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The traditional deterministic analysis for tunnel face stability neglects the uncertainties of geotechnical parameters, while the simplified reliability analysis which models the potential uncertainties by means of random variables usually fails to account for soil spatial variability. To overcome these limitations, this study proposes an efficient framework for conducting reliability analysis and reliability-based design (RBD) of tunnel face stability in spatially variable soil strata. The three-dimensional (3D) rotational failure mechanism of the tunnel face is extended to account for the soil spatial variability, and a probabilistic framework is established by coupling the extended mechanism with the improved Hasofer-Lind-Rackwits-Fiessler recursive algorithm (iHLRF) as well as its inverse analysis formulation. The proposed framework allows for rapid and precise reliability analysis and RBD of tunnel face stability. To demonstrate the feasibility and efficacy of the proposed framework, an illustrative case of tunnelling in frictional soils is presented, where the soil′s cohesion and friction angle are modelled as two anisotropic cross-correlated lognormal random fields. The results show that the proposed method can accurately estimate the failure probability (or reliability index) regarding the tunnel face stability and can efficiently determine the required supporting pressure for a target reliability index with soil spatial variability being taken into account. Furthermore, this study reveals the impact of various factors on the support pressure, including coefficient of variation, cross-correlation between cohesion and friction angle, as well as autocorrelation distance of spatially variable soil strata. The results also demonstrate the feasibility of using the forward and/or inverse first-order reliability method (FORM) in high-dimensional stochastic problems. It is hoped that this study may provide a practical and reliable framework for determining the stability of tunnels in complex soil strata.

This paper presents a critical review of the current challenges in analyzing large, realistic pile groups in soft clay soil under earthquake shaking. The review focuses on three main essentials of numerical analyses, namely soil behavior and constitutive model, pile and pile-soil interface modeling and computational framework.

The behavior of pile foundations under earthquake loading is an important factor affecting the performance of structures. Observations from past earthquakes have shown that piles in firm soils generally perform well, while the performance of piles in soft or liquefied ground can raise some questions. Centrifuge model tests were carried out at the National University of Singapore to investigate the response of pile-soil system under three different earthquake excitations. Some initial tests were done on kaolin clay beds to understand the pure clay behavior under repetitive earthquake shaking. Pile foundations comprising of solid steel, hollow steel and hollow steel pile filled with cement in-fill were then embedded in the kaolin clay beds to study the response of clay-pile system. Superstructural inertial loading on the foundation was modeled by fastening steel weight on top of the model raft. The model test results show that strain softening and stiffness degradation feature strongly in the behaviour of the clay. In uniform clay beds without piles, this is manifested as an increase in resonance periods of the surface response with level of shaking and with successive earthquakes. For the pile systems tested, the effect of the surrounding soft clay was primarily to impose an inertial loading onto the piles, thereby increasing the natural period of the piles over and above that of the pile foundation alone. There is also some evidence that the relative motion between piles and soil leads to aggravated softening of the soil around the pile, thereby lengthening its resonance period of the soil further. The centrifuge model tests were back-analyzed using the finite element code ABAQUS. The analysis shows that the simple non-linear hypoelastic soil model gave reasonably good agreement with the experimental observations. The engineering implication arising from this study so far is that, for the case of relatively short piles in soft clays, the ground surface motions may not be representative of the raft motion. Other than the very small earthquakes, the raft motion has a shorter resonance period than the surrounding soil.