Research Note: On the error behaviour of force and moment sources in simplicial spectral finite elements

The representation of a force or moment point source in a spectral finite-element code for modelling elastic wave propagation becomes fundamentally different in degenerate cases where the source is located on the boundary of an element. This difference is related to the fact that the finite-element basis functions are continuous across element boundaries, but their derivatives are not. A method is presented that effectively deals with this problem. Tests on one-dimensional elements show that the numerical errors for a force source follow the expected convergence rate in terms of the element size, apart from isolated cases where superconvergence occurs. For a moment source, the method also converges but one order of accuracy is lost, probably because of the reduced regularity of the problem. Numerical tests in three dimensions on continuous mass-lumped tetrahedral elements show a similar error behaviour as in the one-dimensional case, although in three dimensions the loss of accuracy for the moment source is not a severe as a full order.     

Contact line friction and surface tension effects on seismic attenuation and effective bulk moduli in rock with a partially saturated crack

The effect of surface phenomena occurring at the interfaces between immiscible fluids and a solid on the seismic attributes of partially saturated rocks has not yet been fully studied. Meanwhile, over the past two decades considerable progress has been made in the physics of wetting to understand effects such as contact line friction, contact line pinning, contact angle hysteresis, and equilibrium contact angle. In this paper, we developed a new rock physics model considering the aforementioned effects on seismic properties of the rock with a partially saturated plane-strain crack. We demonstrated that for small wave-induced stress perturbations, the contact line of the interface meniscus will remain pinned, while the meniscus will bulge and change its shape through the change of the contact angles. When the stress perturbation is larger than a critical value, the contact line will move with advancing or receding contact angle depending on the direction of contact line motion. A critical stress perturbation predicted by our model can be in the range of ∼10²−10⁴ Pa, that is typical for linear seismic waves. Our model predicts strong seismic attenuation in the case when the contact line is moving. When the contact line is pinned, the attenuation is negligibly small. Seismic attenuation is associated with the hysteresis of loading and unloading bulk moduli, predicted by our model. The hysteresis is large when the contact line is moving and negligibly small when the contact line is pinned. Furthermore, we demonstrate that the bulk modulus of the rock with a partially saturated crack depends also on the surface tension and on the contact angle hysteresis. These parameters are typically neglected during calculation of the effecting fluid moduli by applying different averaging techniques. We demonstrate that contact line friction may be a dominant seismic attenuation mechanism in the low frequency limit (<∼10 Hz) when capillary forces dominate over viscous forces during wave-induced two-phase fluid flow.     

A Bayesian model for lithology/fluid class prediction using a Markov mesh prior fitted from a training image

We consider a Bayesian model for inversion of observed amplitude variation with offset data into lithology/fluid classes, and study in particular how the choice of prior distribution for the lithology/fluid classes influences the inversion results. Two distinct prior distributions are considered, a simple manually specified Markov random field prior with a first-order neighbourhood and a Markov mesh model with a much larger neighbourhood estimated from a training image. They are chosen to model both horizontal connectivity and vertical thickness distribution of the lithology/fluid classes, and are compared on an offshore clastic oil reservoir in the North Sea. We combine both priors with the same linearized Gaussian likelihood function based on a convolved linearized Zoeppritz relation and estimate properties of the resulting two posterior distributions by simulating from these distributions with the Metropolis–Hastings algorithm. The influence of the prior on the marginal posterior probabilities for the lithology/fluid classes is clearly observable, but modest. The importance of the prior on the connectivity properties in the posterior realizations, however, is much stronger. The larger neighbourhood of the Markov mesh prior enables it to identify and model connectivity and curvature much better than what can be done by the first-order neighbourhood Markov random field prior. As a result, we conclude that the posterior realizations based on the Markov mesh prior appear with much higher lateral connectivity, which is geologically plausible.     

On Christoffel roots for nondetached slowness surfaces

The only restriction on the values of the elasticity parameters is the stability condition. Within this condition, we examine the Christoffel equation for nondetached qP slowness surfaces in transversely isotropic media. If the qP slowness surface is detached, each root of the solubility condition corresponds to a distinct smooth wavefront. If the qP slowness surface is nondetached, the roots are elliptical but do not correspond to distinct wavefronts; also, the qP and qSV slowness surfaces are not smooth.     

Axially equilibrated displacement‐based beam element for simulating the cyclic inelastic behaviour of RC members

Distributed plasticity beam elements are commonly used to evaluate limit state demands for performance‐based analysis of reinforced concrete (RC) structures. Strain limits are often preferred to drift limits because they directly relate to damage and are therefore less dependent on member geometry and boundary conditions. However, predicting accurately strain demands still represents a major simulation challenge. Tension shift effects, which induce a linear curvature profile in the plastic hinge region of RC columns and walls, are one of the main causes for the mismatch between experimental and numerical estimates of local level quantities obtained through force‐based formulations. Classical displacement‐based approaches are instead suitable to simulate such linear curvature profile. Unfortunately, they verify equilibrium only on an average sense due to the wrong assumption on the axial displacement field, leading to poor deformation and force predictions. This paper presents a displacement‐based element in which axial equilibrium is strictly verified along the element length. The assumed transversal displacement field ensures a linear curvature profile, connecting accurately global displacement and local strain demands. The proposed finite element is validated against two sets of quasi‐static cyclic tests on RC bridge piers and walls. The results show that curvature and strain profiles for increasing ductility demands are significantly improved when axially equilibrated rather than classical displacement‐based or force‐based elements are used to model the structural members. Copyright © 2017 John Wiley & Sons, Ltd.     

芜湖市城市游憩商业区的形成及其空间结构分析

近年来,居民闲暇时间的增多以及生活水平的提高,使得城市的游憩功能愈来愈重要。城市游憩商业区（RBD）作为一种新的功能区,成为本地居民和外地旅游者进行旅游、休闲、娱乐、购物等活动的重要场所。建立了城市RBD的识别模型,据此界定芜湖市RBD的范围,分析了该RBD形成过程及空间结构,并探讨了其形成要素。     

基于力平衡的安全系数统一求解格式

基于力平衡求解安全系数的极限平衡条分法在边稳定分析和设计中得到了广泛地应用。然而,由于条间力假设的不同,各种方法的计算格式也不同,既不便于程序的编写,也不便于人们理解各自方法的优缺点。首次将现有基于力平衡求解安全系数的极限平衡条分法对条间力的假定表示成统一形式,根据力的平衡,导出了简单明了的条间力递推方程。根据条间力递推方程,建立了传统意义下基于力平衡的安全系数统一求解格式,使计算原理更为清晰,计算过程更为简单。在此基础上,如果将严格Janbu法所满足的条块力矩平衡方程表示成条间力的假定,严格Janbu法也可采用基于力平衡的安全系数统一求解格式。     

Numerical modelling of riverbed grain size stratigraphic evolution

For several decades,quantification of riverbed grain size stratigraphic evolution has been based upon the active layer formulation（ALF）,which unfortunately involves considerable uncertainty.While it is the sediment exchange across the bed surface that directly affects the riverbed stratigraphy,it has been assumed in the ALF that the sediment fraction at the lower interface of the active layer is a linear function of the sediment fraction in the flow.Here it is proposed that the sediment fraction of the sediment exchange flux is used directly in estimating the sediment fraction at the lower surface of the active layer.Together with the size-specific mass conservation for riverbed sediment,the modified approach is referred to as the surface-based formulation（SBF）.When incorporated into a coupled non-capacity modelling framework for fluvial processes,the SBF leads to results that agree as well or better than those using ALF with laboratory and field observations.This is illustrated for typical cases featuring bed aggradation and degradation due to graded bed-load sediment transport.Systematic experiments on graded sediment transport by unsteady flows are warranted for further testing the modified formulation.     

Advanced frame element for seismic analysis of masonry structures: model formulation and validation

This paper presents a masonry panel model for the nonlinear static and dynamic analysis of masonry buildings suitable for the seismic assessment of new and existing structures. The model is based on an equivalent frame idealization of the structure and stems from previous research on force‐based frame elements. The element formulation considers axial, bending, and shear deformations within the framework of the Timoshenko beam theory. A phenomenological cyclic section law that accounts for the shear panel response is coupled, through equilibrium between shear and bending forces along the element, with a fiber‐section model that accounts for the axial and bending responses. The proposed panel model traces with a low computational burden and numerical stability the main aspects of the structural behavior of masonry panels and is suitable for analyses of multi‐floor buildings with a relatively regular distribution of openings and with walls and floors organized to grant a box‐like behavior under seismic loads. The model capabilities are validated though analyses of simple unreinforced masonry panels and comparisons with published experimental results. The model accuracy is strongly dependent on the fiber and shear constitutive laws used. However, the formulation is general, and laws different from those employed in this study are easily introduced without affecting the model formulation. Copyright © 2015 John Wiley & Sons, Ltd.