泥石流的二维数学模型

泥石流是在重力作用下,由砂粒石块和水等组成的固液混合物,是一种发生于山区的复杂的地质灾害现象。泥石流主要是由暴雨诱发引起的,它沿着复杂的三维地形高速流动,具有流体流动的特性。为了模拟泥石流的运动规律,预测降雨诱发的泥石流的到达距离和泛滥范围,减少和避免泥石流引起的灾害,把泥石和雨水组成的固液混合物假定为遵循均匀、连续、不可压缩的、非定常的牛顿流体运动规律。基于质量守恒方程和Naiver-stokes方程,采用深度积分方法,推导出了一个模拟泥石流运动的二维数学模型。所有方程式可用有限差分法来求解。结合GIS,该模型可用于预测泥石流的流动距离和泛滥范围,以及泛滥范围内的危险房屋和路段,也可以用于泥石流灾害的风险性分析。     

Effect of property variation and modelling on convection in a fluid overlying a porous layer

An accurate computational analysis is presented for the onset of thermal convection in a two‐layer system which is comprised of a saturated layer of porous material described by Darcy's law, over which lies a layer of the same saturating fluid. The two‐layer system is heated from below and the upper (fluid) surface is allowed to be fixed or stress free. The onset of convection may have a bi‐modal nature in which convection may be dominated by the porous medium or by the fluid depending on the depths of the relative layers, but this is strongly controlled by material parameters. The effect of variation of relevant fluid and porous material properties is investigated in detail, as is the effect of the interface boundary condition between the fluid and the porous medium. Copyright © 2001 John Wiley & Sons, Ltd.     

Coupled theory of mixtures for clayey soils

In this work, elasto-plastic coupled equations are formulated in order to describe the time-dependent deformation of saturated cohesive soils (two-phase state). Formulation of these equations is based on the principle of virtual work and the theory of mixtures for inelastic porous media. The theory of mixtures for a linear elastic porous skeleton was first developed by Biot (Theory of elasticity and consolidation for a porous anisotropic solid, Journal of Applied Physics, 1955, 26, 188–185). An extension of Biot's theory into a nonlinear inelastic media was performed by Prevost (Mechanics of continuous porous media, International Journal of Engineering Science, 1980, 18, 787–800). The saturated soil is considered as a mixture of two deformable media, the solid grains and the water. Each medium is regarded as a continuum and follows its own motion. The flow of pore-water through the voids is assumed to follow Darcy's law. The coupled equations are developed for large deformations with finite strains in an updated Lagrangian reference frame. The coupled behavior of the two-phase materials (soil-water state) is implemented in a finite element program. A modified Cam-clay model is adopted and implemented in the finite element program in order to describe the plastic behavior of clayey soils. Penetration of a piezocone penetrometer in soil is numerically simulated and implemented into a finite element program. The piezocone penetrometer is assumed to be infinitely stiff. The continuous penetration of the cone is simulated by applying an incremental vertical movement of the cone tip boundary. Results of the finite element numerical simulation are compared with experimental measurements conducted at Louisiana State University using the calibration chamber. The numerical simulation is carried out for two cases. In the first case, the interface friction between the soil and the piezocone penetrometer is neglected. In the second case, interface friction is assumed between the soil and the piezocone. The results of the numerical simulations are compared with experimental laboratory measurements.     

高含沙分层流的试验研究

高含沙水流进入低含沙量河流中时,往往形成比较稳定的分层流.通过水槽试验研究了泥浆流同向分层流的深度比,界面剪力在分层流中的作用,闸门开启引起的双向分层流的速度,以及各种分层流的稳定性.     

Three‐dimensional steady‐state response of a railway system on layered half‐space soil medium subjected to a moving train

The paper presents a three‐dimensional study on the steady‐state response of a track system and layered half‐space soil medium subjected to the load induced by the passages of a moving train with the substructure method. Practically, due to the ground water table being several meters beneath the ground surface, the soil profile can be divided into two layers: the upper layer modeled by an elastic medium and the lower layer by a fully saturated poroelastic medium governed by Biot's theory. In the meanwhile, the rails are regarded as an infinitely long Euler beam, and the sleepers are represented by a continuous mass. The effect of the ballast is accounted for by introducing the Cosserat model for granular medium, and the train is described by a series of moving axle point loads, depending on the geometry of the train. The influences of the thickness, the mass and the rigidity of the elastic layer and the mass of the ballast on rail's displacement responses are carefully investigated. Numerical results show that the influences of these parameters are significant for high train velocity, while vanishes for low velocity. Copyright © 2008 John Wiley & Sons, Ltd.     

Structure and reactivity of the dolomite (104)-water interface: New insights into the dolomite problem

The structure and reactivity of the dolomite (104)-water interface was probed in situ with high resolution X-ray reflectivity and surface force microscopy at room temperature. Measurements in stoichiometric solutions alternating between saturated and supersaturated (log IAP/K = 2.3) conditions show that the dolomite surface termination readily changes in response to solution composition, but these changes are self-limiting and partially irreversible. The freshly cleaved dolomite (104) surface in contact with the saturated solution has a stoichiometric termination, a distinct surface hydration layer and small surface structural displacements, similar to those observed previously at the calcite-water interface. After reaction with supersaturated solutions dolomite is terminated by a two-layer thick Ca-rich film with substantial structural displacements of the cations. With subsequent exposure to a saturated solution this surface was transformed to an interfacial structure different from the freshly cleaved surface, having a reduced density of the outermost surface layer and a Ca-rich second layer. These results provide new insight into the lack of dolomite growth in modern carbonate environments (i.e., the “dolomite problem”), suggesting that this behavior is associated with a combination of thermodynamic and kinetic factors, including (1) growth of compositionally modified epitaxial Ca_XMg_2−X(CO₃)₂ layers having thicknesses limited by lattice strain, (2) slow incorporation of Mg during layer growth, and (3) partial irreversibility of surface reactions.     

The fluid dynamics of a basaltic magma chamber replenished by influx of hot,dense ultrabasic magma

This paper describes a fluid dynamical investigation of the influx of hot, dense ultrabasic magma into a reservoir containing lighter, fractionated basaltic magma. This situation is compared with that which develops when hot salty water is introduced under cold fresh water. Theoretical and empirical models for salt/water systems are adapted to develop a model for magmatic systems. A feature of the model is that the ultrabasic melt does not immediately mix with the basalt, but spreads out over the floor of the chamber, forming an independent layer. A non-turbulent interface forms between this layer and the overlying magma layer across which heat and mass are transferred by the process of molecular diffusion. Both layers convect vigorously as heat is transferred to the upper layer at a rate which greatly exceeds the heat lost to the surrounding country rock. The convection continues until the two layers have almost the same temperature. The compositions of the layers remain distinct due to the low diffusivity of mass compared to heat. The temperatures of the layers as functions of time and their cooling rate depend on their viscosities, their thermal properties, the density difference between the layers and their thicknesses. For a layer of ultrabasic melt (18% MgO) a few tens of metres thick at the base of a basaltic (10% MgO) magma chamber a few kilometres thick, the temperature of the layers will become nearly identical over a period of between a few months and a few years. During this time the turbulent convective velocities in the ultrabasic layer are far larger than the settling velocity of olivines which crystallise within the layer during cooling. Olivines only settle after the two layers have nearly reached thermal equilibrium. At this stage residual basaltic melt segregates as the olivines sediment in the lower layer. Depending on its density, the released basalt can either mix convectively with the overlying basalt layer, or can continue as a separate layer. The model provides an explanation for large-scale cyclic layering in basic and ultrabasic intrusions. The model also suggests reasons for the restriction of erupted basaltic liquids to compositions with MgO<10% and the formation of some quench textures in layered igneous rocks.     

Modelling and numerical simulation of two-phase debris flows

Gravity-driven geophysical mass flows often consist of fluid–sediment mixtures. The contemporary presence of a fluid and a granular phase determines a complicated fluid-like and solid-like behaviour. The present paper adopts the mixture theory to incorporate the two phases and describe their respective movements. For the granular phase, a Mohr–Coulomb plasticity is employed to describe the relationship between normal and shear stresses, while for the fluid phase, the viscous Newtonian fluid is taken into account. At the basal topography, a Coulomb sliding condition for the solid phase and a Navier’s sliding condition for the fluid phase are satisfied, while the top free surface is traction-free for both the phases. For the interactive forces between the phases, the buoyancy force and viscous drag force are included. The established governing equations are expressed in a curvilinear coordinate system embedded in a curvilinear reference basal surface, above which an arbitrary shallow basal topography is permitted. Taking into account the typical length characteristics of such geophysical mass flows, the “thin-layer” approximation is assumed, so that a depth integration can be performed to simplify the governing equations. The resulting strongly nonlinear partial differential equations (PDEs) are first simplified and then analysed for a steady state in a travelling coordinate system. We find the current model can reproduce the characteristic shape of some flow fronts. Additionally, a stability analysis for steady uniform flows is performed to demonstrate the development of roll waves that means instabilities grow up and become clearly distinguishable waves. Furthermore, we numerically solve the resulting PDEs to investigate general unsteady flows down a curved surface by means of a high-resolution non-oscillatory central difference scheme with the total variation diminishing property. The dynamic behaviours of the granular and fluid phases, especially, the effects of the drag force and the fluid bed friction are discussed. These investigations can enhance the understanding of physics behind natural debris flows.     

基于2.5维有限元饱和土地基中空沟隔振性能研究

基于Biot饱和多孔介质U-W格式动力控制方程,采用Galerkin法和Fourier变换,推导了饱和土体2.5维有限元方程及黏弹性人工边界,建立了饱和土地基中空沟分析模型,并在波数域中进行求解,通过快速Fourier变换（FFT）进行波数展开,获得三维空间域中结果。算例分析了移动荷载作用下均质饱和土地基、分层饱和土地基、上覆单相弹性层饱和土地基3种饱和土地基模型中空沟的隔振效果。结果表明：饱和土地基中空沟的隔振效果不仅与空沟自身深度有关,还与地基中成层土体的分界面以及土体参数有关,波在不同土体分界面上的透射和反射会影响空沟的隔振效果;饱和土地基中上覆单相弹性层厚度对空沟的隔振效果影响显著,随着上覆单相弹性层厚度的增加,饱和土地基中空沟的隔振效果变好。     

A rigorous finite volume model to simulate subaerial and submarine landslide-generated waves

This paper presents a new landslide-generated wave (LGW) model based on incompressible Euler equations with Savage-Hutter assumptions. A two-layer model is developed including a layer of granular-type flow beneath a layer of an inviscid fluid. Landslide is modeled as a two-phase Coulomb mixture. A well-balanced second-order finite volume formulation is applied to solve the model equations. Wet/dry transitions are treated properly using a modified non-linear method. The numerical model is validated using two sets of experimental data on subaerial and submarine LGWs. Impulsive wave characteristics and landslide deformations are estimated with a computational error less than 5 %. Then, the model is applied to investigate the effects of landslide deformations on water surface fluctuations in comparison with a simpler model considering a rigid landslide. The model results confirm the importance of both rheological behavior and two-phase nature of landslide in proper estimation of generated wave properties and formation patterns. Rigid slide modeling often overestimates the characteristics of induced waves. With a proper rheological model for landslide, the numerical prediction of LGWs gets more than 30 % closer to experimental measurements. Single-phase landslide results in relative errors up to about 30 % for maximum positive and about 70 % for maximum negative wave amplitudes. Two-phase constitutive structure of landslide has also strong effects on landslide deformations, velocities, elongations, and traveling distances. The complex behaviors of landslide and LGW of the experimental data are analyzed and described with the aid of the robust and accurate finite volume model. This can provide benchmark data for testing other numerical methods and models.     

基于海洋分析资料的吕宋海峡水交换的月际变化特征

利用1993—2006年1~12月AIPO(The joining area of Asia and Indian-Pacific Ocean)流场数据,分析了吕宋海峡120°E断面水交换流速结构的平均月际变化特征,并计算了通过该断面的水通量,探讨了水通量及其垂向结构的月际和季节变化特征。结果表明:1在断面的南北方向,西向流和东向流分别大致以19.5°N和21.5°N线为界,二者交替相间分布,呈"两进(西向流入南海)两出(东向流出南海)"的结构;21.5°N以南的300 m以深和21.5°N以北的1 000 m以浅海域,常年存在南海水东向流入太平洋。2上层、深层和整个断面的净水通量几乎均为西向流,净水通量冬季最大,春季和秋季次之,夏季最小。中层除12月外,其他各月的净水通量均为东向流出南海,净水通量春季最大,夏季和秋季次之,冬季最小。3整个断面的净水通量,1~5月和8~11月呈"三明治"结构,6~7月呈2层结构;12月呈单层结构,年平均呈"三明治"结构。     

Relationship of tephra stratigraphy and hydraulic conductivity with slide depth in rainfall-induced shallow landslides in Aso Volcano,Japan

Intense rainfall on July 12, 2012, triggered numerous shallow landslides on steep grassy hillslopes of Aso Volcano, Kyushu, Japan. The hillslopes are mantled by several meters thickness of fallout tephra accumulation from Holocene eruptions. The landslides occurred about 1 m deep in surficial tephra deposits. Stratigraphic surveys of three landslides showed that the tephra deposits beneath the ground consist of two layers, an upper blackish and a lower yellow-brown layer, and that the upper layer represents the accumulation of tephra during the last 1000 years. The surveys also demonstrated that the slip surfaces were formed near the boundary of the two layers, resulting in the sliding of the upper layer. We measured the saturated hydraulic conductivities of both the layers. The hydraulic conductivities of the lower layer are 1 to 2 orders of magnitude lower than those of the upper layer, suggesting that the lower layer acts as an aquiclude. Therefore, pore water pressure locally increases near the boundary between the two layers and failure occurs. We also examined the soil hardness, which has a high correlation with soil shear strength parameters, of the tephra layers at the three landslides. The soil hardness of the lower layer is greater than that of the upper layer in two of the landslides, suggesting that the lower layer collapses less readily than the upper layer. Comparison with previous landslides in the study area demonstrates that this type of rainfall-induced landslide event has occurred in the past and will recur in the future.     

A new cubic equation of state and its applications to the modeling of vapor-liquid equilibria and volumetric properties of natural fluids

A cubic equation of state was developed for both pure systems and mixtures in this study. It has only one empirical constant to be evaluated for each component and two constants for each binary. To test its validity, the saturated properties of 22 pure fluids were calculated with the new equation, as compared with the most frequently used or the most recently published cubic equations. The results indicate that the new equation is superior to the previous cubic equations in the overall performance in vapor pressures and saturated volumes. Its overall average deviation of the saturation pressures from experiments is 0.46%, and the maximum deviation is 3.6%. Its average deviation of the liquid volumes from experiments at the reduced temperatures T_r≤0.95 is 2.80%, and that of vapor volumes is 2.2%. Because of the high accuracy of the new equation for saturation pressures, it can be easily extended to binary mixtures for the prediction of vapor-liquid equilibria (both densities and compositions) with a simple mixing rule, as demonstrated by eight binary systems, including an aqueous mixture.     

矩形移动荷载作用下路面-双层地基系统三维振动分析

考虑路面和地基之间的相互作用,建立了路面-双层地基的三维模型,将车辆荷载模拟成矩形移动荷载,利用Fourier变换方法对车辆荷载作用下路面-双层地基系统的三维振动问题进行了研究。假设地基为上部弹性土体和下部为饱和土体组成的双层混合结构,整个系统置于刚性基岩上。通过引入势函数,利用Lame分解理论和积分变换方法分别对弹性土层和饱和土层进行求解。在Fourier变换域内,联立路面和下卧双层地基系统的的运动方程,获得了车辆荷载作用下路面-双层地基系统三维振动的位移和孔压响应的积分形式解,并利用IFFT算法和自适应数值积分算法得到了数值计算结果。研究结果可为路基动力响应分析提供参考。     

Modeling of Beams on Reinforced Granular Beds

The paper describes a mechanical model for estimating the flexural response of a strip footing, supporting a column (imposing a concentrated load), resting on a compacted granular bed overlying a reinforcement layer for example, geogrids, geomats etc. below which lies a loose soil deposit. The footing is idealized as a beam and the reinforcing element is assumed to have finite bending stiffness and negligible frictional resistance. The upper and lower soil layers are idealized by a series of linear and discrete springs (Winkler springs) of different stiffness values. To find the response of such a model the governing differential equations have been derived and expressed in a nondimensional form. A closed form analytical solution of the same has been obtained subjected to appropriate boundary conditions. Using the present approach the resulting solution for a degenerated case of a long beam is found to be identical to the same of Hetenyi (1946, Beams on elastic foundations, University of Michigan press, Ann Arbor, MI). Parametric studies reveal that the ratio of flexural rigidity of upper and lower beam and the ratio of stiffness of the upper and lower soil layers affect significantly the response of the foundation.     

Characterization of Sabkha Jayb Uwayyid, eastern Saudi Arabia using seismic refraction profiling

Sabkhas are dominant geomorphic features in eastern Saudi Arabia and are of geologic and economic significance. Seismic refraction method was used in the inland sabkha of Jayb Uwayyid to depict its general stratigraphy and determine velocities and thicknesses of the sabkha’s uppermost layers and the water table depth. Data were acquired using a reversed-refraction profile consisting of 48 receivers spaced at 5 m. Data processing included amplitude gain, band-pass filtering, and manual picking of first and second arrivals. Interpretation of the data shows three main layers. The first layer is a sandy layer having an average velocity and thickness of 600 m/s and 15 m, respectively. The second layer has an average velocity and thickness of 2,300 m/s and 113 m, respectively. The third layer has an average velocity of 3,850 m/s. The topmost part of the first layer is composed of a dry to partially saturated clean sand underlain by fully saturated clean sand. However, arrivals from the interface between the partially saturated and fully saturated sands were not recognizable in any shot record, which might be due to the gradual increase of saturation with depth. Arrivals from the second layer were always recognizable on all shot records as first arrivals. On the other hand, arrivals from the third layer were not recognizable on any shot record as first arrivals probably due to the limited extent of the profile relative to the depth of the third layer. Therefore, the velocity of the third layer was calculated by manually picking the second head wave arrival.     

Weak discontinuity in porous media: an enriched EFG method for fully coupled layered porous media

In this paper, a series of multimaterial benchmark problems in saturated and partially saturated two‐phase and three‐phase deforming porous media are addressed. To solve the process of fluid flow in partially saturated porous media, a fully coupled three‐phase formulation is developed on the basis of available experimental relations for updating saturation and permeabilities during the analysis. The well‐known element free Galerkin mesh‐free method is adopted. The partition of unity property of MLS shape functions allows for the field variables to be extrinsically enriched by appropriate functions that introduce existing discontinuities in the solution field. Enrichment of the main unknowns including solid displacement, water phase pressure, and gas phase pressure are accounted for, and a suitable enrichment strategy for different discontinuity types are discussed. In the case of weak discontinuity, the enrichment technique previously used by Krongauz and Belytschko [Int. J. Numer. Meth. Engng., 1998; 41:1215–1233] is selected. As these functions possess discontinuity in their first derivatives, they can be used for modeling material interfaces, generating only minor oscillations in derivative fields (strain and pressure gradients for multiphase porous media), as opposed to unenriched and constrained mesh‐free methods. Different problems of multimaterial poro‐elasticity including fully saturated, partially saturated one, and two‐phase flows under the assumption of fully coupled extended formulation of Biot are examined. As a further development, problems involved with both material interface and impermeable discontinuities, where no fluid exchange is permitted across the discontinuity, are considered and numerically discussed. Copyright © 2014 John Wiley & Sons, Ltd.     

Changes of oceanographic characteristics and the state of pollution in the Izmit bay following the earthquake of 1999

The Izmit Bay is an elongated semi-enclosed bay in the Marmara Sea. It is being increasingly polluted by both domestic and industrial waste discharge since 1970’s. A monitoring program was conducted between 1999-2000 to document the state of pollution in the bay. This includes the effect of Marmara (Izmit) earthquake (magnitude 7.4) that occurred in August 1999. A stable two-layer ecosystem exists in the bay throughout the year due to continuous inflows of the saltier Mediterranean and brackish Black Sea waters to the Marmara basin. Therefore, the principal biochemical characteristics of the bay are governed by the two-layer flow system over the basin. Dissolved oxygen (DO) is generally at a saturated levels in the surface layer which is 10 to 15 m thick, but it is depleted to 60–70 μM in the lower layer, exhibiting a steep gradient in the sharp halocline. When the earthquake occurred, great loads of industrial wastes were released into the bay surface waters, which enhanced primary production in the upper layer and thus large export of particulate organic matter to lower layer and eventually to the bottom. Accordingly, DO was consumed and anoxic condition was established even in the upper layer/halocline interface, the halocline and bottom waters of the eastern and central bay. In this period, concurrent increases were observed in phosphate and ammonia contents at the halocline and in deep waters whilst the nitrate was almost consumed via denitrification processes in the anoxic water. Recently, the industrial C, N and P loads increased by as much as 8 fold within five years (1995–2000) whilst domestic inputs increased by 50%. Total organic matter discharged to the bay increased more than double within the last 15 years. Besides, most factories in the region release toxic wastes into the bay after only partial treatment.     

成层饱和土中考虑横向惯性的单桩纵向振动

基于饱和多孔介质理论,研究了成层饱和黏弹性土层中端承桩的纵向振动特性。首先利用Novak薄层法,得到了土层对纵向振动桩的动力阻抗。其次,将桩等效为Rayleigh-Love杆,给出了成层饱和黏弹性土中端承桩纵向振动的一般分析方法和桩头动力复刚度的解析表达式。具体分析了两层饱和黏弹性土中端承桩的纵向振动特性,得到了桩头动刚度因子和等效阻尼随频率的响应特征,讨论了物理和几何等参数对动刚度因子和等效阻尼的影响。结果表明：桩长径比、土层模量比以及桩土模量比等对桩头动刚度因子和等效阻尼有显著的影响。相比于均质土层中的桩,上层土越硬或下层为软弱土层,桩的动刚度因子和等效阻尼振动幅值增大,其周期随长径比显著变化,且对于大直径桩,动刚度因子和等效阻尼随频率呈振动变化。同时,土体与孔隙水相互作用系数和桩泊松比等的影响相对较小。其结果可作为桩基动力基础设计和动力检测等基础数据。     

Influence of streambed hydraulic conductivity on solute exchange with the hyporheic zone

A conservative solute tracer experiment was conducted in Indian Creek, a small urban stream in Philadelphia, Pennsylvania to investigate the role of subsurface properties on the exchange between streamwater and the hyporheic zone (subsurface surrounding the stream). Sodium Bromide (NaBr) was used as a conservative tracer, and it was monitored in the surface water at two stations and in the upper bed sediments (shallow hyporheic zone extending from 7.5 to 10 cm below the streambed). The hydraulic conductivity (K) of the upper bed sediments and the lower bed sediments (10–12.5 cm below the streambed) was measured in situ. High tracer concentrations were observed in the upper layer at locations where the hydraulic conductivity of the upper layer was larger than that of the lower layer. Low concentrations in the upper layer were observed in the converse case. A statistically significant relationship between the mass retained in the upper layer and the difference of K values between layers was observed.