Fractional dynamics and MDS visualization of earthquake phenomena

This paper analyses earthquake data in the perspective of dynamical systems and fractional calculus (FC). This new standpoint uses Multidimensional Scaling (MDS) as a powerful clustering and visualization tool. FC extends the concepts of integrals and derivatives to non-integer and complex orders. MDS is a technique that produces spatial or geometric representations of complex objects, such that those objects that are perceived to be similar in some sense are placed on the MDS maps forming clusters. In this study, over three million seismic occurrences, covering the period from January 1, 1904 up to March 14, 2012 are analysed. The events are characterized by their magnitude and spatiotemporal distributions and are divided into fifty groups, according to the Flinn–Engdahl (F–E) seismic regions of Earth. Several correlation indices are proposed to quantify the similarities among regions. MDS maps are proven as an intuitive and useful visual representation of the complex relationships that are present among seismic events, which may not be perceived on traditional geographic maps. Therefore, MDS constitutes a valid alternative to classic visualization tools for understanding the global behaviour of earthquakes

Recent advances in engineering characteristics of near-fault ground motions and seismic effects of building structures

Severe damages of civil infrastructures under near-fault ground motions have impelled the community of earthquake engineering to pay intensive attention and investigation to their engineering characteristics and structural seismic effects. This paper reviews the recent research advances of authors in the engineering characteristics of near-fault ground motions and seismic responses and base-isolated performance analysis of building structures. Firstly, two non-structure-specific intensity measures, such as improved effective peak acceleration and velocity (IEPA, IEPV) were proposed. Two frequency content parameters were also suggested, namely the mean period of Hilbert marginal spectrum Tmh, and coefficient of variance of dominant instantaneous frequency of Hilbert spectrum Hcov which reflects the frequency nonstationary degree of ground motions. Meanwhile, a new stochastic model to synthesize near-fault impulsive ground motions with the feature of the strongest pulse was established. Then, the chaotic and fractal/multifractal characteristics of strong earthquake ground motions were analyzed deeply to explore their complexity from a novel perspective of nonlinear dynamics, and the inherent relation between fractal dimensions and period parameters of near-fault motions was exposed. Moreover, the mechanism of interstory deformation of tall building was illustrated based on engineering properties of pulse-like ground motions and generalized drift spectral analysis. Finally, the influence of ground motion properties on the seismic responses and performance of tall structures and base isolated buildings was revealed

Nonlinear dynamical modeling of seismic events induced by stress change due to excavation of horizontal underground chambers

U ovoj disertaciji, cilj istraživanja bio je određivanje dinamičkih svojstava potresa izazvanih promenom naponskog stanja pri izradi horizontalnih podzemnih prostorija. Analiza potresa izvedena je sa dva aspekta – u prvom delu istraživanja izučavane su vremenske serije oscilovanja tla za vreme potresa, a u drugom delu vršena je analiza stabilnosti fenomenološkog Baridž-Knopof modela bloka sa oprugom. Vremenske serije oscilovanja tla proučavane su primenom postupka analize surogat podataka, kao i korišćenjem metoda analize nelinearnih vremenskih serija (primena teoreme o razvijanju skalarne vremenske serije). Analiza vremenskih serija izvedena je za potrese izazvane reaktiviranjem kretanja duž raseda usled napredovanja rudarskih radova, registrovanih na tri lokacije (rudnika) u Poljskoj: rudnici bakra Rudna i Legnic-Glogov, i rudnik uglja Gornja Silezija. Rezultati izvedene analize pokazali su da registrovane vremenske serije oscilovanja tla u pravcu sever-jug i u vertikalnom pravcu pripadaju nelinearnim vremenskim serijama, dok oscilovanja tla u pravcu istok-zapad pripadaju klasi stacionarnih stohastičkih procesa sa Gausovom raspodelom stohastičkog dela, koji mogu biti modifikovani nepoznatom nelinearnom funkcijom. Međutim, iako su oscilovanja tla u pravcu sever-jug i u vertikalnom pravcu nelinearna, primenom teoreme o razvijanju potvrđena je njihova stohastička priroda, i to malom vrednošću determinističkog faktora κ (<1) i niskom greškom unakrsnog predviđanja kod testa stacionarnosti. U drugom delu istraživanja, vršena je analiza stabilnosti kretanja nekoliko varijanti Baridž-Knopof modela, i to: Madariaga modela jednog bloka sa Diterih-Ruina zakonom trenja zavisnim od brzine i stanja, potom Karlson-Langer modela sa jednim i dva bloka i sa zakonom trenja zavisnim samo od brzine, kao i Beker modela sa jednim blokom, Diterih-Ruina zakonom trenja zavisnim od brzine i stanja i sa dve promenljive stanja. Analiza stabilnosti izvedena je numeričkim i analitičkim putem. Numerički je izvršena analiza stabilnosti Karlson-Langer i Beker modela, posmatranjem ponašanja rešenja u blizini ravnotežnog stanja, dok je u slučaja Madariaga modela, bifurkaciona analiza izvedena analitički (standardna lokalna bifurkaciona analiza), a rezultati su potvrđeni numerički u programskom paketu DDE-BIFTOOL...In this dissertation, the aim of the research was to determine the dynamics of seismic events induced by the stress change due to excavation of horizontal underground chambers. The conducted analysis was twofold – in the first part of the research, time series of strong ground motion during the seismic event are analyzed, while in the second part, the stability analysis of phenomenological Burridge-Knopoff spring-block model is conducted. For this purpose, different methods are engaged. The time series analysis was performed using the surrogate data testing and nonlinear time series analysis (delay embedding theorem). These analyzes were performed for the strong ground motion recordings at three different mines in Poland: copper mines Rudna and Legnic-Glogov and coal mine Upper Silezia. In all the examined cases, the results of the analysis indicated that the time series of strong ground motion in north-south and vertical direction, induced by the excavation of underground chambers, belong to nonlinear processes, while the strong ground motion in east-west direction belongs either to a class of stationary linear stochastic processes with Gaussian inputs, or to a class of stationary Gaussian linear processes transformed by some nonlinear function. The nonlinear time series analysis confirmed stochastic nature of strong ground motion, recorded in all directions, by performing the deterministic test (κ<1) and stationarity test (low cross-prediction error). In the second part of the research, the stability analysis is performed for several types of the Burridge-Knopoff model: for Madariaga single-block model with Dieterich-Ruina rate and state dependent friction law, for Carlson-Langer model with one and two blocks and velocity dependent friction law, and for Becker single-block model with Dieterich-Ruina rate and state dependent friction law and two state variables. The stability analysis for these models is conducted numerically and analytically. The numerical analysis was performed for Carlson-Langer and Becker model, by applying the Runge-Kutta fourth-order method. In the case of Madariaga model, the analysis is performed analytically (standard local bifurcation analysis), and the results are later confirmed numerically, using the DDE-BIFTOOL software package..