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

Table 2

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

Variable	Theoretical solutions		Numerical solutions		Differences
A	Ht (m)	Lt (m)	Hn (m)	Ln (m)	ΔH = Ht − Hn (m)	ΔL = Lt − Ln (m)	ΔH/Ht (%)	ΔL/Lt (%)
0.75	9.7143	22.2263	9.7132	22.2264	0.0011	−0.0001	0.0113	−0.0004
0.67	9.7143	19.7567	9.7130	19.7569	0.0013	−0.0002	0.0134	−0.0010
0.50	9.7143	14.8175	9.7120	14.8177	0.0023	−0.0002	0.0237	−0.0013
0.35	9.7143	10.3723	9.7116	10.3724	0.0027	−0.0001	0.0278	−0.0010
0.15	9.7143	4.4453	9.7122	4.4453	0.0021	0.0000	0.0216	0.0000

Note: the parameters in the calculation are B = 0.7, σ_c = 1 × 10⁴ kPa, σ_t = σ_c/100 = 100 kPa, γ = 25.0 kN/m³.