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The seismic response is a critical aspect of structural engineering, as it directly influences the design and safety evaluation of such systems. Structural seismic response becomes more complicated when unavoidable uncertainties in the structure are considered. Therefore, solving and analyzing the stochastic dynamic response of structures efficiently and accurately is of great significance. Various uncertainty quantification methods such as the stochastic finite element method, Monte Carlo method, and polynomial chaos expansion method have made significant progress in this field. However, these methods do not provide a comprehensive study of the seismic response of stochastic structures and efficiency problems rapidly emerge as the number of random variables increases. This paper delivers a comprehensive study of the seismic dynamic response of space truss and reticulated shell structure considering uncertainties in material properties, geometry, and loading. To this end, the finite element model of the structure was first modeled and the deterministic solutions were obtained. Then, polynomial surrogates are modeled for the natural frequency, mode participation factor, mode superposition response, and transient response of the structure under stochastic uncertainties. The sparse grid technique is used to select sparse quadrature points, which overcomes the curse of dimensionality caused by full grid integration. The results demonstrate that the sparse grid-based polynomial chaos expansion is more efficient. Uncertainty quantification reveals the uncertainty of modal analysis, response spectrum analysis, and transient response analysis of space truss and reticulated shell under seismic excitation. In summary, this study provides valuable insights and an efficient and accurate uncertainty quantification tool for the seismic dynamic analysis of stochastic structures, ultimately contributing to safer and more robust structural designs. • Analyzing the seismic dynamic response of stochastic structures comprehensively. • Sparse grid-based PCE for quantifying uncertainty in stochastic dynamics. • Addressing the dimensional catastrophe of traditional non-intrusive PCE. • Sparse grid-based PCE metamodel for post-processing is more efficient and accurate. [ABSTRACT FROM AUTHOR]

To address the issue of low accuracy resulting from approximation errors in conventional interval finite element methods, this study presents an ɛ -accelerated bivariate dimension-reduction interval finite element method. The proposed method aims to accurately and efficiently predict the static response of structures with high dimensionality and large uncertainty parameters. We first approximate the structural interval equilibrium equation using a bivariate dimension-reduction method. An explicit expression for the sequence of displacements is derived by approximating the inverse of the structural interval stiffness matrix using the Neumann series. Adjoint-based sensitivity analysis can effectively avoid the response interval expansion caused by parameter coupling. For improving the convergence speed and computational accuracy, the displacement response sequence is accelerated by a vector ɛ acceleration algorithm and an adaptive strategy. Finally, three engineering structures with uncertain-but-bounded parameters are analyzed with the proposed method. Compared with conventional interval analysis methods, the proposed method effectively balances computational accuracy and efficiency, making it more suitable for non-linear and large uncertainty problems with multiple interval parameters. The study shows that ɛ -accelerated bivariate dimension-reduction interval finite element method has a promising application. • An interval finite element method based on bivariate dimension-reduction is proposed. • Explicit sequences and errors for the bounds of displacements were derived. • Dependencies between parameters are addressed by adjoint-based sensitivity analysis. • Convergence speed and accuracy are improved by the adaptive ɛ algorithm. • Structural response intervals are efficiently and accurately predicted. [ABSTRACT FROM AUTHOR]

The ultimate bearing capacity of an eccentrically loaded strip footing above twin square tunnels buried in rock masses was examined using the generalized Hoek-Brown (GHB) yield criteria. To get reliable findings, the stability assessments were carried out using finite element limit analysis (FELA) code in combination with a sophisticated adaptive remeshing approach. Case studies with two different tunnel layouts, parallel and symmetrical, were examined. Comprehensive parametric analyses were given to demonstrate the effect of load eccentricity, rock mass strength parameters, and tunnel position on the stability of the strip footing. The visualized results of the FELA programme were presented to show how the failure mechanism would change with different influential factors. Moreover, the results were validated by comparing them to earlier investigations. [ABSTRACT FROM AUTHOR]

Random adaptive finite element limit analysis (RAFELA) is introduced to investigate the stability of the footing-voids system with random soils. The emphasis of this study is, for the footing-void system, on quantifying the influence of spatial variability on its bearing capacity and the failure probability. Of particular interest is that random field theory is utilized to characterize the spatial variability of soil, and at the same time, failure probability is calculated by imposing Monte-Carlo simulations on independent cases. Strict close bearing capacity could be obtained within the scope embraced by upper bound (UB) results and lower bound (LB) results. By imposing the proposed modelling, comprehensive parametric studies were carried out, especially for the soil spatial correlation parameters and geometry parameters. The results indicated that the failure probability would increase with the farther distance between the void and the footing, the greater coefficient of variation (COV) and the smaller vertical correlation length. Detailed design tables were presented to assess potential failure probability under different conditions. Typical failure patterns are also summarized, revealing a positive correlation between the failure probability and the diffusion degree of failure curves. [ABSTRACT FROM AUTHOR]

The undrained stability of dual circular tunnels buried in spatially random soils is investigated by imposing the random adaptive finite element limit analysis (RAFELA). The emphasis is on quantifying the effect of influential factors including the geometry parameters and spatially variability parameters on the bearing capacity and failure probability of tunnels by assuming a lognormal distribution on undrained shear strength within a spatial correlation structure. Predictions were obtained by the scope enclosed by upper bound (UB) and lower bound results (LB) results within 5% relative errors. To account for a combined effect simultaneously caused by depths of tunnels, spaces between tunnels, soil weights, and spatially variability parameters on the stability of tunnels, all independent variables are involved in parametric studies in pairs. Results revealed several failure patterns and announced how the stability evolves with changes in tunnel geometry and soil spatial variability. [ABSTRACT FROM AUTHOR]

In this study, finite element limit analysis (FELA) is employed to investigate the undrained seismic bearing capacity of strip footings placed on two-layered slopes. Upper bound theorem (UB), lower bound theorem (LB) and adaptive meshing technique were used in parametric studies to investigate the effects of various factors on seismic bearing capacity N cs and failure mechanism, especially the seismic coefficient k h and the shear strength ratio of top layer and bottom layer c u1 / c u2. The angle of the slope β , the absolute strength of top layer c u /γ B , horizontal offset distance b and the thickness of top layer D are also taken into consideration. Furthermore, the comparisons between present study and previous studies are provided. Detailed design tables are presented to distinguish the failure patterns and estimate the seismic bearing capacity of slopes under different conditions. [ABSTRACT FROM AUTHOR]

Finite element limit analysis (FELA) is used to study the undrained bearing capacity of strip footing above voids in two-layered clays. Based on the FELA results, design charts and equations are provided to calculate the undrained bearing capacity factor N s . The impact of parameters on N s also has been investigated, including undrained shear stress ratio of the soil, thickness of the top layer, location, size, width, height and spacing of the voids. The failure mechanisms for a single void maybe classified into three categories: roof failure, combined roof and wall failure, bearing failure without void failure. [ABSTRACT FROM AUTHOR]

This paper presents a finite beam element method (FBEM) for analyzing the behavior of a two-pile foundation under eccentric and inclined loads located at sloping ground. A simplified physical model for the two-pile foundation is presented by dint of the strain wedge technique and FBEM. The emphasis is on establishing an element stiffness matrix, taking the P -Δ effect, the strengthening effect on the pile stiffness and the Pasternak's soil resistance into consideration. The global stiffness matrix can thus be assembled by these element stiffness matrixes, and the node force and deflection were identified by FBEM. The results are compared with field observations and exhibit satisfactory accuracy. [ABSTRACT FROM AUTHOR]

Adaptive finite element limit analysis (AFELA) is employed to investigate the stability of two circular tunnels at different depths in cohesive-frictional soils subjected to surcharge loading. The upper and lower bounds of the tunnel stability numbers are obtained, with the relative errors being found within ±5%. Five parametric studies are conducted to evaluate the effects of the horizontal and vertical spacing ratio, overburden stress factor, cover depth ratio and soil internal friction angle on the tunnel stability numbers. Design tables and charts are provided to facilitate engineers' use. In addition, typical failure mechanisms are discussed and examined. [ABSTRACT FROM AUTHOR]

Abstract This paper investigates the stability of dual circular tunnels in a rock mass subjected to surcharge loading using adaptive finite element limit analysis (AFELA). The tunnels are modelled under plain-strain conditions, and the rock mass is assumed to be a homogeneous and isotropic material obeying the Hoek-Brown failure criterion. For the studied problem, numerical kinematic and static approaches are employed to calculate the rigorous upper and lower bounds of the stability number N , which has been bracketed within ±5% from above and below. The calculated results are presented in the form of dimensionless stability charts, and the typical failure mechanisms are discussed through parametric studies of the problem variables using the visualized results of AFELA. [ABSTRACT FROM AUTHOR]