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

Table 1

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

Variable	Theoretical solutions		Numerical solutions		Differences
B	Ht (m)	Lt (m)	Hn (m)	Ln (m)	ΔH = Ht − Hn (m)	ΔL = Lt − Ln (m)	ΔH/Ht (%)	ΔL/Lt (%)
0.90	8.4444	8.2800	8.4424	8.2800	0.0020	0.0000	0.0237	0.0000
0.80	9.0000	12.8149	8.9980	12.8150	0.0020	−0.0001	0.0222	−0.0008
0.70	9.7143	19.7567	9.7129	19.7568	0.0014	−0.0001	0.0144	−0.0005
0.60	10.6667	30.3075	10.7078	30.3078	−0.0411	−0.0003	−0.3853	−0.0010
0.50	12.0000	46.1880	12.4712	46.2126	−0.4712	−0.0246	−3.9267	−0.0533

Note: the parameters in the calculation are A = 2/3, σ_c = 1 × 10⁴ kPa, σ_t = σ_c/100 = 100 kPa, γ = 25.0 kN/m³.