Shock compression of zirconia ZrO2 and zircon ZrSiO4 in the pressure range up to 150 GPa

The shock compression state of zirconia ZrO₂ and zircon ZrSiO₄ in the pressure range up to 150 GPa (1.5 Mbar) are studied on the basis of the measurements of shock velocities, particle-velocity histories, free surface motions, and electrical conductivities. Zircon transforms, and zirconia probably does, to high pressure phases up to 90 GPa. The shock velocity (U _s ) — particle velocity (U _p ) Hugoniots can be described as U _s =4.38+1.37 U _p km/s above 90 GPa for ZrO₂, and U _s =6.50+0.49 U _p km/s (mixed phase region), and U _s =1.54+2.30 U _p km/s (high pressure phase region) for ZrSiO₄. The corrected isothermal densities of the high pressure phase ZrSiO₄ are roughly consistent with the isothermal ones of mixtures of ZrO₂ and SiO₂. Bulk sound velocities in the high-pressure phase region of these oxides are discussed in comparison with other dioxides. Electrical conductivities of these oxides increase from lower than 10^?12 S/m to greater than 10⁰ S/m in the shock-stress range up to 70 GPa, and remain as constant values up to higher than 100 GPa.     

Dynamics of unsaturated poroelastic solids at finite strain

We derive the governing equations for the dynamic response of unsaturated poroelastic solids at finite strain. We obtain simplified governing equations from the complete coupled formulation by neglecting the material time derivative of the relative velocities and the advection terms of the pore fluids relative to the solid skeleton, leading to a so‐called u^s ? p^w ? p^a formulation. We impose the weak forms of the momentum and mass balance equations at the current configuration and implement the framework numerically using a mixed finite element formulation. We verify the proposed method through comparison with analytical solutions and experiments of quasi‐static processes. We use a neo‐Hookean hyperelastic constitutive model for the solid matrix and demonstrate, through numerical examples, the impact of large deformation on the dynamic response of unsaturated poroelastic solids under a variety of loading conditions. Copyright © 2011 John Wiley & Sons, Ltd.     

Two formulations for dynamic response of a cylindrical cavity in cross‐anisotropic porous media

Two formulations for calculating dynamic response of a cylindrical cavity in cross‐anisotropic porous media based on complex functions theory are presented. The basis of the method is the solution of Biot's consolidation equations in the complex plane. Employing two groups of potential functions for solid skeleton and pore fluid (each group includes three functions), the u–w formulation of Biot's equations are solved. Difference of these two solutions refers to use of two various potential functions. Equations for calculating stress, displacement and pore pressure fields of the medium are mentioned based on each two formulations. Copyright © 2009 John Wiley & Sons, Ltd.     

A novel insight into vertical ground motion modelling in earthquake engineering

Recent observations of failure and damage of buildings and structures under seismic action has led to an increasing interest for an in-depth analysis of the vertical component of site ground motion. In particular, when dealing with saturated soils, the current engineering practice does not usually go beyond the simplified $u$–$p$ formulation of the Biot's equations describing the coupled hydro-mechanical behaviour, thus neglecting some terms of fluid inertial forces, despite the presence of more refined formulations, for example, the $u$–$U$ formulation. Therefore, a theoretical and numerical validation of the $u$–$p$ formulation as compared with the $u$–$U$ formulation is proposed in this work, where the numerical simulations are compared with the analytical solution for the $u$–$p$ formulation, which is also derived and illustrated in this text. The comparison between the two formulations and the analytical solution is provided for different levels of permeability and dynamic actions, which are representative of a wide scenario of site ground properties and seismic hazard in the vertical direction. In particular, the soil response is analysed in terms of acceleration and pore pressure time history, frequency content, acceleration response spectrum, and amplification ratio of acceleration. This study extends the discussion of the limits of applicability of the $u$–$p$ formulation with respect to the rigorous solution of Biot's equations (obtained here with $u$–$U$ formulation) to the context of a complex dynamic regime provided by the vertical components of real earthquake records, and paves the way for further investigations.     

Numerical simulation of fully saturated porous materials

Fully coupled, porous solid–fluid formulation, implementation and related modeling and simulation issues are presented in this work. To this end, coupled dynamic field equations with u?p?U formulation are used to simulate pore fluid and soil skeleton (elastic–plastic porous solid) responses. Present formulation allows, among other features, for water accelerations to be taken into account. This proves to be useful in modeling dynamic interaction of media of different stiffnesses (as in soil–foundation–structure interaction). Fluid compressibility is also explicitly taken into account, thus allowing excursions into modeling of limited cases of non‐saturated porous media. In addition to these features, present formulation and implementation models in a realistic way the physical damping, which dissipates energy. In particular, the velocity proportional damping is appropriately modeled and simulated by taking into account the interaction of pore fluid and solid skeleton. Similarly, the displacement proportional damping is physically modeled through elastic–plastic processes in soil skeleton. An advanced material model for sand is used in present work and is discussed at some length. Also explored in this paper are the verification and validation issues related to fully coupled modeling and simulations of porous media. Illustrative examples describing the dynamical behavior of porous media (saturated soils) are presented. The verified and validated methods and material models are used to predict the behavior of level and sloping grounds subjected to seismic shaking. Copyright © 2008 John Wiley & Sons, Ltd.     

吸力式筒形基础沉贯过程的大变形有限元模拟

吸力式筒形基础在海洋工程中已获得越来越广泛地应用,其安装过程的数值模拟对指导工程实践具有重要意义。在大型通用有限元软件ABAQUS平台上建立了二维轴对称模型,基于ALE（任意拉格朗日-欧拉法）技术模拟了黏土中吸力筒的大变形沉贯过程。模拟过程利用了子程序VUFIELD控制土体的不排水抗剪强度和弹性模量随土体深度变化。参照离心机试验及理论计算,对模型进行验证。利用已验证模型分析不同吸力下沉贯阻力、土塞高度,并讨论了筒壁摩擦特性。数值计算结果表明,ALE技术能有效地模拟吸力筒贯入过程,避免网格畸变。贯入方式对贯入阻力影响很大,吸力式贯入阻力明显低于压力式贯入阻力。进一步研究发现,随着最终吸力值的增大,沉贯阻力会显著降低,土塞高度会显著提高。对内壁摩擦特性的研究表明,内壁摩擦阻力是导致沉贯阻力改变的主要因素,并且相比吸力式贯入方式,筒壁摩擦特性会对压力式贯入造成更大的影响。     

砂土中筒型基础沉放过程渗流特性和沉贯阻力研究

筒型基础的沉放是一项关键施工过程,沉放时土体在施工负压下产生渗流场,而渗流对基础筒壁的侧摩阻力和端阻力产生影响,导致沉贯阻力难以预测。针对这一问题,首先应用试验和数值模拟的方法,对筒型基础沉贯过程中的渗流特性进行分析,揭示筒壁两侧及筒端土体超孔隙水压力的分布;然后将分析结果应用于沉贯阻力的推导中,并对推导的公式进行验证。研究表明：筒型基础沉贯过程中,筒壁两侧土体的超孔隙水压力沿筒壁深度几乎呈线性变化,在接近筒端时出现非线性变化;不同的沉贯深度下,渗流对沉贯阻力的影响不同,随着沉贯深度的增加,减小的阻力占总沉贯阻力的比值越来越大;通过推导的理论公式计算的试验模型和实际工程的沉贯负压理论计算值与实测值吻合较好。     

Stabilized single-point 4-node quadrilateral element for dynamic analysis of fluid saturated porous media

An accurate and efficient low-order quadrilateral mixed u?Cp element suitable for dynamic analysis of fluid saturated porous media is presented. The element uses physical hourglass stabilization to facilitate single-point integration for the solid phase, and non-residual stabilization of the fluid phase to circumvent instability in the incompressible-impermeable limit due to the use of equal-order interpolation for the displacement and pressure fields. Element behavior is verified and demonstrated through several numerical examples.     

Numerical modelling of dynamic consolidation on granular soils

The application of Pastor–Zienkiewicz constitutive model for sands to dynamic consolidation problems is presented in this paper. This model is implemented in a coupled code formulated in terms of displacements for both solid and fluid phases (u?w formulation), which is firstly compared with u?p_w formulation for some simple examples. Its range of validity, previously established for elastic problems and harmonic loading, is explored. Once the suitability of the u?w formulation has been ascertained for this kind of dynamic problems in soils, one‐ and two‐dimensional (plane strain) dynamic consolidation numerical examples are provided, aiming to give some light into the physics of this ground improvement technique. A ‘wave of dryness’, observed at the soil surface during the impact in field cases, is numerically reproduced and justified. Some hints on the influence of the loading zone size are also given. Copyright © 2007 John Wiley & Sons, Ltd.     

饱和砂土地基中吸力式桶形基础水平承载力研究

吸力式桶形基础不仅承受着上部结构及自身所引起的竖向荷载,还受到波浪、海流、海风等引起的水平荷载作用,在高纬度海域冬季还可能受到海冰的长时间挤压作用。利用三维有限元模型,研究饱和排水砂土条件下吸力式桶形基础的水平极限承载力和失稳模式,分析缓慢施加水平荷载时吸力式桶形基础失稳破坏机制,探讨不同长径比的桶形基础承载性能,研究桶体内外壁土压力分布情况和转动轴位置,并根据极限平衡解法,推导出饱和砂土地基桶形基础水平极限承载力计算公式。研究结果可为砂土地基条件下的吸力式桶形基础的设计提供参考。     

粉土中筒型基础贯入阻力的研究

筒型基础在海洋工程中应用广泛,贯入阻力的准确计算是筒型基础成功应用的关键。在海洋工程中,粉土是介于砂土与黏土间的特殊土,现有计算方法中将粉土等同于砂土,忽略了黏聚力c对贯入阻力的影响。开展了粉土中筒型基础的现场贯入试验,观测了自重下沉阶段与负压贯入阶段筒型基础贯入阻力与贯入深度的关系,提出了粉土中计算沉贯阻力的方法,并对不同筒端形式的减阻效果进行了深入分析。研究结果表明,采用现有规范方法计算粉土中筒型基础的贯入阻力值较实测值偏小20%,提出的两种方法不仅适用于计算粉土中筒型基础的贯入阻力,而且能够反映负压贯入阶段的减阻效果;尖筒端可使筒端阻力减少50%,减阻环可使筒侧摩阻力减少50%,但减阻环会破坏筒壁周围土体,形成渗流通道,导致负压失效。     

无黏性土中筒型基础负压下沉模型试验

筒型基础是海洋结构物特别是海上风力机的重要基础型式之一,其下沉阻力的研究是该种基础型式成功应用的关键。目前对于无黏性土中下沉负压的计算方法主要有以静力触探为基础的(CPT-Based)方法与基于贯入过程中筒体受力平衡的解析方法,但计算结果与工程实测数据均存在偏差。开展了3种不同厚径比筒型基础的负压下沉模型试验,测量了下沉过程中筒内外侧壁、端部土压力以及周围土体的孔压变化;分析了2种方法中计算参数对结果的影响,给出了推荐的参数取值范围;根据实测孔压与数值模拟结果建立了临界负压计算公式。研究表明：砂土中筒型基础负压下沉时筒土间摩擦系数约为0.2,推荐CPT-Based方法中的外侧摩阻力系数为0.002 6～0.007 0,内侧摩阻力系数为0.001,端阻力系数为0.2～0.6;解析法中侧向土压力系数介于静止土压力系数与被动土压力系数之间,端阻力承载系数为40;考虑土体渗透破坏保护机制的临界负压计算公式可以有效地提高筒型基础下沉控制的临界负压,更加接近实际情况。     

Geochemistry, petrofabrics and seismic properties of eclogites from the Chinese Continental Scientific Drilling boreholes in the Sulu UHP terrane, eastern China

We present an integrated study of geochemistry, petrofabrics and seismic properties of strongly sheared eclogites from the Chinese Continental Scientific Drilling (CCSD) project in the Sulu ultrahigh-pressure (UHP) metamorphic terrane, eastern China. First, geochemical data characterize diverse protoliths of the studied eclogites. The positive Eu- and Sr-anomalies, negative Nb anomaly and flat portion of heavy rare earth elements in coarse-grained rutile eclogites (samples B270 and B295) suggest a cumulate origin in the continental crust, whereas the negative Nb anomaly and enrichment of light rare earth elements in retrograde eclogites (samples B504, B15 and B19) imply an origin of continental basalts or island arc basalts. Second, P-wave velocities (V_p) of three typical eclogite samples were measured under confining pressures up to 500 MPa and temperatures to 700 °C. At 500 MPa and room temperature, the mean V_p reaches 8.50-8.53 km/s in samples B270 and B295 but drops to 7.86 km/s in sample B504, and the P-wave anisotropy changes from 1.7-2.7% to 5.5%, respectively. The pressure and temperature derivatives of V_p are larger in the retrograde eclogite than in fresh ones. Third, the electron backscatter diffraction (EBSD) measurements of the eclogites reveal random crystal preferred orientation (CPO) of garnet and pronounced CPO of omphacite, which is characterized by a strong concentration of [001]-axes sub-parallel to the lineation and of (010)-poles perpendicular to the foliation. The asymmetric CPO of omphacite in sample B270 recorded a top-to-the-south shear event during subduction of the Yangtze plate. The calculated fastest V_p is generally sub-parallel to the lineation, but a different deformation environment during exhumation could form second-order variations in omphacite CPO and affect the V_p distribution in eclogites (e.g., the fastest V_p is at ~ 35° from the foliation in sample B295). Comparison between measured and calculated seismic properties indicates that the CPO of omphacite controls the seismic anisotropy of eclogites at high pressure, and compositional layering and retrograde minerals will increase the anisotropy. Calculated P-wave velocities agree well with velocities measured at 500 MPa and room temperature for fresh eclogites, but much higher than those of retrograde eclogite. As a case study, the laboratory-derived V_p-P and V_p-T relationships were used to estimate P-wave velocities of eclogites and peridotites beneath the Western Superior Province, Canada. The results indicate that besides the fabric-induced anisotropy, the direction dependence of pressure and temperature derivatives of V_p can significantly increase seismic anisotropy of eclogites with depth, which results in eclogites being an important candidate for the seismic anisotropy in the upper mantle. Due to their very high density and velocity, garnet-rich eclogites within peridotite could be detected in seismic reflections in subduction zones.     

Dynamics of unsaturated soils using various finite element formulations

Unsaturated soils are three‐phase porous media consisting of a solid skeleton, pore liquid, and pore gas. The coupled mathematical equations representing the dynamics of unsaturated soils can be derived based on the theory of mixtures. Solution of these fully coupled governing equations for unsaturated soils requires tremendous computational resources because three individual phases and interactions between them have to be taken into account. The fully coupled equations governing the dynamics of unsaturated soils are first presented and then two finite element formulations of the governing equations are presented and implemented within a finite element framework. The finite element implementation of all the terms in the governing equations results in the complete formulation and is solved for the first time in this paper. A computationally efficient reduced formulation is obtained by neglecting the relative accelerations and velocities of liquid and gas in the governing equations to investigate the effects of fluid flow in the overall behavior. These two formulations are used to simulate the behavior of an unsaturated silty soil embankment subjected to base shaking and compared with the results from another commonly used partially reduced formulation that neglects the relative accelerations, but takes into account the relative velocities. The stress–strain response of the solid skeleton is modeled as both elastic and elastoplastic in all three analyses. In the elastic analyses no permanent deformations are predicted and the displacements of the partially reduced formulation are in between those of the reduced and complete formulations. The frequency of vibration of the complete formulation in the elastic analysis is closer to the predominant frequency of the base motion and smaller than the frequencies of vibration of the other two analyses. Proper consideration of damping due to fluid flows in the complete formulation is the likely reason for this difference. Permanent deformations are predicted by all three formulations for the elastoplastic analyses. The complete formulation, however, predicts reductions in pore fluid pressures following strong shaking resulting in somewhat smaller displacements than the reduced formulation. The results from complete and reduced formulations are otherwise comparable for elastoplastic analyses. For the elastoplastic analysis, the partially reduced formulation leads to stiffer response than the other two formulations. The likely reason for this stiffer response in the elastoplastic analysis is the interpolation scheme (linear displacement and linear pore fluid pressures) used in the finite element implementation of the partially reduced formulation. Copyright © 2008 John Wiley & Sons, Ltd.     

Higher resolution total velocity <Emphasis Type="Italic">Vt</Emphasis> and <Emphasis Type="Italic">Va</Emphasis> finite-volume formulations on cell-centred structured and unstructured grids

Novel cell-centred finite-volume formulations are presented for incompressible and immiscible two-phase flow with both gravity and capillary pressure effects on structured and unstructured grids. The Darcy-flux is approximated by a control-volume distributed multipoint flux approximation (CVD-MPFA) coupled with a higher resolution approximation for convective transport. The CVD-MPFA method is used for Darcy-flux approximation involving pressure, gravity, and capillary pressure flux operators. Two IMPES formulations for coupling the pressure equation with fluid transport are presented. The first is based on the classical total velocity Vt fractional flow (Buckley Leverett) formulation, and the second is based on a more recent Va formulation. The CVD-MPFA method is employed for both Vt and Va formulations. The advantages of both coupled formulations are contrasted. The methods are tested on a range of structured and unstructured quadrilateral and triangular grids. The tests show that the resulting methods are found to be comparable for a number of classical cases, including channel flow problems. However, when gravity is present, flow regimes are identified where the Va formulation becomes locally unstable, in contrast to the total velocity formulation. The test cases also show the advantages of the higher resolution method compared to standard first-order single-point upstream weighting.     

海上风机吸力式筒形基础抗压承载模式研究

吸力筒基础具有承载能力高、工艺简单、施工方便等优势,越来越广泛地应用于海上风电基础设计中。目前,吸力筒基础抗压承载计算方法尚没有统一的标准。为了降低海上风电基础设计成本,本文基于现有的API规范和地基承载力理论,总结3种不同吸力筒抗压承载模式,并提出“筒盖+筒壁外侧摩阻力”承载模式;根据工程案例和有限元软件PLAXIS验证其合理性,得出“筒壁端+筒壁内外侧摩阻力”承载模式和本文提出的“筒盖+筒壁外侧摩阻力”承载模式的计算结果符合DNV-OS-J101规范标准;按照本文提出的吸力筒抗压承载模式设计吸力筒尺寸,最大可降低13%的设计基础材料成本,有利于为海上风电吸力筒基础设计提供参考依据。     

Three‐dimensional analysis of the seismic behaviour of micropiles used in the reinforcement of saturated soil

This paper includes a numerical study of the behaviour of micropiles used for the reinforcement of saturated soil. Analysis is carried out using the (u–p) formulation (displacement for the solid phase and pore‐pressure for the fluid phase) implemented in a three‐dimensional finite element program. The soil behaviour is described by means of a cyclic elastoplastic constitutive relation which was developed within the framework of the bounding surface concept. The paper is composed of three parts. The first one is concerned with a presentation of the numerical model; the second includes analysis of the seismic behaviour of a single micropile; the last part deals with the group effect under seismic loading. Copyright © 2001 John Wiley & Sons, Ltd.