Limit equilibrium models for tunnel face stability in mixed ground

The heterogeneous geological conditions of mixed ground in the Hualong Cross-River Passage Project in Guangdong Province, China, pose significant challenges to tunnel face stability during shield tunneling operations, leading to complex failure mechanisms that require systematic investigation. Currently, there is a lack of clear criteria for defining and distinguishing between US-LH (upper soft-lower hard) and UH-LS (upper hard-lower soft) strata, and the influence of these two types of strata on the failure mechanisms of the tunnel face remains unclear. This study quantitatively characterizes soft-over-hard ground distributions through the dimensionless strength ratio Q (q_u/q_l), where q_u and q_l represent the unconfined compressive strength of upper and lower strata respectively. The failure mechanism and limit support pressure of the tunnel face under varying strength ration Q were determined through numerical simulations. Two models were established based on the Q, namely the US-LH model (0 < Q < 1) and the UH-LS model (Q > 1). Comparative and parametric analyses were conducted to evaluate the rationality of the proposed model. Key findings reveal: (1) Differential failure zone evolution patterns, with US-LH conditions demonstrating progressive geometrical transformation from initial right-triangular to final trapezoidal configurations, while UH-LS ground maintain persistent right-triangular failure morphology; (2) Normalized pressure σ_p/γD displays consistent Q-dependent behavior across methodologies, characterized by three distinct phases: stability plateau (0 < Q ≤ 1/4), critical peak at Q = 1, and subsequent decay to a constant level (Q ≥ 4), with UH-LS ground requiring lower support pressures for maintaining tunnel face stability than US-LH counterparts; (3) Limit equilibrium analysis identifies 45° + φ/2 as the critical failure angle inducing maximum limit support pressure; (4) Parametric sensitivity analysis demonstrates N_c shows inverse proportionality with limit support pressure, while N_γ and N_v exhibit strong positive correlations. A key contribution of this study lies in the introduction of an unconfined compressive strength ratio, enabling the prediction of the limit support pressure of the tunnel face under various conditions of soft-hard strata. This provides a theoretical basis for setting chamber pressure in practical engineering applications.