Analytical study of freezing behavior of a cavity in thermo-poro-elastic medium

The goal of this paper is to present an analytical solution to have a first insight of the impact of ice formation on the surrounding porous rock on underground cavities like reservoir, pipes, tunnels or wellbores. Among the other analytical solutions found in the literature on this topic, the originality of this work resides in the rigorous theoretical framework of poromechanics, which considers the coupling between liquid water and ice crystal under thermodynamic equilibrium. Liquid water transport, thermal conduction, and elastic properties of the phases are also considered. Two analytical solutions are presented, based on a linearization of the system of governing equations. The first one deals with a spherical cavity within an infinite porous medium leading to an exact analytical solution. It allows validating the Stehfest’s algorithm on the numerical inversion of Laplace Transform, used in the second analytical solution, which considers a cylindrical excavation. The validity of this solution is assessed by comparing its results to that issued from a numerical resolution of the nonlinear system of equations. The analytical solution is then ultimately used to identify the influence of key parameters like the thermal/hydraulic conductivities, the amount of ice formed and the thermal dilatation coefficients on the mechanical response of a cylindrical cavity submitted to an internal frost.     

The contribution of O.S. Vialov to the development of ichnological classification and nomenclature

This work highlights the role of O.S. Vialov, an outstanding Soviet geologist and paleontologist, and Academician of the Academy of Sciences of the Ukrainian SSR, in the creation and development of classification and nomenclature of fossil traces left by organisms.     

A simple holistic hypothesis for the self-destruction of ice sheets

Ice sheets are the only components of Earth’s climate system that can self-destruct. This paper presents the quantitative force balance for bottom-up modeling of ice sheets, as first presented qualitatively in this journal as a way to quantify ice-bed uncoupling leading to self-destruction of ice sheets (Hughes, 2009a). Rapid changes in sea level and climate can result if a large ice-sheet self-destructs quickly, as did the former Laurentide Ice Sheet of North America between 8100 and 7900 BP, thereby terminating the last cycle of Quaternary glaciation. Ice streams discharge up to 90 percent of ice from past and present ice sheets. A hypothesis is presented in which self-destruction of an ice sheet begins when ubiquitous ice-bed decoupling, quantified as a floating fraction of ice, proceeds along ice streams. This causes ice streams to surge and reduce thickness by some 90 percent, and height above sea level by up to 99 percent for floating ice, so the ice sheet undergoes gravitational collapse. Ice collapsing over marine embayments becomes floating ice shelves that may then disintegrate rapidly. This floods the world ocean with icebergs that reduce the ocean-to-atmosphere heat exchange, thereby triggering climate change. Calving bays migrate up low stagnating ice streams and carve out the accumulation zone of the collapsed ice sheet, which prevents its recovery, decreases Earth’s albedo, and terminates the glaciation cycle. This sequence of events may coincide with a proposed life cycle of ice streams that drain the ice sheet. A first-order treatment of these life cycles is presented that depends on the longitudinal force balance along the flowbands of ice streams and gives a first approximation to ice-bed uncoupling at snapshots during gravitational collapse into ice shelves that disintegrate, thereby removing the ice sheet. The stability of the Antarctic Ice Sheet is assessed using this bottom-up approach.     

屋檐冰柱初期生长规律实验分析

屋檐冰柱是中高纬度地区常见的冰现象, 其破碎断裂可能对人们的生产和生活带来不利影响。同样在桥梁工程、 隧道工程和输电工程中也经常受到冰柱的影响, 造成危险和工程设施的损害, 但由于缺乏对冰柱生长发育规律的探索, 导致冰柱冰害防治及处理方式仅以机械破坏和加热为主, 成本较高。利用室外实验获取屋檐冰柱的初步生长发育规律, 以此指导在低温室内利用金属载体精准滴定模拟屋檐冰柱初期生长规律实验。实验中通过观测水滴流速及冰柱形成速率（长度、 直径和冰重）, 得出了冰柱性状和时间、 供给水量的相互关系。结果表明： 屋檐冰柱形成和水流分布受冰柱发育程度的影响, 冰柱表面水流流速与冰柱发育过程之间存在互馈关系, 冰柱形态阻力与径流集中产生的流速增量又影响着冰柱发育速度。试验过程及试验数据不仅仅对屋檐冰柱具有解释分析的作用, 对其他工程实际也具有指导意义, 可为屋檐冰柱的防治方法研究提供依据和借鉴。     

On Garg's solution of Biot's equations for wave propagation in a one-dimensional fluid-saturated elastic porous solid

Garg's approximate analytical solutions of Biot's equations for wave propagation in a fluid-saturated elastic porous solid of infinite extent subjected to a velocity boundary condition of a Heaviside function at one end are examined for small and large drag. Garg's approximations were apparently introduced to facilitate exact inversion of Laplace transforms of certain quantities. The approximate solutions are compared with carefully evaluated numerical inverses of the Laplace transform solutions for different soils with widely varying properties. It is seen that for most soils (clays, silts and, sands) the error in Garg's approximate solutions in insignificant, and the solutions can be used as benchmarks for verifying numerical analysis procedures such as finite element codes.     

黑龙江呼玛段炸药破冰试验研究

黑龙江几乎每年开河期都有不同程度的冰坝发生, 由此引发的洪水泛滥给人们生命财产带来了巨大损失, 而防凌爆破是预防冰坝发生的主要手段之一。为了确保开河期间不发生因冰坝造成的凌汛灾害, 2018年开河前在黑龙江呼玛段实施防凌爆破。通过冰厚、 水深同步测量的冰水情数据分析, 找到河道狭窄、 流速缓慢的地方为冰坝潜在发生的位置, 采取针对性的爆破。分析了爆破坑实测直径与炸药用量、 冰厚、 水深间的关系, 并将爆破后呼玛段测量数据带入本项目组提出的爆破坑半径计算新公式中, 计算值和实测值较为接近, 可为北方高寒区河流冰下爆破提供参考。     

Geostatistical Assessment of Ice Content Distribution Within the Glacier Bonnard

The Glacier Bonnard is a rock glacier located in the State of Valais, Switzerland. It overhangs a settlement and its slow downward constant creep constitutes an environmental hazard. It is therefore important to understand the glacier’s internal structure, particularly in terms of ice content, in order to evaluate its current global dynamic and future evolution. Following preliminary geophysical investigations, several boreholes have been drilled to measure the thickness of the glaciated mass and the vertical distribution of lithology and ice content. These new data are helpful in assessing the amount of ice within the Glacier Bonnard. Two geostatistical modeling approaches are considered: a direct modeling of ice content and an indirect approach linking together lithology and ice content by the use of the plurigaussian algorithm. Comparisons between these approaches are made in terms of ice content prediction and of global ice mass within the sampled area; they underline the benefit of the geostatistical modeling and particularly the advantages of the indirect approach.     

Capabilities and limitations of numerical ice sheet models: a discussion for Earth-scientists and modelers

The simulation of dynamically coupled ice sheet, ice stream, and ice shelf-systems poses a challenge to most numerical ice sheet models. Here we review present ice sheet model limitations targeting a broader audience within Earth Sciences, also those with no specific background in numerical modeling, in order to facilitate cross-disciplinary communication between especially paleoglaciologists, marine and terrestrial geologists, and numerical modelers. The ‘zero order’ (Shallow Ice Approximation, SIA)-, ‘higher order’-, and ‘full Stokes’ ice sheet models are described conceptually and complemented by an outline of their derivations. We demonstrate that higher order models are required to simulate coupled ice sheet-ice shelf and ice sheet-ice stream systems, in particular if the results are aimed to complement spatial ice flow reconstructions based on higher resolution geological and geophysical data. The zero order SIA model limitations in capturing ice stream behavior are here illustrated by conceptual simulations of a glaciation on Svalbard. The limitations are obvious from the equations comprising a zero order model. However, under certain circumstances, simulation results may falsely give the impression that ice streams indeed are simulated with a zero order SIA model.     

东南极冰盖/冰架变化监测与预测技术研究

南北极是研究全球变化的关键区域。＂十一五＂期间我国在南极地区系统开展了东南极冰盖/冰架变化监测与预测技术研究,对认识全球气候变化具有重要作用。通过项目实施,建立和发展了一批现场观测体系,发展了冰盖观测新技术并集成应用于东南极冰盖的综合观测,拓展了对冰穹A地区的新认识和新发现;在冰穹A边缘地区钻取的一支浅冰芯恢复了过去约780年的气候记录,记录了东南极地区存在小冰期的明显证据;发展了东南极冰盖积累和等时年层流动模型,研究在冰盖浅层、中层和深部的变化特征,反演了冰穹A地区的古积累率分布。本文概要介绍该项目基本情况。     

Calving processes and the dynamics of calving glaciers

Calving of icebergs is an important component of mass loss from the polar ice sheets and glaciers in many parts of the world. Calving rates can increase dramatically in response to increases in velocity and/or retreat of the glacier margin, with important implications for sea level change. Despite their importance, calving and related dynamic processes are poorly represented in the current generation of ice sheet models. This is largely because understanding the ‘calving problem’ involves several other long-standing problems in glaciology, combined with the difficulties and dangers of field data collection. In this paper, we systematically review different aspects of the calving problem, and outline a new framework for representing calving processes in ice sheet models. We define a hierarchy of calving processes, to distinguish those that exert a fundamental control on the position of the ice margin from more localised processes responsible for individual calving events. The first-order control on calving is the strain rate arising from spatial variations in velocity (particularly sliding speed), which determines the location and depth of surface crevasses. Superimposed on this first-order process are second-order processes that can further erode the ice margin. These include: fracture propagation in response to local stress imbalances in the immediate vicinity of the glacier front; undercutting of the glacier terminus by melting at or below the waterline; and bending at the junction between grounded and buoyant parts of an ice tongue. Calving of projecting, submerged ‘ice feet’ can be regarded as a third-order process, because it is paced by first- or second-order calving above the waterline.First-order calving can be represented in glacier models using a calving criterion based on crevasse depth, which is a function of longitudinal strain rate. Modelling changes in terminus position and calving rates thus reduces to the problem of determining the ice geometry and velocity distribution. Realistic solutions to the problem of modelling ice flow therefore depend critically on an appropriate choice of sliding law. Models that assume that basal velocities are controlled by basal drag can replicate much of the observed behaviour of calving glaciers with grounded termini, but an important limitation is that they cannot be used to model floating glacier termini or ice shelves. Alternative sliding laws that parameterise drag from the glacier margins provide more flexible and robust ways of representing calving in ice sheet models. Such models can explain a remarkable range of observed phenomena within a simple, unifying framework, including: downglacier increases in velocity and strain rates where basal and/or lateral drag diminishes; flow acceleration in response to thinning through time; the tendency for glaciers to stabilise at ‘pinning points’ in relatively shallow water or fjord narrowings; the constraints on ice shelf stability; and the contrasts in calving rates between tidewater and freshwater calving glaciers. Many unresolved issues remain, however, including the role played by the removal of backstress in the acceleration of retreating calving glaciers, and the controls on melting at and below the waterline.     

Cylindrical cavities and classical rat‐hole theory occurring in bulk materials

The phenomenon of stable cylindrical cavities known as rat‐holes in stockpiles and hoppers is well known but is not properly understood, and existing theory is unsatisfactory, in that it is believed not to properly incorporate actual material properties. Here the classical rat‐hole theory of Jenike and his coworkers is re‐examined, with a view to examining the validity of the so‐called ‘stable rat‐hole equation’, which is widely used in practice. For certain plastic regimes, new exact analytical solutions are determined for two special values of the angle of internal friction. One of the exact results may be used as the basis of an approximate solution valid for small angles of internal friction. Further, these exact and approximate solutions are compared with a full numerical solution of the governing differential equations. One of the approximations used by Jenike and his coworkers is shown to be invalid. Copyright © 2000 John Wiley & Sons, Ltd.     

Ice stream sticky spots: A review of their identification and influence beneath contemporary and palaeo-ice streams

Rapidly-flowing ice streams are the arterial drainage routes in continental ice sheets and exert a major influence on ice sheet mass balance. Recent observations have revealed that ice stream flow exhibits considerable variability, with relatively rapid changes taking place in speed and direction. This spatial and temporal variability is intimately linked to the conditions at the base of the ice streams and the distribution of localised patches of basal friction, known as ‘sticky spots’. In this paper, we provide a detailed review of sticky spot observations from both contemporary and palaeo-ice stream beds in order to better understand their nature and influence. Observations and theoretical considerations reveal four primary causes of ‘stickiness’: (i), bedrock bumps; (ii), till-free areas; (iii), areas of ‘strong’ (well drained) till; and (iv), freeze-on of subglacial meltwater. These may act together in one location, or in isolation; and a progressive increase in their distribution could lead to ice stream shut-down. Bedrock bumps are influential under active ice streams, where they provide form drag and can create thinner ice which increases the likelihood of basal freeze-on. Increased bed roughness may prevent the lateral migration of some ice streams but bedrock bumps are unlikely to cause ice stream shut-down because, over long time-scales, ice stream erosion might be expected to reduce their amplitude. The influence of till-free areas beneath an ice stream will depend critically on the amount of water that might be drawn out of the surrounding till to lubricate such areas. They are likely to be most important in ice stream onset zones but their identification has proved difficult beneath active ice streams. If an ice stream operates solely by till deformation, it is conceivable that a progressive increase in the exposure of till-free areas could lead to shut-down through a process of sediment exhaustion. Areas of strong, well drained till have been identified beneath both active and ancient ice streams and are most likely to result from the reorganisation of subglacial meltwater. The collapse of an inefficient ‘cannalised’ system to a more efficient ‘channelised’ system can occur rapidly and this mechanism has been hypothesised as a candidate for ice stream shut-down in both contemporary and palaeo-settings. Basal freeze-on has also been observed and inferred from beneath modern and palaeo-ice streams, and a reduction in basal meltwater supply coupled with ice stream drawdown and the advection of cold ice increases the likelihood of switching off an ice stream. A paucity of data from ice stream sticky spots limits a better understanding of their nature, distribution and evolution beneath ice streams. Future technological advances are likely to improve the resolution of the data collected from the beds of modern ice streams but well-preserved palaeo-ice stream beds also hold potential for investigating their influence on ice stream flow and we present simple landsystems models to aid their identification. Such data will considerably enhance the basal boundary condition in ice stream models which will, ultimately, refine our predictions of the response of contemporary ice sheets to future changes in climate.     

Exact solutions for one‐dimensional consolidation of single‐layer unsaturated soil

Based on the Fredlund consolidation theory of unsaturated soil, exact solutions of the governing equations for one‐dimensional consolidation of single‐layer unsaturated soil are presented, in which the water permeability and air transmission are assumed to be constants. The general solution of two coupled homogeneous governing equations is first obtained. This general solution is expressed in terms of two functions psi₁ and ψ₂, where ψ₁ and ψ₂, respectively, satisfy two second‐order partial differential equations, which are in the same form. Using the method of separation of variables, the two partial differential equations are solved and exact solutions for three typical homogeneous boundary conditions are obtained. To obtain exact solutions of nonhomogeneous governing equations with three typical nonhomogeneous boundary conditions, the nonhomogeneous boundary conditions are first transformed into homogeneous boundary conditions. Then according to the method of undetermined coefficients and exact solutions of homogenous governing equations, the series form exact solutions are put forward. The validity of the proposed exact solutions is verified against other analytical solutions in the literature. Copyright © 2011 John Wiley & Sons, Ltd.     

A depositional model for stratigraphic complexes and facies superimposition in lodgement tills

A typical stratigraphy below a streamlined till plain in Northumberland, England, consists of cross-cutting lodgement till units, within and between which occur repeated shoestring interbeds of ‘cut and fill’ channels. Till units have erosional lower contacts; in certain cases marked changes in erratic content and local ice flow direction are evident from one till unit to another. These lodgement till complexes have hitherto been described by ‘tripartite’ schemes of lower grey till (s) and upper reddened till (s) identified with respect to ‘middle’ fluvial horizons; regional correlation proceeding on the basis of matching ‘middle’ horizons, with the whole sequence commonly interpreted as evidence for multiple glaciation. Data indicates, by way of contrast, that these lodgement till complexes were deposited during a single phase of subglacial deposition. Till deposition was not continuous but was interrupted by erosional episodes. Changes in the mix of bedrock lithologies transported by the glacier down a single flow line or by lateral displacement of basal ice flow units within the glacier result in till units of different facies to be emplaced when deposition recommences, a process referred to as ‘unconformable facies superimposition’. Subglacial meltwater flow was also a characteristic of the glacier bed; channeled glaciofluvial sediment bodies are found as ribbon-like inclusions in the till and appear to have been deposited rapidly. These so-called ‘middle’ fluvial horizons occur repeatedly in section, their lateral extent at any given exposure being dependent upon the orientation of the exposure with respect to former ice flow direction. These lenses act as internal drainage blankets and have accelerated postglacial soil formation in the drier climate of eastern Britain accounting for the reddened colour of upper till(s). It is suggested that this model of subglacial deposition can be employed in other areas of northern England characterized by subglacial (lodgement till plain) terrains.     

Transient response of a circular cavity in a poroelastic medium

This paper considers the transient response of a pressurized long cylindrical cavity in an infinite poroelastic medium. To obtain transient solutions, Biot's equations for poroelastodynamics are specialized for this problem. A set of exact general solutions for radial displacement, stresses, pore pressure and discharge are derived in the Laplace transform space by using analytical techniques. Solutions are presented for three different types of prescribed transient radial pressures acting on the surface of a permeable as well as an impermeable cavity surface. Time domain solutions are obtained by inverting Laplace domain solutions using a reliable numerical scheme. A detailed parametric study is presented to illustrate the influence of poroelastic material parameters and hydraulic boundary conditions on the response of the medium. Comparisons are also presented with the corresponding ideal elastic solutions to portray the poroelastic effects. It is noted that the maximum radial displacement and hoop stress at the cavity surface are substantially higher than the classical static solutions and differ considerably from the transient elastic solutions. Time histories and radial variations of displacement, hoop stress, pore pressure and fluid discharge corresponding to a cavity in two representative poroelastic materials are also presented.     

Reconstructing the last Irish Ice Sheet 1: changing flow geometries and ice flow dynamics deciphered from the glacial landform record

The glacial geomorphological record provides an effective means to reconstruct former ice sheets at ice sheet scale. In this paper we document our approach and methods for synthesising and interpreting a glacial landform record for its palaeo-ice flow information, applied to landforms of Ireland. New, countrywide glacial geomorphological maps of Ireland comprising >39,000 glacial landforms are interpreted for the spatial, glaciodynamic and relative chronological information they reveal. Seventy one ‘flowsets’ comprising glacial lineations, and 19 ribbed moraine flowsets are identified based on the spatial properties of these landforms, yielding information on palaeo-ice flow geometry. Flowset cross-cutting is prevalent and reveals a highly complex flow geometry; major ice divide migrations are interpreted with commensurate changes in the flow configuration of the ice sheet. Landform superimposition is the key to deciphering the chronology of such changes, and documenting superimposition relationships yields a relative ‘age-stack’ of all Irish flowsets. We use and develop existing templates for interpreting the glaciodynamic context of each flowset – its palaeo-glaciology. Landform patterns consistent with interior ice sheet flow, ice stream flow, and with time-transgressive bedform generation behind a retreating margin, under a thinning ice sheet, and under migrating palaeo-flowlines are each identified. Fast ice flow is found to have evacuated ice from central and northern Ireland into Donegal Bay, and across County Clare towards the south-west. Ice-marginal landform assemblages form a coherent system across southern Ireland marking stages of ice sheet retreat. Time-transgressive, ‘smudged’ landform imprints are particularly abundant; in several ice sheet sectors ice flow geometry was rapidly varying at timescales close to the timescale of bedform generation. The methods and approach we document herein could be useful for interpreting other ice sheet histories. The flowsets and their palaeo-glaciological significance that we derive for Ireland provide a regional framework and context for interpreting results from local scale fieldwork, provide major flow events for testing numerical ice sheet models, and underpin a data-driven reconstruction of the Irish Ice Sheet that we present in an accompanying paper – Part 2.     

The axisymmetric consolidation of a semi‐infinite transversely isotropic saturated soil

This paper presents an exact analytical solution to fully coupled axisymmetric consolidation of a semi‐infinite, transversely isotropic saturated soil subjected to a uniform circular loading at the ground surface. The analysis is under the framework of Biot's general theory of consolidation. First, the governing equations of consolidation are transformed into a set of equivalent partial differential equations with the introduction of two auxiliary variables. These partial differential equations are then solved using Hankel–Laplace integral transforms. Once solutions in the transformed domain have been obtained, the actual solutions in the physical domain for displacements and stress components of the solid matrix, pore‐water pressure and fluid discharge can be finally obtained by direct numerical inversion. The accuracy of the numerical solutions developed is confirmed by comparison with an existing exact solution for an isotropic and saturated soil that is a special case of the more general problem addressed. Numerical analyses are also presented to investigate the influence of the degree of material anisotropy on the consolidation settlement. Copyright © 2005 John Wiley & Sons, Ltd.     

Evaluation of a numerical model of the British–Irish ice sheet using relative sea‐level data: implications for the interpretation of trimline observations

The glacial isostatic adjustment (GIA) of the British Isles is complex due to the interplay between local and non‐local signals. A number of recent studies have modelled the GIA response of the British Isles using relative sea‐level data. This study extends these previous analyses by using output from a numerical glaciological model as input to a GIA model. This is a necessary step towards more realistic GIA models, and although there have been similar studies for the major late Pleistocene ice sheets, this is the first study to do so for the British Isles. We test three reconstructions, classed as ‘minimal’, ‘median’ and ‘maximal’ in terms of their volume at maximum extent, and find it is possible to obtain good data–model fits. The minimal reconstruction is clearly preferred by the sea‐level data. The ice reconstructions tested were not constrained by geomorphological information of past ice extent (lateral and vertical). As a consequence, the reconstructions extend further than much of this information suggests, particularly in terms of ice thickness. It is notable, however, that the reconstructions produce good fits to many sea‐level data from central, mountainous regions (e.g. Scottish highlands), which lends support to the suggestion that trimlines, often used as an constraint on the palaeo ice surface location, are in fact features formed at the transition from warm‐ to cold‐based ice and so mark a minimum constraint on the ice surface altitude. Based on data–model misfits, suggestions are made for improving the ice model reconstructions. However, in many locations, the cause of the misfit could be due to non‐local, predominantly Fennoscandian ice and so interpretation is not straightforward. As a result, we suggest that future analyses of this type consider models and observations for both Fennoscandia and the British Isles. Copyright © 2012 John Wiley & Sons, Ltd.     

基于分形的冰塔林形态模拟初探

冰塔林在低纬度高海拔地区的大型冰川上发育广泛, 如何评估其对冰川总体积的贡献意义显著.对冰塔林的形态特征进行了初步探讨, 结果表明: 东绒布冰川冰塔林呈现出分形特点, 其盒维数在1.3～1.9之间, 无标度区间约为40～160 m. 通过构建冰塔林消融模型, 认为冰塔林区域的整体消融率(约50%)不依赖于其地形参数的变化; 估计珠峰东绒布冰川冰塔林体积对冰川总体积的贡献率约为3.7%, 可以忽略.     

Analytical solutions of long nonlinear internal waves: Part I

The Gardner equation is an extension of the Korteweg–de Vries (KdV) equation. It exhibits basically the same properties as the classical KdV, but extends its range of validity to a wider interval of the parameters of the internal wave motion for a given environment. In this paper, we derive exact solitary wave solutions for the generalized Gardner equation that includes nonlinear terms of any order. Unlike previous studies, the exact solutions are derived without assuming their mathematical form. Illustrative examples for internal solitary waves are also provided. The traveling wave solutions can be used to specify initial data for the incident waves in internal waves numerical models and for the verification and validation of the associated computed solutions.