岩土毕业设计外文翻译

1、Dynamic Response of Pile Foundation in Partially Saturated Soils非饱和土中桩基的动力响应NadarajahRavichandran1，A.M. ASCE and H. K. Shada2，S. M. ASCE. 1Department of Civil Engineering，Clemson University，320 Lowry Hall，Clemson，SC 29634；PH (864) 656-2818；email: 2Department of Civil Engineering，Cl

2、emson University，123 Lowry Hall，Clemson，SC 29634；PH (864) 506-4438；email: ABSTRACT Pile foundations are integral part of many civil engineering structures such as highway bridges and tall buildings. Dynamic soil-pile interaction during seismic event is a complex problem and the complexity is further

3、 increased when such piles are located in unsaturated soils with varying degree of saturation (dos). In this paper, the overall response of piles located in unsaturated soil with two different dos is investigated using fully coupled finite element computer code. An elastoplasticmaterial model is use

4、d to represent the stress-strain behavior of the soil skeleton. The effect of dos on the period and the spectral acceleration is discussed. Liquid and gas pressure (matric suction) development and dissipation around the pile during seismic event are also discussed. The analyses reveal that lateral d

5、isplacement at the ground surface and the superstructure level, the predominant period and the spectral accelerations are influenced by the initial degree of saturation of the soil.摘要桩基础是公路桥梁和高层建筑等众多土木结构不可或缺的一部分。 在地震过程中的动态桩土的相互作用的研究是一个复杂的课题，并且当桩位于有不同程度的饱和度（DOS）的非饱和土中时，其复杂性会进一步增加。在本文中，位于有两个不同的dos的非饱和

6、土中的桩的整体响应采用了完全耦合的有限元计算机代码。利用弹塑性的材料模型被用来表示土骨架的应力 - 应变行为。并对饱和度对周期和谱加速度的影响以及在地震过程中桩身周围液体和气体压力（吸力）的发展与消散进行了讨论。分析表明，在地面和上层建筑层面的横向位移、主要周期和谱加速度受土壤最初的饱和度的影响。INTRODUCTION简介Most engineering structures made of soils or other engineering materials are ultimately supported on the earths surface that may consist

7、of fully saturated soil, unsaturated soil or fully dry soil. In unsaturated soil, the pore space is partly filled with water and the rest with air. The amount of water present in the unsaturated soil influences the soil behavior when subjected to structural and environmental loadings. In addition to

8、 the bulk phases, the interface, known as contractile skin, between the liquid and the gas also affects the dynamics of unsaturated soils. The pressure difference between the liquid and the gas phase maintained by the contractile skin is the matric suction. A change in soil moisture due to change in

9、 weather will cause a change in matric suction. Matric suction is one of the important variables in the characterization of unsaturated soil. The matric suction together with the net stress are considered as the state variables that control the mechanical behavior of unsaturated soils (Fredlund and

10、Rahardjo, 1993). Therefore, for numerical studies of the behavior of the unsaturated soil, coupled governing equations taking into account the interaction between the bulk phases and interfaces have to be written to correctly represent the unsaturated soil behavior. The problem becomes more complica

11、ted when structural elements are embedded into the unsaturated soil.大多数由土壤或其它工程材料建成的工程结构最终均是支撑于由完全饱和的土壤、非饱和土或完全干燥的土壤构成的大地表面。在非饱和土中，孔隙空间部分被水填充，其余部分为空气。在受到结构和环境荷载的影响时，不饱和土壤中水的含量会影响到土的特性除了体相，在液体与气体之间被称为收缩层的界面也会影响非饱和土的动力特性。存在于收缩层之间的液相与气相的压力差是吸力。天气变化所引起的土壤中水分的变化会带来基质吸力的变化。基质吸力是非饱和土特征中的一个重要变量。基质吸力的连同净压力被认

12、为是控制非饱和土的力学特性的状态变量(Fredlund和Rahardjo,1993)。因此,对于非饱和土性质的数值研究,考虑了体相与界面之间的相互作用的耦合控制方程必须书写正确，这样才能变现出非饱和土的性质。而当结构因素参与到非饱和土中时，此问题会变得更加复杂。A typical analysis procedure for a soil-structure interaction problem might involve free field site response analysis of soil followed by a dynamic analysis of thestruct

13、ure. The base shear and the bending moment on the structure at the ground surface level are calculated using the Acceleration Design Response Spectrum (ADRS) calculated for the site at the ground surface. Such an analysis, however, will not capture the influence of the structure on the soil response

14、 or the true influence of soil on the structure. In the case of unsaturated soil, the amount of water present in the soil (degree of saturation) will influence the pile behavior. The influence of partial saturation on the behavior of pile foundation subjected to static axial load is studied by Georg

15、iadis et al. (2003) and it shows that the load capacity (ultimate pile load) increases as soil becomes unsaturated. Also it shows that the partial saturation influences the pile behavior when the pile (top to tip) is in unsaturated soil. Since they have carried out static analysis with vertical load

16、ing, the tip of the pile should be in unsaturated soil to recognize the influence of partial saturation but for dynamic analysis the partial saturation is expected to be significant even if the tip is outside the partial saturation zone. Finite element analyses of partially saturated soil predicted

17、larger ultimate load increase than similar analyses of saturated soils, i.e., saturated soil analyses significantly under predicted the load capacity. Also in partially saturated finite element analyses, excessive settlement is recognized because of the collapse experienced by the soil under the tip

18、 of the pile and this settlement could not be recognized with saturated finite element analyses (Georgiadis et al., 2003). This literature study shows the importance of unsaturated soilpile interaction analysis to predict the overall dynamic response of piles and the soil. 一个典型的分析土-结构动力相互作用问题的过程可能包含

19、自由站点响应分析和一个动态的结构分析。在地面表层的结构计算基底剪力和弯矩用到了加速度设计反应谱（ADRS），这是一个专供地表计算的站点。然而，这样的分析无法得到土层响应对于结构的影响和土壤对于结构的直接影响。在不饱和的土层的情况下，土层中的含水量（饱和度），会影响桩的特性。Georgiadis等（2003）研究了部分饱和土层在静态轴向荷载下对桩基础特性的影响。研究表明，桩的承载能力（极限荷载）随着土层不饱和度的增加而提高。此外，研究也表明，当桩尖端位于不饱和土层中时，部分饱和会影响到桩的特性。由于他们已经利用垂直加载进行了静态分析，桩的前段应当被置于非饱和土层中以便确定部分饱和的影响，但对于动

20、态分析而言，即使桩的前端在部分饱和土层之外，部分饱和的影响仍然是十分显著的。部分饱和土的有限元分析相比其他类似的饱和土分析而言，能得到较大幅度的极限荷载的增长，饱和土分析的结果显著低于预计的承载能力。此外，在部分饱和土的有限元分析中，大量的计算是被认可的，因为桩的前端下的土层会破坏并且这种计算在饱和土的有限元分析中能够得到认可（Georgiadis等，2003）。本文献通过研究分析非饱和土层中土与桩的相互作用，来预测桩和土层的整体动态响应。In this paper, the response of pile foundations in unsaturated soil subjected

21、to base shaking is investigated using coupled finite element program. Stress-strain behavior of unsaturated soil is represented by an elastoplastic model and of structure is modelled using a linear elastic model. The response of pile and the soil with two different initial degree of saturation are p

22、resented and compared. The results of the analysis show that the dynamic responses such as predominant period, displacement and spectral amplification factor are influenced by the initial degree of saturation of the soil. 在本文中，分析在不饱和土层中的桩基础受到基础震动时的响应采用的是耦合有限元程序。非饱和土的应力-应变特性用弹塑性模型来表示，结构的应力-应变特性则用线弹性模

23、型来表示。介绍桩和最初有着两种不同饱和度的土层的响应并将二者加以对比。研究结果表明诸如主要周期、位移和光谱放大系数的动态响应会受到土层最初饱和度的影响。SUMMARY OF GOVERNING EQUATIONS AND FINITE ELEMENT 控制方程和有限元的总结FORMUALTIONS公式The key equations governing the dynamics of unsaturated soils are summarized in this section in usual solid mechanics notations. For the detailed des

24、cription refer Ravichandran and Muraleetharan (2009). 在本节中，我们用通常的固体力学公式总结了控制非饱和土动态的关键方程。有关的详细说明请参阅：Ravichandran and Muraleetharan (2009)。Mass balance equations质量守恒方程Solid phase: (1) where n is the porosity (volume of voids/total volume) of the unsaturated soil system, is the velocity vector of the s

25、olid phase, is the divergence.固相：（1）其中n是非饱和土的孔隙率（容积空隙/总体积），是固相的速度矢量，是散度。Liquid phase:Incorporating the mass balance equation for the solid phase into the mass balance equation for the liquid phase, the following equation can be derived for the mass balance of the liquid phase. where u is the displac

26、ement of the solid phase, is the displacement of the liquid phase,is the bulk modulus of the liquid phase, S is the matric suction, is the volume fraction of the liquid phase, is the liquid pressure,is the gas pressure, and is the volumetric strain of solid skeleton. 液相：将固相的质量平衡方程推广到液相的质量守衡方程，下列方程可推

27、导出液相的质量守衡方程。其中，u为固相位移，是液相位移，是液相体积模量，S为基质吸力，是液相的体积分数，是液体的压力，为气体的压力，是固体骨架的体积应变。Gas phase: Similar to the liquid phase, the mass balance for the gas phase can be expressed as Whereis the displacement of the gas phase, is the volume fraction of the gas phase, and is the bulk modulus of the gas phase.气相：

28、与液相类似，气相的质量平衡可表示为 其中，为位移气相，为气相的体积分数，是气相体积模量。Momentum balance equations 动量平衡方程The momentum balance equations for these fluids are essentially the generalized Darcys flow equations.Linear momentum balance for the mixture: Linear momentum balance for the liquid: Linear momentum balance for the gas: whe

29、reis the total stress tensor, is the gravitational acceleration vector,is the inverted permeability tensor of the liquid phase (i.e., in 1-D k k / where k = coefficient of permeability of liquid).is the inverted permeability tensor of the gas phase, and is the Kronecker delta. The total stress tenso

30、r can beexpressed in terms of net stress and pore gas pressure液体的动量平衡方程在本质上是广义达西定律。混合态的线性动量平衡液态的线性动量平衡气态的线性动量平衡其中，为总应力张量，是重力加速度矢量，是液相的反相渗透张量（即，在1-D中，其中，k 为液体的渗透系数）。是气相的反相渗透张量，为克罗内克增量。总应力张量可以用净应力（）和孔隙气压表示。FINITE ELEMENT FORMULATION AND SIMULATION TOOL 有限元公式和仿真工具The system of equations (2 through 6) w

31、hich takes into account the relative accelerations and velocities is called the complete formulation (Ravichandran and Muraleetharan, 2009). The system of equations simplified by neglecting the relative accelerations and velocities of the pore fluids is called the reduced formulation or simplified f

32、ormulation (Ravichandran and Muraleetharan, 2009 ). In this particular study the reduced formulation is used to gain initial insights into the behavior of the pile foundation subjected to earthquake shaking.方程组（2至6式）考虑了相对加速度和速度，因此称为完全方程（Ravichandran and Muraleetharan, 2009）。而忽略了相对孔隙流体的加速度和速度的方程组，被称为

33、缩减的方程或简化方程（Ravichandran and Muraleetharan, 2009）。在此特定的研究中，简化方程用来初步探求桩基础受到地震震动时的特性。Reduced formulation 缩减的方程The permeability coefficient of water or air in unsaturated soil system is a function of water content and is related through the soil water characteristic curve. These permeability coefficient

34、s in unsaturated state are smaller than that in the saturated soil state especially in low degree of saturation state. Therefore, it is reasonable to assume that the unsaturated soil behave under undrained conditions especially under rapid loadings such as earthquake loading. To simulate such undrai

35、ned conditions, the set of governing equations described in the previous section can be simplified by neglecting the relative velocities and accelerations of the pore liquid and gas phases but includes the accelerations and velocities of the solid phase. This system of equations will consist of mome

36、ntum balance equation for the mixture and mass balance equations for the liquid and gas phases. In this case, the momentum balance equation is solved considering the solid displacements as the primary nodal unknowns. The liquid and gas pressures are calculated using the mass balance equations and ar

37、e coupled to maintain pressure balance between liquid and gas phases. The changes in liquid pressure and gas pressure are directly related to the deformation of the solid skeleton and not to the flow of the fluids since it is assumed to be undrained. The final set of equations for the reduced formul

38、ation is summarized below. 非饱和土中的水或空气的渗透系数是水分含量的一个函数，并且与土壤水分特征曲线有关。不饱和状态，尤其是饱和程度低的状态下的渗透系数小于饱和土的状态的渗透系数。因此，假设非饱和土在不排水条件下，尤其是在如地震荷载等快速加载条件下的行为是合理的。为了模拟这样的不排水条件，在上一节所描述的一组方程可以适当简化，忽略空隙液相或气相的相对速度和加速度，但应考虑固相的加速度和速度。这个方程组由混合物的动量平衡方程和液体与气体的质量守恒方程组成。在这种情况下，动量平衡方程用来求解以固体位移为主要节点的未知量。液体和气体的压力使用质量守恒方程求解，并耦合到在液

39、相和气相之间以保持压力平衡。液体压力和气体压力的变化与固体骨架变形有着直接的关系，因为假定其为不排水，所以变化与流动的液体无关。最后一组方程简化后如下Corresponding finite element equations for the reduced formulation are derived using four-node quadrilateral isoparametric elements with linear interpolation functions. The major advantage of using this simplified formulation

40、 is the computational efficiency. To further increase the computational efficiency, the element matrices and vectors are evaluated using a novel uniform gradient element formulation (single point integration for 4 node quadrilateral elements) with hourglass control scheme for computational efficienc

41、y(Ravichandranand Muraleetharan, 2009). Downloaded from by CENTRAL SOUTH UNIVERSITY on 05/24/13. Copyright ASCE. For personal use only; all rights reserved.采用四节点四边形等单元与线性插值功能来推导与简化后的方程相应的有限元方程。使用这种简化的方程的主要优点是提高计算效率。为了进一步增加计算效率,单元矩阵和向量计算使用新颖的均匀梯度单元方程(单点集成4节点四边形单元)，其以沙漏控制流程来提高计算效率（Ravi

42、chandran and Muraleetharan, 2009）。The reduced, and complete formulations are implemented into a finite element software called TeraDysac (Ravichandran, 2005). However, the soil-pile interaction problem shown in this paper is simulated using the reduced formulation only. In contrast to conventional c

43、ode development procedure in geotechnical engineering research practice, the TeraDys ac is developed within a finite element framework (Anatech Corp, 2001). A framework represents a collection of software components for building various finite element applications such as input/output service, memor

44、y management, and parallel processing technology. By collecting these software components into a single toolkit, a framework enables the application developer to leverage these components into many differen t applications. The resulting computer code with the new physics, in this case various finite

45、 element formulations for dynamics of unsaturated soils, will have the features similar to commercial software and can be readily used by graduate students and industry personnel.被简化的方程和完全的方程均被应用于TeraDysac有限元分析软件（Ravichandran，2005年）。然而，本文所示的桩与土相互作用问题仅仅模拟采用了简化的方程。与传统的岩土工程研究实践的代码开发过程相比，TeraDysac是利用有限元

46、的框架进行开发的（Anatech公司，2001年）。这个框架代表了一个建立各种有限元的应用程序的软件组件的集合：如输入/输出服务、内存管理和并行处理技术。通过收集这些软件组件并集成到一个单一的工具包，这个框架能使应用程序开发人员将这些组件应用到许多不同的程序上。在这种情况下，有众多的有限元方程可以用来求解非饱和土的动力特性。这种带有新特征的计算机代码将有类似的商业软件的功能，并可以很容易地供研究生和行业人员食使用。EXAMPLE: SOIL-PILE INTERACTION ANALYSIS 例：桩土相互作用分析The finite element mesh for the example p

47、roblem is shown in Figure 1 The structure consists of a sing le column with a large mass on top (superstructure) supported on a pile foundation. The stress -strain behavior of the solid skeleton is modelled using an elstoplastic material model based on bounding surface concept. The bounding surface

48、model for satura ted soil was developed by Dafalias and Herrman (Dafalias and Herrman, 1986) and the saturated soil model was later modified by Muraleetharan and Nedunuri(Muraleetharan and Nedunuri, 1998) to incorporate the suction relate d behavior such as loading collapse curve (LC curve) proposed

49、 by Alonso et al (Alansoet al., 1990) and Wheeler and Sivakumar (Wheeler and Sivakumar, 1995). The elastoplastic ma terial model parameters calibrated using laboratory tests (Vinayagam, 2002) and arelisted in Table 1 and the corresponding suction related model parameters are listed in Table 2. The s

50、uction-degree of saturation relationship is modeled using the soil water characteristics curve proposed by van Genuchten (1980). Timoshenko beam theory is utilized to represent the beam behavior. The structural element nodes are connected to the solid nodes and move together i.e., no special interfa

51、ce elements are utilized between the soil and the structure to capture the opening and closing of gaps or relative movement in the vertical direction. The structural element consists of three components: superstructure, pier and the foundation. The superstructure is modelled by a single element of c

52、oncentrated mass at the top of the pier. Very high density is used for that particular element to represent the mass of a superstructure. The structure is assumed to behave elastically. The structural properties and the elastic material model parameters are listed in Table 3. The acceleration time h

53、istory (Kobe acceleration time history) applied at the base of the mesh is shown in Figure 2. The in situ stresses were calculated for the mesh and used as the initial stresses for the dynamic analysis. A lateral earth pressure coefficient of 0.5 was used to calculate the corresponding horizontal st

54、resses. The predicted responses using TeraDysac for unsaturated soil are discussed in the next section. 图1所示的是例子的有限元网格，该结构由一根单独的柱组成，柱的上端承受着较大的质量（上层建筑），下部则由桩基础支撑。固体骨架的应力-应变特性是以一个基于边界表面概念的弹塑性材料模型进行分析。饱和土的边界表面模型是由Dafalias和Herrman创建(Dafalias和Herrman, 1986)的。饱和土模型后来被MuraleetharanNedunuri修改（MuraleetharanN

55、edunuri，1998年），他加入了诸如如破坏曲线（LC曲线）等的相关行为。此曲线由Alonso等人（Alanso等，1990）、Wheeler和Sivakumar (Wheeler和Sivakumar, 1995)提出。采用实验室测试的弹塑性材料模型参数标准（Vinayagam，2002）列于表1，相应的相吸模型参数列于表2。以饱和度关系的相吸程度最为模型，此模型使用由van Genuchten（1980）提出土壤水特征曲线建立。 Timoshenko的梁理论用来解释表示梁的性质。结构单元节点与固体节点相连接并与之一起移动。在土层和结构之间，没有特定的界面单元能够被用来测定气体的进出或垂直

56、方向的相对运动。结构单元由三个部分组成：上部结构，桥墩和基础。上部结构等效为一个单独的集中质量单元作用于桥墩顶部。这个单元采用非常高的密度来反映上部结构的质量。假定此结构弹性工作，结构特性和弹性材料模型参数列于表3。在网格基础上的加速度时程曲线（Kobe加速时程）如图2所示。为网格计算原位应力并把它作为初始应力来进行动态分析。使用横向的土压力系数为0.5，计算出相应的水平应力。使用非饱和土的TeraDysac理论来预测的相应的反应将在下一节讨论。图1 示例的二维有限元网格图2 基础运动加速度随时间变化曲线RESULTS AND DISCUSSION结果与讨论Analyses were perf

57、ormed for initial degree of saturations of 43% and 70% to investigate the effect of degree of saturation on the coupled performance of piles subjected to earthquake shaking. The horizontal displacement time histories at nodes N1 and N2 are shown in Figure 3. The soil with initial dos of 70% shows sl

58、ightly larger horizontal displacement compared to the soil with in itial dos of 43%, i.e., the soil with higher dos shows softer response compared to the lower dos. The horizontal spectral accelerations obtained at nodes N1, N2 and N3 using 5% damping are shown in Figure 4. Simulations with higher initial dos show higher spectral acceleration values at all three nodes (See Figures 4(a), (b), (c). The soil with higher initial dos seems to show higher amplificati on factor compared to that of lower initial dos. The response spectra at nodes N1, N2 and N3 for initial dos of 43% and 70% are s