Bounds on Amplification Factors, Element-Node and Node-Node Equivalence for Square Finite Elements in Kinematic Shallow Water Equations

The upper and lower bounds of amplification factors of lumped finite element schemes are compared with nodal (integer or half-integer multiple of) eigen-value solutions of consistent finite element scheme at element and node levels of error analysis. The closeness or proximity between bounds on solutions of amplification factors and eigen-solutions reveals that the two methods, consistent and lumped finite element schemes are equivalent. The element error solutions of lumped mass matrix assumption and consistent nodal solution denotes the element-node error equivalence and the nodal solutions of all of the finite element schemes denote the node-node error equivalence for square finite elements in kinematic wave shallow water equations. The comparison plots of lumped and consistent finite element schemes are presented in this paper for illustration.

Dynamic amplification factors of girder and cables of extradosed bridges during sudden cable failure

The rupture of a cable in cable-supported bridges is an accidental condition that should be considered during the design phase due the impact that this situation could have on the structural safety of the bridge and users. For that reason, design guidelines suggest carrying out a pseudo-static analysis where the failing cable is replaced by a load of the same magnitude as the pre-rupture tension but applied in the opposite direction and multiplied by a dynamic amplification factor (DAF) between 1.5 and 2.0. Previous studies in cable-stayed bridges have shown that the pseudo-static approach may not be suitable. Due to the wide use of extradosed bridges in infrastructure projects around the world, a computational analysis was performed in this investigation to estimate the dynamic amplification factors of extradosed bridge girders and cables when sudden failure of an extradosed cable occurs. The main goal of the study is to determine whether the pseudo-static approach suggested in the guidelines is acceptable. Linear response history analyses were performed by using computational models of extradosed bridges in which the girder stiffness and the suspension (lateral or central) and cable layout (fan or harp) of the cables were modified. From the analysis, the DAFs were calculated and compared to those recommended in the design guidelines. The calculated DAFs for the axial forces and bending moment in the girder of the bridges and for the axial forces in the extradosed cables were smaller than 2.0. However, in some cases the DAF for shear forces were higher than 2.0, especially when the girder stiffness was relatively low. The results indicate that the recommendations of the design guidelines are adequate for extradosed bridges, which is a result of the relatively high stiffness of the girder and low inclination of extradosed cables. Despite this, response history analyses like the one performed in this study are recommended to assess the response of the bridge under cable breakage.

A Novel Method for Predicting Local Site Amplification Factors Using 1-D Convolutional Neural Networks

The analysis of site seismic amplification characteristics is one of the important tasks of seismic safety evaluation. Owing to the high computational cost and complex implementation of numerical simulations, significant differences exist in the prediction of seismic ground motion amplification in engineering problems. In this paper, a novel prediction method for the amplification characteristics of local sites was proposed, using a state-of-the-art convolutional neural network (CNN) combined with real-time seismic signals. The amplification factors were computed by the standard spectral ratio method according to the observed records of seven stations in the Lower Hutt Valley, New Zealand. Based on the geological exploration data from the seven stations and the geological hazard information of the Lower Hutt Valley, eight parameters related to the seismic information were presumed to influence the amplification characteristics of the local site. The CNN method was used to establish the relationship between the amplification factors of local sites and the eight parameters, and the training samples and testing samples were generated through the observed and geological data other than the estimated values. To analyze the CNN prediction ability for amplification factors on unrecorded domains, two CNN models were established for comparison. One CNN model used about 80% of the data from 44 seismic events of the seven stations for training and the remaining data for testing. The other CNN model used the data of six stations to train and the remaining station’s data to test the CNN. The results showed that the CNN method based on the observation data can provide a powerful tool for predicting the amplification factors of local sites both for recorded positions and for unrecorded positions, while the traditional standard spectral ratio method only predicts the amplification factors for recorded positions. The comparison of the two CNN models showed that both can effectively predict the amplification factors of local ground motion without records, and the accuracy and stability of predictions can meet the requirements. With increasing seismic records, the CNN method becomes practical and effective for prediction purposes in earthquake engineering.

GMPE-Consistent Hard-Rock Site Adjustment Factors for Western North America

Developing of site amplification factors for hard-rock conditions that are consistent with GMPE models at lower velocities.

Thermomechanical Characterization of Carbon Black Reinforced Rubbers During Rapid Adiabatic Straining

The thermo-mechanical properties of carbon black reinforced natural and styrene butadiene rubbers are investigated under rapid adiabatic conditions. Eleven carbon black grades with varying surface area and structure properties at 40 parts per hundred (phr) loading are studied and the unreinforced equivalents are included for reference. The results show a strong correlation of the modulus, mechanical hysteresis, temperature rise and calculated crystallinity of the rubbers measured in tensile extension with strain amplification factors. This highlights the influence of matrix overstraining on microstructural deformations of the rubber upon extension. The strain amplification factors are calculated via the Guth-Gold equation directly from carbon black type and loading, allowing a correlation of the fundamental morphological properties of carbon black with thermal and mechanical properties of rubbers upon extension. Analysis of the thermal measurements of the rubber compounds upon extension and retraction and contrasting between crystallizing and non-crystallizing rubbers reveals that a substantial irreversible heat generation is present upon extension of the rubber compounds. These irreversible effects most likely originate from microstructural damage mechanisms which have been proposed to account for the Mullins Effect in particle reinforced rubbers.

Incorporating dwelling mounds into induced seismic risk analysis for the Groningen gas field in the Netherlands

In order to inform decision-making regarding measures to mitigate the impact of induced seismicity in the Groningen gas field in the Netherlands, a comprehensive seismic risk model has been developed. Starting with gas production scenarios and the consequent reservoir compaction, the model generates synthetic earthquake catalogues which are deployed in Monte Carlo analyses, predicting ground motions at a buried reference rock horizon that are combined with nonlinear amplification factors to estimate response spectral accelerations at the surface. These motions are combined with fragility functions defined for the exposed buildings throughout the region to estimate damage levels, which in turn are transformed to risk in terms of injury through consequence functions. Several older and potentially vulnerable buildings are located on dwelling mounds that were constructed from soils and organic material as a flood defence. These anthropogenic structures are not included in the soil profile models used to develop the amplification factors and hence their influence has not been included in the risk analyses to date. To address this gap in the model, concerted studies have been identified to characterize the dwelling mounds. These include new shear-wave velocity measurements that have enabled dynamic site response analyses to determine the modification of ground shaking due to the presence of the mound. A scheme has then been developed to incorporate the dwelling mounds into the risk calculations, which included an assessment of whether the soil-structure interaction effects for buildings founded on the mounds required modification of the seismic fragility functions.

Reduction of Bias and Uncertainty in Regional Seismic Site Amplification Factors for Seismic Hazard and Risk Analysis

Site amplification factors in National Building Codes are typically specified as a function of the average shear wave velocity over the first 30 m (Vs30) or site class (A, B, C, D and E) for defined ranges of Vs30 and/or ranges of depth to bedrock. However, a single set of amplification factors may not be representative of site conditions across the country, introducing a bias in seismic hazard and seismic risk analyses. This is exemplified by significant differences in geological settings between East and West coast locations in North America. Western sites are typically characterized by lower impedance contrasts between recent surface deposits and bedrock in comparison to Eastern sites. In North America, site amplification factors have been derived from a combination of field data on ground motions recorded during West Coast earthquakes and numerical models of site responses that are meant to be representative of a wide variety of soil profiles and ground motions. The bias on amplifications and their impact on seismic hazards is investigated for the Montreal area, which ranks second for seismic risks in Canada in terms of population and hazard (PGA of 0.25 g for a 2475 years return period). Representative soil profiles at several locations in Montreal are analyzed with 1-D site response models for natural and synthetic ground motions scaled between 0.1 to 0.5 g. Since bedrock depths are typically shallow (<30 m) across the island, bedrock shear wave velocities have a significant influence on the impedance contrast and amplifications. Bedrock shear wave velocity is usually very variable due to the differences in rock formations, level of weathering and fracturing. The level of this uncertainty is shown to be greatly decreased when rock quality designation (RQD) data, common information when bore hole data are logged, is available since it is highly correlated with both shear and compression wave velocities. The results are used to derive region-specific site amplification factors as a function of both Vs30 and site fundamental frequency and compared to those of the National Building Code of Canada (2015). The results of the study indicate that there are large uncertainties associated with these parameters due to variability in soil profiles, soil properties and input seismic ground motions. Average and confidence intervals for the mean and for predictions of amplification factors are calculated for each site class to quantify this uncertainty. Amplifications normalized relative to class C are obtained by accounting for the correlation between site class amplifications for given ground motions. Non-linearity in the analysis of equivalent linear 1-D site response is taken into account by introducing the non-linear G/Gmax and damping ratios curves. In this method, it is assumed that the shear strain compatible shear modulus and damping ratio values remains constant throughout the duration of the seismic excitation. This assumption is not fully applicable to a case when loose saturated soil profile undergo heavy shaking (PGA > 0.3 g). In this study, all simulations with input motion PGA >0.3 g have been performed by using the EL method instead of the NL method considering that cohesive soils (clay and silt) at Montreal sites are stiff and cohesionless soils (sand and gravel) are considerably dense. In addition, the field and laboratory data required to perform NL analyses are not currently available and may be investigated in future works.

Investigation on the Robustness of Rotor/Stator Contact Interactions with Respect to Small Mistuning

In this work, the impact of small mistuning on rotor/stator contact interactions is investigated. First, a detailed study of a rotor/stator interaction between the first bending modes and the second engine order is presented in the tuned case. Then, a numerical investigation on the effect of mistuning on the studied rotor/stator contact interaction is carried out. In particular, a stochastic analysis is performed to evaluate the robustness of the interaction with respect to the mistuning level. Simulations are conducted using a reduced order model (ROM) of an industrial bladed disk that combines both physical degrees of freedom (along blades tip for contact treatment) and modal coordinates. Mistuning is introduced in the tuned ROM by means of a modified version of the component mode mistuning method that allows to keep physical degrees of freedom within the reduced basis. Nonlinear amplification factors, i.e. the amplification factors in the context of contact nonlinearities, are compared with their linear counterparts, the latter are computed using a linear forcing on each blade using a two nodal diameters traveling wave excitation on the mistuned and the tuned bladed disk. The comparison between the linear and nonlinear amplification factor for each sample highlights that no correlation exists between a mistuning pattern leading to high amplifications in a linear context or when contact nonlinearities are taken into account. Therefore, dedicated analyses on the effect of mistuning should be undertaken with contact nonlinearities considerations at the design stage especially if intentional mistuning is considered.