Geometry of growth strata in a transpressive fold belt in field and analogue model: Gosau Group at Muttekopf,Northern Calcareous Alps,Austria

The thrust sheets of the Northern Calcareous Alps were emplaced during Late Cretaceous thrust‐dominated transpression expressed by thrust sheets segmented by closely spaced tear faults. Thrust sheet‐top sediments were deposited during thrusting and associated fold growth and were controlled by active folding and tearing. We observe two types of angular unconformities: (1) Angular unconformities above folds between tear faults conform with the model of progressive unconformities. Across these unconformities dip decreases upsection. (2) Here, we define progressive unconformities that are related to tear faults and are controlled by both folding and tearing. Across these unconformities both strike and dip change. In growth strata overlying folds dissected by high‐angle faults, such unconformities are expected to be common. We used analogue modelling to define the geometry of the tear faults and related unconformities. Within the syn‐tectonic sediments, a steep, upward flattening thrust within a broader, roughly tulip‐shaped drag zone develops. The thrust roots in the tear fault in pre‐tectonic deposits and is curved upward toward the downthrown block. Vertical offset on the thrust is related to differential vertical uplift caused by, for example, growth of folds with different wavelength and amplitude on either side of the tear fault. Formation of progressive unconformities is governed by the relationship between the rates of deposition and vertical growth of a structure. Fault‐related progressive unconformities are additionally controlled by the growth of the vertical step across the tear fault. When the rates of vertical growth of two neighbouring folds separated by a tear fault are similar, the rate of growth across the tear fault is small; if the first differ, the latter is high. Episodic tear fault activity may create several angular unconformities attached to a tear fault or allow the generation of angular unconformities near tear faults in sedimentary systems that have a rate of deposition too high to generate classical progressive unconformities between the tear faults.     

Proportional stress and strain paths in barodesy

Asymptotic behaviour of soil deserves particular attention: If soil is deformed with a proportional strain path, the resulting stress path approaches asymptotically a proportional stress path. In this arcticle, we review existing experimental evidence on this phenomenon and discuss it in the frame of barodesy. Here, the presented relation is a modification of a barodetic expression and includes Jáky's relation, inhibits tensile stress and is able to predict asymptotic stress ratios based on experimental findings. The proposed relation is compared with experimental data as well as with the so‐called stress‐dilatancy relations and other constitutive relations proposed so far. Copyright © 2015 John Wiley & Sons, Ltd.     

Height-integrated flow in the convective Planetary Boundary Layer

Field data are analyzed in order to study the layer-averaged winds in the unstable, entraining, baroclinic, advective and non-stationary Planetary Boundary Layer (PBL). The relationship between the actual and geostrophic winds is described using three different equation sets. The results of these analytical expressions are compared with measurements from the Öresund experiment which was carried out during the period May 15 to June 14, 1984.     

Complex Site Effects in Thessaloniki (Greece): II. 2D SH Modelling and Engineering Insights

This paper presents results of numerical modelling of site response for Thessaloniki, obtained with two different 2D methods; a finite difference and a finite element method. Ground motion across a 2D model of the subsoil of the city has been simulated for vertically incident SH waves. The predominance of locally generated surface waves is very clear in the synthetic seismograms of a weak event and of stronger ones. These results are then compared with the observations in time domain and frequency domain. The role of the soil formations with high attenuation in the lateral propagation and the effect of the differential motion close to the lateral variations are also pinpointed. The stronger events were finally used to compute strong ground motion in order to reveal and to discuss practical engineering aspects such as peak ground acceleration value, the most familiar indicator in seismic norms, the soil to rock spectral coefficients for the period bandwidth of interest, and the aggravation factor in terms of 2D to 1D response spectra as a useful ruler to account for complex site effects.     

Direct estimation of the seismic demand and capacity of oscillators with multi‐linear static pushovers through IDA

SPO2IDA is introduced, a software tool that is capable of recreating the seismic behaviour of oscillators with complex quadrilinear backbones. It provides a direct connection between the static pushover (SPO) curve and the results of incremental dynamic analysis (IDA), a computer‐intensive procedure that offers thorough demand and capacity prediction capability by using a series of nonlinear dynamic analyses under a suitably scaled suite of ground motion records. To achieve this, the seismic behaviour of numerous single‐degree‐of‐freedom (SDOF) systems is investigated through IDA. The oscillators have a wide range of periods and feature pinching hysteresis with backbones ranging from simple bilinear to complex quadrilinear with an elastic, a hardening and a negative‐stiffness segment plus a final residual plateau that terminates with a drop to zero strength. An efficient method is introduced to treat the backbone shape by summarizing the analysis results into the 16, 50 and 84% fractile IDA curves, reducing them to a few shape parameters and finding simpler backbones that reproduce the IDA curves of complex ones. Thus, vast economies are realized while important intuition is gained on the role of the backbone shape to the seismic performance. The final product is SPO2IDA, an accurate, spreadsheet‐level tool for performance‐based earthquake engineering that can rapidly estimate demands and limit‐state capacities, strength reduction R‐factors and inelastic displacement ratios for any SDOF system with such a quadrilinear SPO curve. Copyright © 2006 John Wiley & Sons, Ltd.     

Buckling and vibration analysis of flexible beams resting on an elastic half-space

The present paper deals with the buckling and vibration of prismatic beams resting on an elastic half-space. The computational procedure developed herein utilizes the advantages of both an analytical approach and a finite element scheme. This is accomplished by deriving exact frequency and axial force dependent stiffness matrices using the analytical solutions of the governing differential equation as ‘shape functions’. The major advantages of the proposed approach over previous ones are pointed out and discussed in detail. Numerical results demonstrating the performance of the proposed method are presented in the final part of the paper.     

Modelling of R/C members accounting for shear failure localisation: Hysteretic shear model

Reinforced concrete (R/C) frame buildings designed according to older seismic codes represent a large part of the existing building stock worldwide. Their structural elements are often vulnerable to shear or flexure‐shear failure, which can eventually lead to loss of axial load resistance of vertical elements and initiate vertical progressive collapse of a building. In this study, a hysteretic model capturing the local shear response of shear‐deficient R/C elements is described in detail, with emphasis on post‐peak behaviour; it differs from existing models in that it considers the localisation of shear strains after the onset of shear failure in a critical length defined by the diagonal failure planes. Additionally, an effort is made to improve the state of the art in post‐peak shear response modelling, by compiling the largest database of experimental results for shear and flexure‐shear critical R/C columns cycled well beyond the onset of shear failure and/or up to the onset of axial failure, and developing empirical relationships for the key parameters defining the local backbone post‐peak shear response of such elements. The implementation of the derived local hysteretic shear model in a computationally efficient beam‐column finite element model with distributed shear flexibility, which accounts for all deformation types, will be presented in a companion paper.     

Modelling of R/C members accounting for shear failure localisation: Finite element model and verification

Reinforced concrete (R/C) frame buildings designed according to older seismic codes represent a large part of the existing building stock worldwide. Their structural elements are often vulnerable to shear or flexure‐shear failure, which can eventually lead to loss of axial load resistance of vertical elements and initiate vertical progressive collapse of a building. In this study, a computationally efficient member‐type finite element model for the hysteretic response of shear critical R/C frame elements up to the onset of axial failure is presented; it accounts for shear‐flexure interaction and considers, for the first time, the localisation of shear strains, after the onset of shear failure, in a critical length defined by the diagonal failure plane. Its predictive capabilities are verified against experimental results of column and frame specimens and are shown to be accurate not only in terms of total response, but also with regard to individual deformation components. The accuracy, versatility, and simplicity of this finite element model make it a valuable tool in seismic analysis of complex R/C buildings with shear deficient structural elements.