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.

Probabilistic limit state design methodof the axial resistance of post grouting pile

The reliability of post grouting pile axial resistance was studied by proposing a design method for its probabilistic limit state,which is represented by the partial coefficients of load,end,and side resistance.The hyperbolic,modified hyperbolic,and polynomial models were employed to predict the ultimate bearing capacity of test piles that were not loaded to damage in field tests.The results were used for the calculation and calibration of the reliability index.The reliability of the probabilistic limit state design method was verified by an engineering case.The results show that the prediction results obtained from the modified hyperbolic model are closest to those obtained through the static load test.The proposed corresponding values of total,side,and end resistance partial coefficients are 1.84,1.66,and 2.73 when the dead and live load partial coefficients are taken as 1.1 and 1.4,respectively.Meanwhile,the corresponding partial coefficients of total,side,and end resistance are 1.70,1.56,and 2.34 when the dead and live load partial coefficients are taken as 1.2 and 1.4,respectively.

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.

Experimental Design of Measuring Soil-Water Characteristic Curve of Unsaturated Soil Using Bayesian Approach

Soil-water characteristic curve (SWCC) is significant to estimate the site-specific unsaturated soil properties (such as unsaturated shear strength and coefficient of permeability) for geotechnical analyses involving unsaturated soils. Determining SWCC can be achieved by fitting data points obtained according to the prescribed experimental scheme, which is specified by the number of measuring points and their corresponding values of the control variable. The number of measuring points is limited since direct measurement of SWCC is often costly and time-consuming. Based on the limited number of measuring points, the estimated SWCC is unavoidably associated with uncertainties, which depends on measurement data obtained from the prescribed experimental scheme. Therefore, it is essential to plan the experimental scheme so as to reduce the uncertainty in the estimated SWCC. This study presented a Bayesian approach, called OBEDO, for probabilistic experimental design optimization of measuring SWCC based on the prior knowledge and information of testing apparatus. The uncertainty in estimated SWCC is quantified and the optimal experimental scheme with the maximum expected utility is determined by Subset Simulation optimization (SSO) in candidate experimental scheme space. The proposed approach is illustrated using an experimental design example given prior knowledge and the information of testing apparatus and is verified based on a set of real loess SWCC data, which were used to generate random experimental schemes to mimic the arbitrary arrangement of measuring points during SWCC testing in practice. Results show that the arbitrary arrangement of measuring points of SWCC testing is hardly superior to the optimal scheme obtained from OBEDO in terms of the expected utility. The proposed OBEDO approach provides a rational tool to optimize the arrangement of measuring points of SWCC test so as to obtain SWCC measurement data with relatively high expected utility for uncertainty reduction.