Limit Analysis of Collapse Mechanisms for Tunnel Roofs Subjected to Pore Water Pressure: A Numerical Approach

Table 3

Comparison of height H and width L of collapse block between theoretical solutions and numerical solutions with varied parameter σ_t/σ_c.

Variable	Theoretical solutions		Numerical solutions		Differences
σt/σc	Ht (m)	Lt (m)	Hn (m)	Ln (m)	ΔH = Ht − Hn (m)	ΔL = Lt − Ln (m)	ΔH/Ht (%)	ΔL/Lt (%)
1/50	19.4286	32.0949	19.4247	32.0949	0.0039	0.0000	0.0201	0.0000
1/75	12.9524	24.1641	12.9502	24.1643	0.0022	−0.0002	0.0170	−0.0008
1/100	9.7143	19.7567	9.7129	19.7568	0.0014	−0.0001	0.0144	−0.0005
1/200	4.8571	12.1617	4.8566	12.1617	0.0005	0.0000	0.0103	0.0000
1/300	3.2381	9.1565	3.2378	9.1565	0.0003	0.0000	0.0093	0.0000

Note: the parameters in the calculation are A = 2/3, B = 0.7, σ_c = 1 × 10⁴ kPa, γ = 25.0 kN/m³.