Nonlinear vibrations of soil strata according to instrumental and numerical data

Исследования нелинейных явлений в грунтах, начатые в России почти 60 лет назад, явились стимулом современного развития исследований сейсмоаномальных явлений в комплексе геофизических показателей, наблюдающихся при сильных и разрушительных землетрясениях. Кроме чисто научных интересов большой интерес вызывает вопрос прогнозирования поведения грунтов и сооружений с точки зрения адекватности ожидаемому проявлению сейсмического воздействия. Адекватное изучение нелинейности, являющейся неотъемлемой характеристикой природных явлений, позволит приблизить соответствующее антисейсмические мероприятия к реальным особенностям проявлений сейсмического эффекта при сильных землетрясениях. Цельюработы являлось построение расчетной модели, описывающей явления, наблюдаемые в грунтовой среде при сильных сейсмических воздействиях и сопоставление расчетных данных с результатами инструментальных наблюдений. Методы. В работе анализируется иснтрументальная запись, полученная на слабых грунтах, на сонове вейвлет нанализа. Моделируются импульсы различной проолжитлеьности в среде с различной стпенью проявления нелинейных свойст (кртутизны нелиненйой заивисисмоти напряжение -деформация) методом конечных элементов. Результаты. В результате установлены различия в спектральном составе моделируемых импульсов. Сильное проявление нелинейных свойств характеризуется резкими изменениями фаз колебаний, в фазах высокой скорости нарастания амплитуд. В нелинейных спектрах происходит перераспределение энергии в более высокочастотную область, кратную основному пику, тем сильнее, чем сильнее нелинейность кривой наряжение-деформация. Studies of nonlinear phenomena in soils, which began in Russia almost 60 years ago, have stimulated the modern development of studies of seismically anomalous phenomena in the complex of geophysical indicators observed during strong and destructive earthquakes. In addition to scientific interests, the issue of forecasting the behavior of soils and structures from the point of view of adequacy to the expected manifestation of seismic impact is of great interest. An adequate study of nonlinearity, which is an integral characteristic of natural phenomena, will make it possible to bring the corresponding antiseismic measures closer to the real features of the manifestations of the seismic effect during strong earthquakes. Aim. The aim of the work was to build a computational model describing the phenomena observed in a soil medium under strong seismic effects and to compare the computed data with the results of instrumental observations. Methods.The paper analyzes an instrumental record obtained on soft soils using wavelet analysis. With the help of the finite element method pulses of different duration are modeled in a medium with different degrees of nonlinear properties manifestation (steepness of nonlinear stress-strain dependence). Results. As a result, differences in the spectral composition of the modeled pulses were determined. A strong manifestation of nonlinear properties is characterized by sharp changes in the phases of vibrations, in the phases of a high rate of amplitude rise. In nonlinear spectra, the energy is redistributed to a higher frequency region, which is a multiple of the main peak and the stronger the nonlinearity of the stress-strain curve is stronger.

An experimental approach on calcarenite reservoir dilation factor

The time of flight of a plane wavefront generated from an acoustic pulse is expected to decrease when the medium length between the wave emitter and receiver is shortened. This simple idea is extrapolated to the case of reservoir compaction in order to obtain a geophysical parameter R (dilation factor) that relates the rock deformation to the variation of time of flight (also called time-lapse time shift in 4D seismics) or acoustic velocity of a plane wave propagating in the same direction of deformation. Interpretation of a few laboratory compressive tests with simultaneous ultrasonic acquisition, performed on oil-saturated calcarenite samples, are presented and discussed. The samples were subjected to several stress regimes and simultaneous ultrasonic acquisitions. Despite the formerly ultrasonic acquisition rate limitations, it was possible to obtain R values for various lateral-vertical stress ratios for each sample's linear and nonlinear stress-strain trends.

Modelling and Simulation of Deformation and Failure of Reinforced Concrete Beams under Four-Point Bending

A new mathematical model for the four-point bending of reinforced concrete beams is developed and investigated. The model takes into account multi-modulus concrete behavior, nonlinear stress-strain relationships, and damage evolution. An algorithm for a numerical implementation of the model is proposed. The corresponding boundary value problem is solved by the hp-version of the least-squares collocation method in combination with an acceleration of an iterative process based on Krylov subspaces and parallelizing. Special attention is given to the influence of mathematical model parameters on the results of numerical simulation. The results are compared with experimental data and three-dimensional simulation. A satisfactory agreement is shown

MCMC inversion of the transient and steady-state creep flow law parameters of dunite under dry and wet conditions

The rheology of the upper mantle impacts a variety of geodynamic processes, including postseismic deformation following great earthquakes and post-glacial rebound. The deformation of upper mantle rocks is controlled by the rheology of olivine, the most abundant upper mantle mineral. The mechanical properties of olivine at steady state are well constrained. However, the physical mechanism underlying transient creep, an evolutionary, hardening phase converging to steady state asymptotically, is still poorly understood. Here, we constrain a constitutive framework that captures transient creep and steady state creep consistently using the mechanical data from laboratory experiments on natural dunites containing at least 94% olivine under both hydrous and anhydrous conditions. The constitutive framework represents a Burgers assembly with a thermally activated nonlinear stress-versus-strain-rate relationship for the dashpots. Work hardening is obtained by the evolution of a state variable that represents internal stress. We determine the flow law parameters for dunites using a Markov chain Monte Carlo method. We find the activation energy $$430\pm 20$$ 430 ± 20 and $$250\pm 10$$ 250 ± 10 kJ/mol for dry and wet conditions, respectively, and the stress exponent $$2.0\pm 0.1$$ 2.0 ± 0.1 for both the dry and wet cases for transient creep, consistently lower than those of steady-state creep, suggesting a separate physical mechanism. For wet dunites in the grain-boundary sliding regime, the grain-size dependence is similar for transient creep and steady-state creep. The lower activation energy of transient creep could be due to a higher jog density of the corresponding soft-slip system. More experimental data are required to estimate the activation volume and water content exponent of transient creep. The constitutive relation used and its associated flow law parameters provide useful constraints for geodynamics applications. Graphical Abstract

Cross-Sectional Analysis of the Resistance of Rc Members Subjected to Bending With/without Axial Force

The paper presents section models for analysis of the resistance of RC members subjected to bending moment with or without axial force. To determine the section resistance the nonlinear stress-strain relationship for concrete in compression is assumed, taking into account the concrete softening. It adequately describes the behavior of RC members up to failure. For the reinforcing steel linear elastic-ideal plastic model is applied. For the ring cross-section subjected to bending with axial force the normalized resistances are derived in the analytical form by integrating the cross-sectional equilibrium equations. They are presented in the form of interaction diagrams and compared with the results obtained by testing conducted on RC columns under eccentric compression. Furthermore, the ultimate normalized bending moment has been derived for the rectangular cross-section subjected to bending without axial force. It was applied in the cross-sectional analysis of steel and concrete composite beams, named BH beams, consisting of the RC rectangular core placed inside a reversed TT welded profile. The comparisons made indicated good agreements between the proposed section models and experimental results.

Post-buckling behavior estimation of rigidly supported cylindrical composite panels in case shear

We present the solution of the geometrically nonlinear problem of the shear-critical behavior of a thin composite cylindrical panel of small curvature of orthotropic structure. The obtained solution considers the conditions of all-round rigid support. The expression for determining the membrane stresses arising in the supercritical state is given. When considering a linear problem, expressions for determining the critical shear flow are given. A method for determining the nonlinear stress-strain state in the overcritical state for a given thickness and stacking of an orthotropic panel is presented. The obtained solutions can be used in the design of load-bearing cylindrical panels, as well as in the analysis of geometrically nonlinear behavior of defects such as delaminations.

A Comparison of Shell and Solid Finite Element Models of Austenitic Stainless Steel Columns in Compression

The subject of this article is the implementation of new knowledge on material and geometric characteristics obtained from an experimental research program in advanced numerical modelling of compressed columns made of austenitic stainless steel using the ANSYS Classic software. Nonlinear stress–strain curves were obtained using our own experimental program and studied in terms of identifying the most suitable nonlinear material model. Additional material and geometric characteristics were obtained from literature and other independent research. Numerical models differing in mesh density localization, formulation of element integration, non-linear material model, and initial geometric imperfections were created and compared. The aim of the models was the ultimate limit state of a strut of circular hollow cross-section stressed by compression and analysed using the geometrically and materially nonlinear solution with consideration to the influence of initial imperfections. Static resistance and limit state deformations are compared for each model. The paper presents the analysis of model uncertainty by comparing SHELL and SOLID FE models, which must be characterized before the start of the analysis of the random influence of imperfections on the limit states. The mean values and the coefficients of variation are practically the same for both approaches. In summary, the presented models can be considered sufficiently validated and eligible for integration in tandem with simulation sampling methods.