q/kPa
e1/kPa
e2/kPa
e0/kPa
e0/q
Remark
Platts pressure arch theory
240.23
70.19
101.69
85.94
0.36
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 side wall, e0 = (e1 + e2)/2。
Modified Platts pressure arch theory
225.46
82.34
113.58
97.96
0.43
Railway specification method
301.91
90.57
150.96
120.76
0.40
Fraldi limit analysis method
310.25
115.28
160.32
137.80
0.44
Field measured data
200.10
66.38
95.20
80.79
0.40
Upper-bound theorem of limit analysis
k = 0.40
368.97
147.59
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。
