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

Table 4

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

Variable	Theoretical solutions		Numerical solutions		Differences
γ (kN/m^3)	Ht (m)	Lt (m)	Hn (m)	Ln (m)	ΔH = Ht − Hn (m)	ΔL = Lt − Ln (m)	ΔH/Ht (%)	ΔL/Lt (%)
25.0	9.7143	19.7567	9.7129	19.7568	0.0014	−0.0001	0.0144	−0.0005
22.5	10.7937	21.9519	10.7922	21.9520	0.0015	−0.0001	0.0139	−0.0005
20.0	12.1429	24.6959	12.1412	24.6959	0.0017	0.0000	0.0140	0.0000
17.5	13.8776	28.2239	13.8757	28.2240	0.0019	−0.0001	0.0137	−0.0004
15.0	16.1905	32.9278	16.1883	32.9279	0.0022	−0.0001	0.0136	−0.0003

Note: the parameters in the calculation are A = 2/3, B = 0.7, σ_c = 1 × 10⁴ kPa, σ_t = σ_c/100 = 100 kPa.