An efficient probabilistic design approach for tunnel face stability by inverse reliability analysis

In order to maintain the safety of underground constructions that significantly involve geo-material uncertainties,this paper delivers a new computation framework for conducting reliability-based design(RBD)of shallow tunnel face stability,utilizing a simplified inverse first-order reliability method(FORM).The limit state functions defining tunnel face stability are established for both collapse and blow-out modes of the tunnel face failure,respectively,and the deterministic results of the tunnel face support pressure are obtained through three-dimensional finite element limit analysis(FELA).Because the inverse reliability method can directly capture the design support pressure according to prescribed target reliability index,the computational cost for probabilistic design of tunnel face stability is greatly reduced.By comparison with Monte Carlo simulation results,the accuracy and feasibility of the proposed method are verified.Further,this study presents a series of reliability-based design charts for vividly understanding the limit support pressure on tunnel face in both cohesionless(sandy)soil and cohesive soil stratums,and their optimal support pressure ranges are highlighted.The results show that in the case of sandy soil stratum,the blowout failure of tunnel face is extremely unlikely,whereas the collapse is the only possible failure mode.The parametric study of various geotechnical uncertainties also reveals that ignoring the potential correlation between soil shear strength parameters will lead to over-designed support pressure,and the coefficient of variation of internal friction angle has a greater influence on the tunnel face failure probability than that of the cohesion.

Randomized Algorithms for Probabilistic Optimal Robust Performance Controller Design

Polynomial-time randomized algorithms were constructed to approximately solve optimal robust performance controller design problems in probabilistic sense and the rigorous mathematical justification of the approach was given. The randomized algorithms here were based on a property from statistical learning theory known as (uniform) convergence of empirical means (UCEM). It is argued that in order to assess the performance of a controller as the plant varies over a pre-specified family, it is better to use the average performance of the controller as the objective function to be optimized, rather than its worst-case performance. The approach is illustrated to be efficient through an example.