On the simulation of the seismic energy transmission mechanisms

In recent years, considerable attention has been paid to research and development methods able to assess the seismic energy propagation on the territory. The seismic energy propagation is strongly related to the complexity of the source and it is affected by the attenuation and the scattering effects along the path. Thus, the effect of the earthquake is the result of a complex interaction between the signal emitted by the source and the propagation effects. The purpose of this work is to develop a methodology able to reproduce the propagation law of seismic energy, hypothesizing the "transmission" mechanisms that preside over the distribution of seismic effects on the territory, by means of a structural optimization process with a predetermined energy distribution. Briefly, the approach, based on a deterministic physical model, determines an objective correction of the detected distributions of seismic intensity on the soil, forcing the compatibility of the observed data with the physical-mechanical model. It is based on two hypotheses: (1) the earthquake at the epicentre is simulated by means of a system of distortions split into three parameters; (2) the intensity is considered coincident to the density of elastic energy. The optimal distribution of the beams stiffness is achieved, by reducing the difference between the values of intensity distribution computed on the mesh and those observed during four regional events historically reported concerning the Campania region (Italy)

Probabilistic assessment of historical masonry walls retrofitted with through-The-Thickness confinement devices

A very popular and efficient technique for structural retrofit of historical masonry buildings is represented by Jacketing techniques coupled with Through-The-Thickness (TTJ) ties since the triaxial stress state induced by confinement increases structural ductility and strength. In this respect, the authors have recently developed an Equivalent Single Layer (ESL) Firstorder Shear Deformation (FSDT) shell theory capable of modeling the TTJ interaction at the global structural level by a computationally less expensive 2D continuum layered formulation. The present contribution investigates the sensitivity of the TTJ formulation, used in conjunction with MITC finite elements, with respect to the constitutive uncertainties of an existing masonry panel. To this end, constitutive parameters of the existing structure are characterized by means of random variables which take into account masonry nonhomogeneities as well as the state of knowledge of structural parameters. All remaining mechanical and loading parameters are treated herein as deterministic variables and dimensioned according to common design practices of Italian and European code regulations. Therefore, a Monte Carlo simulation is performed in order to get the probability distributions of the structural responses. A subsequent reliability analysis aims to investigate the influence of TTJ confinement devices on the ultimate limit state of plane elements. Moreover, comparisons are made between the results obtained by the investigated methodology and simpler and more empirical estimates of the strength increment based on the Italian building code recommendations

A MITC-based procedure for the numerical integration of a continuum elastic-plastic theory of through-the-thickness-jacketed shell structures

Through-the-Thickness Jacketing (TTJ) is a technique for repairing and retrofitting shell structures by inducing in the shell core a beneficial confining stress state created by a net of broadly distributed retrofitting links crossing the shell thickness and tying externally applied layers. The paper presents the derivation, the algorithmic implementation and the numerical assessment of a predictor-corrector computational strategy for the integration of a shell FE-model obtained by combining a discrete MITC quadrilateral element with a layered continuum-based generalized shell theory of TTJ-reinforced structures, essentially based upon a Winkler-like idealization of TTJ. This theory of Through-the-Thickness-Jacketed Shells (TTJS) captures the onset of complex triaxial stress states originated by the interaction between core and TTJ reinforcements. Results of benchmark numerical applications in OpenSees with flat and curved elastic–plastic shell structures are presented in order to assess and illustrate the consistency and the general modelling features of the proposed TTJS-MITC framework endowed with the Drucker-Prager elastic-perfectly-plastic idealization of the nonlinear behavior of the material composing the shell. Numerical results exhibit quadratic convergence and show that the model captures marked strength increments over the in-plane membrane response, albeit these are lower when the response is predominantly of out-of-plane flexural type

Implementation and finite-element analysis of shell elements confined by Through-The-Thickness uniaxial devices

This contribution presents the implementation in OpenSees of an integration procedure based on a recently developed theory concerning stress integration along the chords of a shell element reinforced with uniaxial transverse links. Such a model has been developed in order to account for transverse confinement effects induced by through-the-thickness jacketing of masonry and reinforced concrete existing structures. In particular, transverse confinement induces a triaxial stress state in the core material of the shell increasing the stress spherical part and resulting in strength and ductility increments. In order to perform structural analyses with reduced computational costs, the presented tool permits to compute the response of plane elements confined by uniaxial devices. To this end, the implemented object accounts for the mutual interaction of uniaxial reinforcements with a triaxial core by means of equilibrium and compatibility equations involving several object classes of the OpenSees framework. Integration of the triaxial stress state along the thickness of a shell element is therefore performed by numerically solving the equilibrium/compatibility equation system. The adopted implementation strategy is summarized and modeling features are discussed. In conclusion, numerical examples show some possible applications of the proposed tool in common structural design practices

A continuum theory of through–the–thickness jacketed shells for the elasto-plastic analysis of confined composite structures: Theory and numerical assessment

The paper proposes a generalized shell formulation devised for the triaxial stress analysis of Through-the-Thickness (TT) confining mechanisms induced by TT Jacketing (TTJ) devices in laminated composite structures, such as masonry walls retrofitted by stirrups-tied FRP sheets and TT jacketed concrete sandwich panels. Assuming a smeared description of TT reinforcements, the proposed shell formulation is constructed as an enhancement of the classical laminated shell formulation based on the Equivalent Single Layer Mindlin First-order Shear Deformation Theory (ESL-FSDT). This enhancement captures TT stretching by adding the TT displacement field among the kinematic variables and permits to describe the smeared TTJ interaction between transverse uniaxial reinforcements and confined layers in terms of continuum equilibrium and compatibility equations. Statics and kinematics of the shell are developed by following standard work-association arguments and encompassing both TT-laminated and TT-functionally graded structures. A nonlinear elasto-plastic constitutive behavior of the core material and of the TT reinforcements is considered and explicit representations of the elasto-plastic tangent operator are derived. The TTJ formulation is combined with a MITC finite element formulation and implemented in the research FE code Opensees. Results of nonlinear structural analyses of walls subject to in-plane and out-of-plane bending show that the proposed TTJ approach provides physically meaningful predictions of the structural response and is capable to efficiently track a complex triaxial confining interaction which ultimately results into marked global structural effects of increased stiffness, strength and ductility. © 2017 Elsevier Lt

A Computational Strategy for Eurocode 8-Compliant Analyses of Reinforced Concrete Structures by Seismic Envelopes

A procedure is presented for performing Eurocode 8-compliant spectral analyses of reinforced concrete structures by means of seismic response envelopes. To account for global torsion effects in the computation of the supreme envelope an algorithmic rotational response spectrum is defined. The presented strategy turns out to be particularly appropriate for finite element models including accidental eccentricity due to mass shifting since seismic envelopes can be computed by making reference to a single structural model rather than to separate models characterized by different signs of the accidental eccentricity. The proposed procedure is theoretically formulated and numerically tested by analyzing a rotationally stiff and a rotationally flexible building as well as two irregular structures. Moreover, it is compared with an alternative formulation derived from a recently proposed strategy concerning accidental torsion. The results show that the proposed procedure is coherent with the analysis procedures provided by standard codes and computationally more efficient

A class of uniaxial phenomenological models for simulating hysteretic phenomena in rate-independent mechanical systems and materials

We present a general formulation of a class of uniaxial phenomenological models, able to accurately simulate hysteretic phenomena in rate-independent mechanical systems and materials, which requires only one history variable and leads to the solution of a scalar equation for the evaluation of the generalized force. Two specific instances of the class, denominated Bilinear and Exponential Models, are developed as an example to illustrate the peculiar features of the formulation. The Bilinear Model, that is one of the simplest hysteretic models which can be emanated from the proposed class, is first described to clarify the physical meaning of the quantities adopted in the formulation. Specifically, the potentiality of the proposed class is witnessed by the Exponential Model, able to simulate more complex hysteretic behaviors of rate-independent mechanical systems and materials exhibiting either kinematic hardening or softening. The accuracy and the computational efficiency of this last model are assessed by carrying out nonlinear time history analyses, for a single degree of freedom mechanical system having a rate-independent kinematic hardening behavior, subjected either to a harmonic or to a random force. The relevant results are compared with those obtained by exploiting the widely used Bouc–Wen Model

An Accurate and Computationally Efficient Uniaxial Phenomenological Model for Steel and Fiber Reinforced Elastomeric Bearings

We present a uniaxial phenomenological model to accurately predict the complex hysteretic behavior of bolted steel reinforced elastomeric bearings and unbonded fiber reinforced elastomeric bearings. The proposed model is based on a set of only five parameters, directly associated with the graphical properties of the hysteresis loop, leads to the solution of an algebraic equation for the evaluation of the isolator restoring force, requires only one history variable, and can be easily implemented in a computer program. The proposed model is validated by means of experimental tests and numerical simulations. In particular, the results predicted analytically are compared with some experimental results selected from the literature. Furthermore, numerical accuracy and computational efficiency of the model are assessed by performing nonlinear time history analyses on a single degree of freedom mechanical system and comparing the results with those associated with a modified version of the celebrated Bouc-Wen model

Analysis of stress partitioning in biphasic mixtures based on a variational purely-macroscopic theory of compressible porous media: recovery of Terzaghi’s law

The mechanics of stress partitioning in two-phase porous media is predicted on the basis of a variational purely-macroscopic theory of porous media (VMTPM) with compressible constituents. Attention is focused on applications in which undrained flow (UF) conditions are relevant, e.g., consolidation of clay soils and fast deformations in cartilagineous tissues. In a study of the linearized version of VMTPM we have recently shown that, as UF conditions are approached (low permeability or fast loading), Terzaghi’s effective stress law holds as a general property of rational continuum mechanics and is recovered as the characteristic stress partitioning law that a biphasic medium naturally complies with. The proof of this property is obtained under minimal constitutive hypotheses and no assumptions on internal microstructural features of a particular class of material. VMTPM predicts that such property is unrelated to compressibility moduli of phases and admits no deviations from Terzaghi’s expression of effective stress, in contrast with most of the currently available poroelastic theoretical frameworks. This result is presently illustrated and discussed. Simulations of compressive consolidation tests are also presented; they are obtained via a combined analytical-numerical integration technique, based on the employment of Laplace transforms inverted numerically via de Hoog et al.’s algorithm. The computed solutions consistently describe a transition from drained to undrained flow which confirms that Terzaghi’s law is recovered as the limit UF condition is approached and indicate a complex mechanical behavior