The design of geosynthetic-reinforced and pile-supported (GRPS) embankments is traditionally optimized by searching for the most cost-effective solution among several workable candidates. The candidates are usually based on experiences of engineers, and the real optimal design could be therefore missed. This paper intends to address the above-mentioned issue by systematically optimizing the design of GRPS embankments considering simultaneously the cost and the safety in the entire design space. It is thus a multi-objective optimization (MOO) problem that differs from the studies only focusing on minimizing the construction cost. A practical MOO procedure is proposed in this paper, and it is applied to an illustrative GRPS embankment case. A set of nondominated optimal designs (Pareto front) are obtained at first, allowing an informed design decision. Then, four candidates located on the Pareto front are highlighted. Each of them represents an attractive design: the safest, the least-cost, the best trade-off (knee point) considering the two objectives, and the cheapest one for a target safety requirement. Finally, the optimal design can be selected from these four candidates depending on specific project purposes. For the case study, the knee point design leads to improvements in both the two defined objectives (i.e., decreased cost and increased safety) compared to the initial design, showing great benefits of performing a MOO analysis. By using the procedure, the optimal designs are also efficiently determined for the cases of different embankment heights.

Due to the complex geological conditions, the construction of underground tunnels in the rocks exhibiting creep behaviors is a great challenge and the structures’ long-term stability is of main importance. The excavation by tunnel boring machines (TBM) of a tunnel that is supported by a double flexible/concrete liner is considered a potential technical solution. However, the efficiency of such a support system on the stability at long-term of a tunnel must be verified in the real condition by considering both the effects of uncertainties of the time-dependent rock behavior and anisotropy of initial stress state. In this paper, the subset simulation and the Sobol global sensitivity analysis are chosen to estimate the failure probability of the tunnel supports and quantify the importance of different random parameters, respectively. The results reveal that considering the anisotropy of initial stresses increases the failure probability, especially in the concrete support elements. In addition, the parameters of initial stresses are the ones of main importance for both liners according to the Sobol indices. Therefore, the anisotropy of initial stresses and the related uncertainties should be considered for reliable tunnel designs.

A rotation of the anisotropic soil fabric pattern is commonly observed in natural slopes with a tilted stratification. This study investigates the rotated anisotropy effects on slope reliability considering spatially varied soils. Karhunen–Loève expansion is used to generate the random fields of the soil shear strength properties (i.e., cohesion and friction angle). The presented probabilistic analyses are based on a meta-model combining Sparse Polynomial Chaos Expansion (SPCE) and Global Sensitivity Analysis (GSA). This method allows the number of involved random variables to be reduced and then the computational efficiency to be improved. Two kinds of deterministic models, namely a discretization kinematic approach and a finite element limit analysis, are considered. A variety of valuable results (i.e., failure probability, probability density function, statistical moments of model response, and sensitivity indices of input variables) can be effectively provided. Moreover, the influences of the rotated anisotropy, autocorrelation length, coefficient of variation and cross-correlation between the cohesion and friction angle on the probabilistic analysis results are discussed. The rotation of the anisotropic soil stratification has a significant effect on the slope stability, particularly for the cases with large values of autocorrelation length, coefficient of variation, and cross-correlation coefficient.