Substructure Approach Research Articles

A procedure for addressing the soil-abutment interaction problem in the safety assessment of bridges

The paper proposes a methodology for assessing the seismic soil-foundation-abutment response in the spirit of the sub-structure approach. The methodology is suitable for conventional bridge abutments characterized by massive structural components and accommodates for various structural and soil configurations, from both stratigraphic and topographic perspectives. The abutment is assumed to be rigid, which is a generally acceptable hypothesis given the typical geometry of conventional bridge abutments with walls, orthogonal wingwalls, and a concrete deep or strip foundation. The methodology aligns with codes, which foresees a linear behaviour for the abutments and suggest a low behaviour factor to account for dissipative capabilities due to the backfills and the radiation phenomena in the soil. The soil is assumed to perform elastically, but the overall soil nonlinearity induced by seismic wave propagation can be incorporated into the method using a linear equivalent representation of soil properties. The methodology is applied to a real case study in order to demonstrate its effectiveness in addressing the soil-structure interaction problem and to provide practical suggestions for the method implementation, including possible simplifications.

Time history analysis of multi- storey building with basement story accounting for soil–structure interaction

Soil-Structure Interaction (SSI) is the effects of the soil (underlying and surrounding the structure) on the response of the structure. This study is a contribution in the soil structure interaction (SSI) field, as this interaction affects the seismic behavior of structures. Two series of Time History data were used in the analysis of reinforced concrete moment resisting frame building consisting of 9 stories with embedded basement storey building. The two approaches of SSI modeling that are substructure approach and direct approaches were compared with each other. Generally, and within the limits of this study, it was found that the responses of Substructure approach were identical with that of the direct approach in the two cases for all stories except for the Ground storey. It seems that SSI affects the higher stories rather than the lower stoerys. The dynamic analysis results comparison between the two approaches of modeling soil structure interaction, favored the substructure approach on the direct approach as the direct approach is time consuming. Also, the study found out that modeling the structure with only vertical spring led to doubtable results, which reflect present that is choosing this method represents the worst option. On the other hand, and according to the analysis results, study suggested that keeping use the fixed approach in design buildings (with embedded portion) does not represent the better choice. It is concluded that, the responses of Substructure approach is identical with that of the Direct approach in all cases for all stories except for the Ground storey. It seems that SSI affects the higher stories rather than the lower storey.

Liquid Sloshing in Soil-Supported Multiple Cylindrical Tanks Equipped with Baffle under Horizontal Excitation

The dynamic behavior of liquid storage tanks is one of the research issues about fluid–structure interaction problems. The analysis errors of the dynamics of multiple adjacent tanks can exist if neglecting soil–tank interaction since tanks are typically supported on flexible soil. In the present paper, the dynamics of a group of baffled cylindrical storage tanks supported on a circular surface foundation and undergoing horizontal excitation are analytically examined. For upper multiple tank–liquid–baffle subsystems, accurate solutions to the velocity potential for liquid sloshing are acquired according to the subdomain partition technique. A theoretical model is utilized to portray the continuous sloshing of each tank. For the soil–foundation subsystem, a lumped-parameter model is used to characterize the impacts of soil on upper-tank structures using Chebyshev complex polynomials that present the fitting results of horizontal, rocking, and coupling impedance functions. Then, a model of the soil–foundation–tank–liquid–baffle system is constructed on the basis of the substructure approach. The present sloshing frequencies, sloshing height, and hydrodynamic shear as well as the moment under rigid/soft soil foundations are compared to the available exact results and the numerical results to prove the validity of the present model. The error of the maximum sloshing height between the present and the numerical solutions is within 5.27%; the solution efficiency of system dynamics from the present model is 40–50 times faster than that from the ADINA model. A detailed parameter analysis of the dynamic characteristics and earthquake responses of the coupling system is presented. The research novelty is that an equivalent analytical model is presented, and it allows for investigating the dynamics of soil-supported multiple cylindrical tanks with a baffle, providing acceptable accuracy and high calculation efficiency.

Numerical study on train-induced vibrations: A comparison of timber and concrete buildings

This paper deals with the prediction of train-induced building vibrations by using a numerical framework. The framework is based on a sub-structure approach, where a sequence of different models are used. The free-field ground vibrations and the track receptance are calculated using 2.5D technique where the railway track is represented by finite elements that couple to a dynamic stiffness of the underlying soil, which in turn is obtained from the Green’s function of a horizontally layered half-space using a layer transfer matrix approach. A planar multi-body model of the train, coupled to the track receptance, is used for calculating the train–track interaction forces as the train runs over an uneven rail. Finally, the building response to the incident wavefield is calculated using a 3D finite element model, accounting for the soil dynamic stiffness.The framework is used to evaluate the vibrations in two buildings with identical layout, one lightweight wooden building and one heavyweight concrete building, due to a passenger train passing by at two different speeds. It was found that the difference in response between the two buildings were small. Compared to the incident wavefield, an amplification of the response inside the building was found in frequency bands around the fundamental natural frequencies of the slabs; however for higher frequencies and in terms of the 1 s running RMS velocity the building response was reduced. Further, it was found that accounting for soil-structure-interaction, as opposed to simply enforcing the free-field displacements at the building foundations, significantly reduced the building response in terms of 1 s RMS velocity.

Another explicit forms of dynamic substructuring approaches using dynamic constraints at joint nodes

ABSTRACT The dynamic substructuring design describes the dynamic responses in the modal, frequency and physical domains using coupling methods at joint nodes. This paper presents dynamic structuring methods to modify existing substructuring methods by merging the concept of interfacial forces in the satisfaction of compatibility conditions at joint nodes. The algorithms correspond to a type of model reduction approaches that use a few modes of substructures with the assumption of pseudo-masses at the joint nodes of the substructures. It was verified through numerical examples that the pseudo-masses rarely affected the dynamic responses of the synthesized structure. A frequency response function-based substructuring method was derived by applying interface forces at joint nodes to frequency response function (FRF). The proposed dynamic substructuring methods are expressed in explicit forms for synthesizing substructures without any numerical schemes. The validity of the proposed method was illustrated using two numerical examples. The limitations of this study are evaluated using numerical examples.

A simple TD-BEM model for heterogeneous orthotropic hill-shaped topographies

A simple numerical model named DASBEM was successfully developed to analyze the seismic heterogeneous orthotropic hill-shaped topographies by a time-domain boundary element method (TD-BEM) based on half-space Green’s functions. The model was elaborated only by discretizing the hill surface and its interface with the underlying half-space through the use of image source theory and the substructure approach. To improve the model at the corners, the double node procedure was applied to the extreme nodes of the quadratic elements. An attenuation ratio is implemented in the boundary equations using a decremental exponential function. After presenting the technique, a validation example is presented alongside the literature to measure the convergence with an isotropic response. Next, a sample Gaussian-shaped hill model is prepared under propagating obliquely incident SH-waves as a common sample topography and the surface response is obtained by considering some significant parameters as well as the shape ratio, isotropy factor, frequency content, and angle of the incident wave. The ground surface response is sensitized in two time and frequency domains. The results showed that the amplitude of the response was not only dependent on the impedance ratio but also the orthotropy ratio, which was always effective in orienting the wave-front to amplify the ground movement.Graphical

Distributed real-time hybrid simulation method for dynamic response evaluation of floating wind turbines

Limited land and near coast spaces led to the development of floating wind turbine (FWT) farms in unlimited space of deep water with steady winds. Experimental evaluation of dynamic responses of FWT is essential to ensure its safe operation. However, due to laboratory limitations and scaling issues, realistic FWT responses are difficult to be replicated on scaled-down test specimens. To facilitate larger-scale testing of FWT and apply realistic wind and wave loads, distributed real-time hybrid simulation (dRTHS) method is proposed which combines the testing of FWT substructures at geographically distributed laboratories using wind tunnels and wave tanks. In this research, dRTHS experimental method for FWT is developed and its feasibility is verified through a series of virtual dRTHS (vdRTHS) and proof-of-the-concept partial dRTHS tests. The equation of motion of a prototype FWT structure under coupled aerodynamic and hydrodynamic loads was partitioned to represent the wind turbine tower and platform substructures, based on which substructural formulation was derived. During the vdRTHS, two distributed real-time controllers were used to simulate the physical testing of the two substructures tested in the wind tunnel and water tank, respectively, with interfacing data being transferred in real-time through a network. FWT responses from vdRTHS match well with those obtained from numerical simulations of the whole FWT model and the substructured models, demonstrating that the feasibility of the proposed dRTHS method. In addition, the substructuring approach, the vdRTHS testing platform, and the method to overcome network communication delay are effective in the vdRTHS resulting in reliable FWT dynamic responses under coupled loading conditions. Furthermore, the proposed dRTHS concept was verified through a partial distributed physical tests during which the wind turbine substructure was tested physically, while the platform substructure and the hydrodynamic loads were simulated numerically.

Mistuning Sensitivity of a Fan Bladed-Disk With Geometrical Nonlinearities

Abstract In order to decrease their environmental impact, turbo-engine manufacturers tend to increase the span of fan blades while maintaining a slender profile. This design leads to more pronounced geometrical nonlinear effects. Computing the frequency response function of such structures is complicated due to the size of their associated finite element model. Classical substructuring approaches are no longer efficient to reduce the size of the problem as all the nodes of the system must be kept since they experience nonlinear behaviors. Different reduction methodologies have been defined in the past decades to tackle such nonlinear systems. Among these strategies, the direct normal form (DNF) extends the theory of normal form to finite element models. This methodology is here applied to a single blade model. Based on the assumption of a fairly rigid disk and the cyclic symmetric properties, a full cyclic symmetric reduced-order model is computed. In this work, this methodology is extended to account for random mistuning. Such a strategy allows to perform, for instance, fast parametric studies. This paper studies the sensitivity of the random mistuning on a nonlinear open rotor system in order to help turbo-engineers in their design phase. Three ranges of the excitation level are studied. At a low level of excitation, the system is close to the linear case. For higher forcing amplitude, a high amplification factor (AF) due to the merge of an isolated branch is observed, which is detrimental for the structure. For the last range (containing the highest forcing amplitudes), the nonlinearities are highly activated, and low values of the amplification factor are obtained due to the spread of the vibrational energy over the frequency range.

Adaptive Sampling-Based Bayesian Model Updating for Bridges Considering Substructure Approach

Adaptive Sampling-Based Bayesian Model Updating for Bridges Considering Substructure Approach

A hybrid sub-structuring method for prediction of air inlet sound transmission

Air inlets coupled with mechanically controlled ventilation systems are widely used to renew polluted indoor air. They are generally positionned at the top of windows inducing a reduction of the sound insulation. As the harmful consequences of noisy environments on human health are more and more highlighted, it becomes necessary to maximize the sound insulation while ensuring a sufficient fresh air flow. To this end, efficient numerical simulation appears to be a promising way for studying air inlet acoustic behavior: many parameters can be considered without the need to carry out costly and time-consuming laboratory tests. This work aims at developing a reliable numerical model reproducing the acoustic laboratories used by manufacturers for the measurements of air inlet sound reduction index. The low frequency range is studied in the present paper as the measurement uncertainties arising from experimental conditions are the greatest at these frequencies. In order to make the calculations computationally efficient, the proposed model uses a sub-structuring approach called the Patch Transfer Function (PTF) method, and combines analytical or numerical solutions, depending on the subdomain considered. Each subsystem of complex geometries is discretized using finite elements. Conversely, the PTF of simple geometries are analytically computed from a modal decomposition, enriched with a quasi-static correction numerically computed. As empirical improvements pointed out the benefits of the addition of melamine foams, porous material modeling is introduced in the study based on an equivalent fluid model.

A global decoupling technique for subtractive modelling on acoustic and vibration problems

The reverse Condensed Transfer Function (rCTF) method is a substructuring approach based on the concept of condensed mechanical receptance and acoustical impedance. Its objective is to predict the vibroacoustic response of a subsystem which was initially part of a global system, from information taken from the global system and the subtracted subsystem which must be removed. This paper proposes an extended formulation to improve the convergence of the rCTF method for subtractive modelling. The fundamentals of the rCTF method have been proposed recently considering only the decoupling interface between the global system and the subtracted subsystem. This approach of decoupling, called the local approach, exhibits some numerical issues. In order to circumvent them, the decoupling interface is extended in this study to account for a second interface, internal to the subtracted subsystem. The numerical performances of this extension, called the global approach, are firstly studied on an academic rod decoupling case which allows parametric studies. Then, a comparison between the local and global approaches is proposed for the scattering problem of an acoustic plane wave by a rigid sphere in an infinite water medium.

A Problem-Independent Machine Learning (PIML) enhanced substructure-based approach for large-scale structural analysis and topology optimization of linear elastic structures

Structural analysis for structures composed of highly heterogeneous materials which often involves the solution of large-scale linear algebraic equations is very time-consuming even within the linear elastic regime. Furthermore, the tremendous computational cost of iterative large-scale finite element analysis also prevents the widespread use of topology optimization as a powerful design tool especially when the desired design resolution is very high. In order to break the bottleneck hindering the efficient solutions of large-scale structural analysis and design optimization problems, in the present article, a general machine learning (ML) enhanced substructure-based framework is proposed. The essential idea is resorting to the classical substructure-based finite element analysis approach and establishing an implicit mapping between the parameters characterizing the material distribution within a substructure and the corresponding condensed stiffness matrix/numerical shape functions through offline trained deep neural networks. In contrast to most of the existing ML enhanced approaches, the proposed framework is truly independent of the forms of structural geometry, boundary condition and external load, and can be applied to solve various boundary value problems governing by the same type of partial differential equation once the offline training is completed. Armed with modern artificial intelligence techniques, the proposed approach in some sense revives the classical substructure approach in finite element analysis. Compared with the traditional paradigm, it can achieve 104–105 times solution efficiency for tested large-scale examples with satisfactory accuracy. The effectiveness of the approach was also validated for the non-adjoint topology optimization problems, i.e., 3D compliant mechanism design. Finally, to demonstrate the proposed approach’s capability in dealing with extremely large-scale three-dimensional problems, a three-dimensional topology optimization problem with about 109 design variables and 3×109 degrees of freedom (Dofs) is solved on a laptop without resorting to any parallel computing techniques.

Исследование смягчения вибраций и переизлученного шума в зданиях, создаваемых при движении железнодорожного транспорта

Purpose: To present an integrated methodology that will model the entire environment, from the source of vibration to the re-radiated noise within buildings. Conduct a brief parametric analysis to show the potential of this approach in evaluating the effectiveness of mitigation measures for vibration and re-radiated noise. Methods: Estimate sound pressure levels generated in residential compartments as a result of train travel; analyze the coupled train-trail-ground-construction system; solve the acoustic part of the problem. Results: A numerical model based on the substructuring approach is considered. A measure to reduce the level of vibration and re-radiated noise inside the building has been studied, which consists in a continuous “floating slab-track” system, for which different values of the elastic mat stiffness under the slab have been considered. It has been found that the effectiveness of this measure comes from a positive combination of two essential factors: the frequency content of the response and the cutoff frequency assigned to each solution adopted. Practical significance: A comprehensive methodology for determining ground vibration and re-radiated noise caused by railway traffic is presented. The dependence is obtained, that the efficiency of reduction of vibration level and re-radiated noise inside the building, will be higher, if the solution with low cutoff frequency is applied and the response has the most significant frequency content at high frequencies.

SHM method for locating damage with incomplete observations based on substructure’s connectivity analysis

In this study, a structural health monitoring (SHM) method is proposed for damage localization with incomplete observations, which combines a substructuring approach and connectivity analysis of a substructure. The substructuring approach aims to isolate and monitor several substructures individually. The connectivity among the substructural degree-of-freedom (DOFs) was calculated based on the multivariate and conditional Granger causality analysis, and the health of the substructure was determined by analyzing connectivity variations. This method determines whether the substructure is damaged, and it also allows the location of damage within the substructure. It is not necessary to have a dynamic model of the structure; it only requires the use of accelerometers. The proposed method was evaluated numerically and experimentally using a three-dimensional truss structure.

Substructural damage identification using autoregressive moving average with exogenous inputs model and sparse regularization

Substructuring approaches possess many superiorities over traditional global approaches in damage identification because large-size global structures are replaced by small and manageable substructures. This paper proposes a substructural time series model for locating and quantifying the damage in complex systems. A substructural autoregressive moving average with exogenous inputs (ARMAX) model is established to extract the frequencies and mode shapes of substructures as indicators for damage detection. The detection of structural damage is essentially an inverse problem, and the damage in structure bears sparse properties. The inverse problem of substructural damage identification is efficiently solved via sparse regularization, and structural damage can be located and quantified through the nonzero terms in the solution vector. The accuracy of the proposed method is demonstrated by the numerical simulation of a frame structure and shaking table test of a shear building structure. As the substructural properties are more sensitive to local structural damage than the global properties, the substructural ARMAX model is quite accurate and efficient to be used in the damage identification of a complex system.

Macromechanism Approach for Vulnerability Assessment of Buildings on Shallow Foundations in Liquefied Soils

The damage caused by seismic shaking and liquefaction-induced permanent ground deformation has conventionally been assessed as two separate problems often by different engineers. However, the two problems are inherently linked, since ground shaking causes liquefaction, and liquefaction-induced soil softening affects ground shaking. Modelling both problems within a single numerical model is complex for both the engineer and the software, and most finite element software only have the capabilities to address one of them. To improve the estimates of the seismic performance of buildings on liquefiable soil, a new sub-structuring approach is proposed called the macro-mechanism approach. This approach allows the soil-liquefaction-foundation-structure interaction to be considered in a series of sub-models accounting for the major nonlinear mechanisms of the system at a macro level. The proposed approach was implemented in the open-source finite element software OpenSees and then applied to a case study of a building where significant liquefaction- and shaking-induced damage was observed after the 1999 Mw 7.4 Kocaeli Earthquake. The case study building was also simulated using two different commercial software programs, the finite difference software FLAC, and the finite element software PLAXIS, by two different research teams. A comparison between the results from the macro-mechanism approach compared to full numerical models shows that the macro-mechanism approach can capture the extent of the foundation deformation and provide more realistic estimates of the building damage than full approaches since the FLAC and PLAXIS models consider elastic elements for the building.

A comparative study of the novel externally-attached precast SRC braced-frames for seismic retrofitting under near-field spectrum-compatible non-stationary stochastic earthquake

Seismic retrofitting is a hot issue in the field of earthquake engineering, and the externally-attached substructure approach is a well-known solution due to its no-disturbing construction and high-efficiency improvement. In this paper, a comparative study of a novel externally-attached precast steel-reinforced-concrete (SRC) braced-frames for seismic retrofitting is performed, and the near-field spectrum-compatible non-stationary stochastic earthquakes are generated as the excitation to reflect the input uncertainty. The construction and simulation approaches of the novel substructure are first introduced, and then the generation theories of near-field spectrum-compatible non-stationary stochastic earthquake are explained. The comparative study of five scenarios is conducted, via a 3-span-5-story existing reinforced concrete frame, and a series of performance indices are adopted for analysis, including the inter-story deformation, inter-story shear force, section-mechanical performance, and energy-consumption capacity. In general, the comparison study verifies the effectiveness of the novel externally-attached SRC braced-frames for retrofitting, and the external frame obviously reduces the axial force of the existing beams and columns, which indicates that the shear demand is transferred to the external substructures and the damage accumulation is well controlled after retrofitting. Although the inter-story performance and energy-dissipation capacity of the external substructures are not as direct as the bare brace scenarios, the external frames alleviate the potential premature damage of the existing joints and avoid the infills or facades of the existing building to place external braces, which provides a practical reference for the engineering application and future research.

Initial structural damage detection approach via FE-based data augmentation and class activation map

Damage is generally initiated locally and spread to the entire structure. To avoid the destruction of the entire structure, it is crucial to detect and act on damage at an early stage through the real-time monitoring of the entire structure. However, the attachment of the many sensors to obtain sufficient detection resolution could change the structural dynamic characteristics of the structure. To compensate for these shortcomings, research has been conducted on digital image correlation (DIC) as a non-contact method of displacement/strain measurement. In addition, the real-time monitoring of a structure using DIC equipment is relatively straightforward. The final goal of this study is to predict the location of damage using the displacement of the structure surface which can be via DIC. This paper introduces a method for monitoring damage locations using a class activation map (CAM) network. The feasibility of the proposed process using the finite element method for an example considering the experimental situation was confirmed. To generate training data, the finite element method was used to obtain the displacement and strain of a target structure. Herein, sub-structuring approach with data augmentation using Gaussian integration point interpolation were employed to obtain the benign performance of the proposed approach. Thus, the proposed CAM network could classify the presence or absence of damage by considering strain fields. Moreover, the relevant result of the CAM network is a CAM image, which indicates the location of the damage. Finally, this CAM network was applied to a tensile specimen example and show good performance in the classification and detection of damage locations.

Estimation of Soil–Structure Model Parameters for the Millikan Library Building Using a Sequential Bayesian Finite Element Model Updating Technique

We present a finite element model updating technique for soil–structure system identification of the Millikan Library building using the seismic data recorded during the 2002 Yorba Linda earthquake. A detailed finite element (FE) model of the Millikan Library building is developed in OpenSees and updated using a sequential Bayesian estimation approach for joint parameter and input identification. A two-step system identification approach is devised. First, the fixed-base structural model is updated to estimate the structural model parameters (including effective elastic modulus of structural components, distributed floor mass, and Rayleigh damping parameters) and some uncertain components of the foundation-level motion. Then, the identified structural model is used for soil–structure model updating wherein the Rayleigh damping parameters, the stiffness and viscosity of the soil subsystem (modeled using a substructure approach), and the foundation input motions (FIMs) are estimated. The identified model parameters are compared with state-of-practice recommendations. While a specific application is made for the Millikan Library, the present work offers a framework for integrating large-scale FE models with measurement data for model inversion. By utilizing this framework for different civil structures and earthquake records, key structural model parameters can be estimated from the real-world recorded data, which can subsequently be used for assessing and improving, as necessary, state-of-the-art seismic analysis and structural modeling techniques. This paper presents an effort towards using real-world measurements for large-scale FE model updating in the soil and structure, uniform soil time domain for joint parameter and input estimation, and thus paves the way for future applications in system identification, health monitoring, and diagnosis of civil structures.

Identification of nonlinear bolted lap joint parameters using instantaneous power flow balance-based substructure approach

Identification of nonlinear bolted lap joint parameters using instantaneous power flow balance-based substructure approach