A detailed planetary boundary layer (PBL) flow over complex terrain can be simulated by nesting mesoscale numerical weather prediction (NWP) models and microscale computational fluid dynamics (CFD). When fully prescribed lateral boundaries are encountered, the over-specified treatment of CFD or limited-area models may result in ill-posedness and numerical instabilities. Such behaviors are due to inconsistent governing equations, turbulent viscosity models, and underlying surfaces between meso- and micro-scale formulations. In this study, by applying the relaxation treatment in marginal zones of CFD, its wind components are forced toward the externally specified NWP values. The relaxation schemes, deduced from simple advective transport equations, are optimized using genetic algorithms. Their numerical abilities in absorbing wave reflections on shallow-water systems are more efficient than the published approach. Then, key questions concerning the selection of relaxation strength, turbulence model constants, and prognostic variables specified on NWP–CFD nested boundaries are systemically investigated in the neutrally stratified Askervein Hill case. The relaxation scheme from simpler systems also performs effectively in CFD and decreases the adaption distance of wind velocities near over-specified outlet boundaries. A full set approach to obtain well-posed PBL solutions from the microscale domains sustained with inflow boundaries from NWP is proposed and validated.

Three soil-arching evolution patterns in unreinforced piled embankments were observed in a series of two-dimensional (2D) model tests using a multitrapdoor test setup. These include the triangular expanding pattern, the tower-shaped evolution pattern, and the equal settlement pattern. The inclination of the slip surfaces and the height of the vertical slip surfaces that enclose the tower-shaped arches were found to be the critical parameters describing the arching evolution. Three analytical models were proposed to describe the evolution processes of the three arching-evolution patterns and to find the stress distributions of the corresponding processes. Load distribution equations were also derived from these models. Using the empirical relationships between the inclination of the slip surfaces and the tower height and settlement, the stress distribution ratio during the entire evolution process was calculated. The models matched the model tests well.