Nonlinear Dynamic Computer Research Articles

Machine learning-driven feature importance appraisal of seismic parameters on tunnel damage and seismic fragility prediction

This study proposes a machine learning-driven approach for the analysis of the feature importance of seismic parameters on tunnel damage and seismic fragility prediction. The Incremental Dynamic Analysis (IDA) method serves as the fundamental database for vulnerability analysis. Strength and deformation yield criteria are chosen to comprehensively assess the impact of different seismic parameters on the vulnerability of tunnels to seismic events. Three machine learning algorithms, namely Extreme Gradient Boosting (XGBoost), Random Forest (RF), and Support Vector Machine (SVM), are utilized to develop models for classifying and regressing tunnel damage under seismic conditions. Following parameter tuning, the models' performance in multi-classification, binary classification, and regression prediction is assessed, with XGBoost and RF models exhibiting outstanding performance. Feature importance analysis of seismic parameters in XGBoost and RF models for multi-classification, binary classification, and regression is performed using Shapley additive explanations (SHAP). The correlation analysis between SHAP-based feature values and predictions reveals that Peak Ground Displacement (PGD) has the highest influence in the regression model. Utilizing the interaction dependencies among crucial features in the regression model, fragility curves for tunnels based on these key features are effectively derived. The predicted fragility curves closely align with those derived from IDA, illustrating the time-saving and high-performance capabilities of machine learning in nonlinear dynamic computations.

A general hyper-reduction strategy for finite element structures with nonlinear surface loads based on the calculus of variations and stress modes

The presence of nonlinear and state-dependent surface loads within structural dynamic applications often causes an increased computational effort for time integration. Although the degrees of freedom (DOFs) of finite element (FE) models can be reduced significantly via model order reduction (MOR), the determination of nonlinear effects usually depends on the full physical domain. This paper introduces a hyper-reduction (HR) approach, which allows the computation of nonlinear surface loads by a limited number of integration points. One of the fundamental underlying concepts is the creation of mode bases for both the MOR and the reduced load computation, whereby the latter ones are denoted as stress modes. These can be determined a priori from linear FE analyses, for which no fully nonlinear dynamic computations are required. Another relevant step includes the formulation of the contact law based on the calculus of variations, combined with the use of these stress modes. The resulting relationships are in the dimension of the stress modes subspace but still rely on the full physical domain, which is why in this paper, the empirical cubature method (ECM) is proposed to obtain a reduction of the integration points. Based on these theoretical concepts, a general HR framework for nonlinear and state-dependent surface loads is outlined. For a demonstration of the proposed procedure, a planar crank drive with an elastohydrodynamic (EHD) contact between the piston and the cylinder is presented. The quality of the results and the potential for saving computing time are demonstrated by comparing the HR approach with conventional solution techniques.

Seismic vulnerability evaluation of historical masonry churches: Proposal for a general and comprehensive numerical approach to cross-check results

Abstract The seismic vulnerability evaluation of existing masonry churches is an important issue in earthquake engineering. The Italian Guidelines for the built heritage suggest a quantitative assessment of vulnerability by means of a technique that uses the upper bound theorem of limit analysis on 28 pre-assigned failure mechanisms, assuming masonry unable to withstand tensile stresses. In the framework of the kinematic theorem, the failure mechanism activating in reality is that associated to the lowest multiplier. Whilst the approach is very straightforward, it is intrinsically affected by possible inaccuracies, both because the real geometry of the church is accounted for only in an approximate way and the choice to limit the analysis to 28 mechanisms could exclude from computations the real mechanism occurring, with the consequent overestimation of the collapse acceleration. In this paper a general approach relying into the collection of different numerical procedures is proposed to all practitioners interested in a precise estimation of the seismic vulnerability of masonry churches, with an indication of all the steps to follow to predict with fair accuracy their load carrying capacity. The approach comprises the determination of eigen-frequencies and modes, spectral analyses (both assuming an elastic behavior for masonry), limit analyses with FEM and pre-assigned failure mechanisms, pushover and non-linear dynamic computations. A case study is discussed in order to calibrate the procedure and discuss the actual accuracy of the results obtained.

DEM numerical approach for masonry aqueducts in seismic zone: two valuable Portuguese examples

Two engineering applications of the distinct element method to the analysis of historic masonry aqueducts in Portugal are presented. The commercial software Universal distinct element code is utilised to analyse Aguas Livres in Lisbon and Amoreira in Elvas aqueducts, modelling two meaningful portions of the structures by means of distinct blocks and frictional interfaces. The aqueducts portions are assumed subjected to several different earthquakes with variable intensity and frequency contents, in order to have an insight into their non-linear behaviour when subjected to different accelerograms and estimate the seismic vulnerability by means of non-linear dynamic computations.

Soil–foundation modelling in laterally loaded historical towers

The seismic stability analysis of historical towers requires reliable soil–structure interaction (SSI) modelling. To avoid the complexity of non-linear dynamic computations, engineers frequently resort to simplified static approaches, such as the so-called pushover analyses. Their outcomes are deeply affected by the foundation response under horizontal/moment (HM) loading. This paper encompasses a comprehensive SSI modelling process, taking as a reference case study the embedded shallow footing of the Ghirlandina tower in Modena, Italy. First, a finite-element (FE) soil–foundation model is developed with an inhomogeneous distribution of the undrained soil strength, related to the in situ inhomogeneity of the stress state. Total stress FE analyses are then performed to derive the undrained failure locus of the footing and numerical data about its pre-failure performance. This locus is found to exhibit distorted HM cross-sections, depending on the vertical load and hardly reproducible through standard analy...

Blast response and failure analysis of pile foundations subjected to surface explosion

This paper presents the response of pile foundations to ground shocks induced by surface explosion using fully coupled and non-linear dynamic computer simulation techniques together with different material models for the explosive, air, soil and pile. It uses the Arbitrary Lagrange Euler coupling formulation with proper state material parameters and equations. Blast wave propagation in soil, horizontal pile deformation and pile damage are presented to facilitate failure evaluation of piles. Effects of end restraint of pile head and the number and spacing of piles within a group on their blast response and potential failure are investigated. The techniques developed and applied in this paper and its findings provide valuable information on the blast response and failure evaluation of piles and will provide guidance in their future analysis and design.

Soil–foundation modelling in laterally loaded historical towers

The seismic stability analysis of historical towers requires reliable soil–structure interaction (SSI) modelling. To avoid the complexity of non-linear dynamic computations, engineers frequently resort to simplified static approaches, such as the so-called pushover analyses. Their outcomes are deeply affected by the foundation response under horizontal/moment (HM) loading. This paper encompasses a comprehensive SSI modelling process, taking as a reference case study the embedded shallow footing of the Ghirlandina tower in Modena, Italy. First, a finite-element (FE) soil–foundation model is developed with an inhomogeneous distribution of the undrained soil strength, related to the in situ inhomogeneity of the stress state. Total stress FE analyses are then performed to derive the undrained failure locus of the footing and numerical data about its pre-failure performance. This locus is found to exhibit distorted HM cross-sections, depending on the vertical load and hardly reproducible through standard analytical formulae. The FE evidences are then condensed into a simple elasto-plastic HM ME model, reproducing the outcomes of the inhomogeneous FE model, and employable for the pushover seismic analysis of historical towers.

Identification of progressive collapse pushover based on a kinetic energy criterion

The progressive collapse phenomenon is generally regarded as dynamic. Due to the impracticality of nonlinear dynamic computations for practitioners, an interest arises for the development of equivalent static pushover procedures. The present paper proposes a methodology to identify such a procedure for sudden column removals, using energetic evaluations to determine the pushover loads to apply. In a dynamic context, equality between the cumulated external and internal works indicates a vanishing kinetic energy. If such a state is reached, the structure is sometimes assumed able to withstand the column removal. Approximations of these works can be estimated using a static computation, leading to an estimate of the displacements at the zero kinetic energy configuration. In comparison with other available procedures based on such criteria, the present contribution identifies loading patterns to associate with the zero-kinetic energy criterion to avoid a single-degree-of-freedom idealisation. A parametric study over a family of regular steel structures of varying sizes uses non-linear dynamic computations to assess the proposed pushover loading pattern for the cases of central and lateral ground floor column failure. The identified quasi-static loading schemes are shown to allow detecting nearly all dynamically detected plastic hinges, so that the various beams are provided with sufficient resistance during the design process. A proper accuracy is obtained for the plastic rotations of the most plastified hinges almost independently of the design parameters (loads, geometry, robustness), indicating that the methodology could be extended to provide estimates of the required ductility for the beams, columns, and beam-column connections.

Linear and nonlinear seismic response of a 52‐storey steel frame building

This paper presents the results of a study on the seismic behaviour of a well-instrumented 52-storey steel frame building in Los Angeles, California. This building has been subjected to ground motions from several earthquakes among which the records obtained during the 1991 Sierra Madre earthquake and the 1994 Northridge earthquake were selected for this study. Detailed time and frequency domain analyses of the recorded motions from these two earthquakes were conducted to determine the dynamic characteristics of the structure. This information was used to calibrate a three dimensional dynamic computer model of the building. Nonlinear dynamic computer analyses were then employed to investigate the response of the structure during severe ground shaking. The results of this study showed that by performing a linear three-dimensional analysis, the response of the building during past earthquakes can be reproduced with confidence. The results also show that because of the torsional response of this high-rise building is not negligible, two-dimensional analysis is not feasible for reliably predicting its nonlinear response during earthquakes. By further performing a nonlinear three-dimensional analysis, the state and sequence of damage could also be predicted. The study also included an investigation of the effectiveness of pushover analysis for predicting the nonlinear behaviour of the building. This type of analysis has the deficiency of excluding the participation of higher modes, which is obvious for high-rise buildings, especially for shaking from near-field type ground motions. Improvements to the pushover analysis for such a type of shaking were explored. Copyright © 2000 John Wiley & Sons, Ltd.

Efficient numerical modelling for the design of friction damped braced steel plane frames

A novel friction damping system for the aseismic design of framed buildings has been proposed by Canadian researchers. The system has been shown experimentally to perform very well and is an exciting development in earthquake resistant design.The design of a building equipped with the friction damping system is achieved by determining the optimum slip load distribution to minimize structural response. The optimum slip load distribution is usually determined using the general nonlinear dynamic computer program DRAIN-2D, which requires extensive computer time and is not practical for most design offices.This paper describes a new, efficient, numerical modelling approach for the design of friction damped braced frames. The hysteretic properties of the friction devices are derived theoretically and included in a friction damped braced frame analysis program, which is adaptable to a microcomputer environment. The optimum slip load distribution is determined by minimizing a relative performance index derived from energy concepts. The new numerical approach is much more economical to use than DRAIN-2D and is of great value for the practical design of friction damped braced frames. Key words: braced frames, brake lining, performance index, damping, dynamics, earthquakes, energy, friction.