巖土畢業(yè)設(shè)計(jì)外文翻譯

Dynamic Response of Pile Foundation in Partially Saturated Soils非飽和土中樁基的動(dòng)力響應(yīng)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，Clemson 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 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 used 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 displacement 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.摘要樁基礎(chǔ)是公路橋梁和高層建筑等眾多土木結(jié)構(gòu)不可或缺的一部分。 在地震過程中的動(dòng)態(tài)樁土的相互作用的研究是一個(gè)復(fù)雜的課題，并且當(dāng)樁位于有不同程度的飽和度（DOS）的非飽和土中時(shí)，其復(fù)雜性會(huì)進(jìn)一步增加。在本文中，位于有兩個(gè)不同的dos的非飽和土中的樁的整體響應(yīng)采用了完全耦合的有限元計(jì)算機(jī)代碼。利用彈塑性的材料模型被用來表示土骨架的應(yīng)力 - 應(yīng)變行為。并對(duì)飽和度對(duì)周期和譜加速度的影響以及在地震過程中樁身周圍液體和氣體壓力（吸力）的發(fā)展與消散進(jìn)行了討論。分析表明，在地面和上層建筑層面的橫向位移、主要周期和譜加速度受土壤最初的飽和度的影響。INTRODUCTION簡(jiǎn)介Most engineering structures made of soils or other engineering materials are ultimately supported on the earths surface that may consist 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 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 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 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 complicated when structural elements are embedded into the unsaturated soil.大多數(shù)由土壤或其它工程材料建成的工程結(jié)構(gòu)最終均是支撐于由完全飽和的土壤、非飽和土或完全干燥的土壤構(gòu)成的大地表面。在非飽和土中，孔隙空間部分被水填充，其余部分為空氣。在受到結(jié)構(gòu)和環(huán)境荷載的影響時(shí)，不飽和土壤中水的含量會(huì)影響到土的特性除了體相，在液體與氣體之間被稱為收縮層的界面也會(huì)影響非飽和土的動(dòng)力特性。存在于收縮層之間的液相與氣相的壓力差是吸力。天氣變化所引起的土壤中水分的變化會(huì)帶來基質(zhì)吸力的變化?；|(zhì)吸力是非飽和土特征中的一個(gè)重要變量?；|(zhì)吸力的連同凈壓力被認(rèn)為是控制非飽和土的力學(xué)特性的狀態(tài)變量(Fredlund和Rahardjo,1993)。因此,對(duì)于非飽和土性質(zhì)的數(shù)值研究,考慮了體相與界面之間的相互作用的耦合控制方程必須書寫正確，這樣才能變現(xiàn)出非飽和土的性質(zhì)。而當(dāng)結(jié)構(gòu)因素參與到非飽和土中時(shí)，此問題會(huì)變得更加復(fù)雜。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 thestructure. 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 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 Georgiadis 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 loading, 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 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 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. 一個(gè)典型的分析土-結(jié)構(gòu)動(dòng)力相互作用問題的過程可能包含自由站點(diǎn)響應(yīng)分析和一個(gè)動(dòng)態(tài)的結(jié)構(gòu)分析。在地面表層的結(jié)構(gòu)計(jì)算基底剪力和彎矩用到了加速度設(shè)計(jì)反應(yīng)譜（ADRS），這是一個(gè)專供地表計(jì)算的站點(diǎn)。然而，這樣的分析無法得到土層響應(yīng)對(duì)于結(jié)構(gòu)的影響和土壤對(duì)于結(jié)構(gòu)的直接影響。在不飽和的土層的情況下，土層中的含水量（飽和度），會(huì)影響樁的特性。Georgiadis等（2003）研究了部分飽和土層在靜態(tài)軸向荷載下對(duì)樁基礎(chǔ)特性的影響。研究表明，樁的承載能力（極限荷載）隨著土層不飽和度的增加而提高。此外，研究也表明，當(dāng)樁尖端位于不飽和土層中時(shí)，部分飽和會(huì)影響到樁的特性。由于他們已經(jīng)利用垂直加載進(jìn)行了靜態(tài)分析，樁的前段應(yīng)當(dāng)被置于非飽和土層中以便確定部分飽和的影響，但對(duì)于動(dòng)態(tài)分析而言，即使樁的前端在部分飽和土層之外，部分飽和的影響仍然是十分顯著的。部分飽和土的有限元分析相比其他類似的飽和土分析而言，能得到較大幅度的極限荷載的增長，飽和土分析的結(jié)果顯著低于預(yù)計(jì)的承載能力。此外，在部分飽和土的有限元分析中，大量的計(jì)算是被認(rèn)可的，因?yàn)闃兜那岸讼碌耐翆訒?huì)破壞并且這種計(jì)算在飽和土的有限元分析中能夠得到認(rèn)可（Georgiadis等，2003）。本文獻(xiàn)通過研究分析非飽和土層中土與樁的相互作用，來預(yù)測(cè)樁和土層的整體動(dòng)態(tài)響應(yīng)。In this paper, the response of pile foundations in unsaturated soil subjected 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 presented 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，分析在不飽和土層中的樁基礎(chǔ)受到基礎(chǔ)震動(dòng)時(shí)的響應(yīng)采用的是耦合有限元程序。非飽和土的應(yīng)力-應(yīng)變特性用彈塑性模型來表示，結(jié)構(gòu)的應(yīng)力-應(yīng)變特性則用線彈性模型來表示。介紹樁和最初有著兩種不同飽和度的土層的響應(yīng)并將二者加以對(duì)比。研究結(jié)果表明諸如主要周期、位移和光譜放大系數(shù)的動(dòng)態(tài)響應(yīng)會(huì)受到土層最初飽和度的影響。SUMMARY OF GOVERNING EQUATIONS AND FINITE ELEMENT 控制方程和有限元的總結(jié)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 description refer Ravichandran and Muraleetharan (2009). 在本節(jié)中，我們用通常的固體力學(xué)公式總結(jié)了控制非飽和土動(dòng)態(tài)的關(guān)鍵方程。有關(guān)的詳細(xì)說明請(qǐng)參閱：Ravichandran and Muraleetharan (2009)。Mass balance equations質(zhì)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 solid phase, is the divergence.固相：（1）其中n是非飽和土的孔隙率（容積空隙/總體積），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 displacement 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：將固相的質(zhì)量平衡方程推廣到液相的質(zhì)量守衡方程，下列方程可推導(dǎo)出液相的質(zhì)量守衡方程。其中，u為固相位移，是液相位移，是液相體積模量，S為基質(zhì)吸力，是液相的體積分?jǐn)?shù)，是液體的壓力，為氣體的壓力，是固體骨架的體積應(yīng)變。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.氣相：與液相類似，氣相的質(zhì)量平衡可表示為 其中，為位移氣相，為氣相的體積分?jǐn)?shù)，是氣相體積模量。Momentum balance equations 動(dòng)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: whereis 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 tensor can beexpressed in terms of net stress and pore gas pressure液體的動(dòng)量平衡方程在本質(zhì)上是廣義達(dá)西定律。混合態(tài)的線性動(dòng)量平衡液態(tài)的線性動(dòng)量平衡氣態(tài)的線性動(dòng)量平衡其中，為總應(yīng)力張量，是重力加速度矢量，是液相的反相滲透張量（即，在1-D中，其中，k 為液體的滲透系數(shù)）。是氣相的反相滲透張量，為克羅內(nèi)克增量?？倯?yīng)力張量可以用凈應(yīng)力（）和孔隙氣壓表示。FINITE ELEMENT FORMULATION AND SIMULATION TOOL 有限元公式和仿真工具The system of equations (2 through 6) which 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 formulation (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.方程組（2至6式）考慮了相對(duì)加速度和速度，因此稱為完全方程（Ravichandran and Muraleetharan, 2009）。而忽略了相對(duì)孔隙流體的加速度和速度的方程組，被稱為縮減的方程或簡(jiǎn)化方程（Ravichandran and Muraleetharan, 2009）。在此特定的研究中，簡(jiǎn)化方程用來初步探求樁基礎(chǔ)受到地震震動(dòng)時(shí)的特性。Reduced formulation 縮減的方程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 coefficients 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 undrained 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 momentum 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 are 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 formulation is summarized below. 非飽和土中的水或空氣的滲透系數(shù)是水分含量的一個(gè)函數(shù)，并且與土壤水分特征曲線有關(guān)。不飽和狀態(tài)，尤其是飽和程度低的狀態(tài)下的滲透系數(shù)小于飽和土的狀態(tài)的滲透系數(shù)。因此，假設(shè)非飽和土在不排水條件下，尤其是在如地震荷載等快速加載條件下的行為是合理的。為了模擬這樣的不排水條件，在上一節(jié)所描述的一組方程可以適當(dāng)簡(jiǎn)化，忽略空隙液相或氣相的相對(duì)速度和加速度，但應(yīng)考慮固相的加速度和速度。這個(gè)方程組由混合物的動(dòng)量平衡方程和液體與氣體的質(zhì)量守恒方程組成。在這種情況下，動(dòng)量平衡方程用來求解以固體位移為主要節(jié)點(diǎn)的未知量。液體和氣體的壓力使用質(zhì)量守恒方程求解，并耦合到在液相和氣相之間以保持壓力平衡。液體壓力和氣體壓力的變化與固體骨架變形有著直接的關(guān)系，因?yàn)榧俣ㄆ錇椴慌潘?，所以變化與流動(dòng)的液體無關(guān)。最后一組方程簡(jiǎn)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 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 efficiency(Ravichandranand Muraleetharan, 2009). Downloaded from by CENTRAL SOUTH UNIVERSITY on 05/24/13. Copyright ASCE. For personal use only; all rights reserved.采用四節(jié)點(diǎn)四邊形等單元與線性插值功能來推導(dǎo)與簡(jiǎn)化后的方程相應(yīng)的有限元方程。使用這種簡(jiǎn)化的方程的主要優(yōu)點(diǎn)是提高計(jì)算效率。為了進(jìn)一步增加計(jì)算效率,單元矩陣和向量計(jì)算使用新穎的均勻梯度單元方程(單點(diǎn)集成4節(jié)點(diǎn)四邊形單元)，其以沙漏控制流程來提高計(jì)算效率（Ravichandran 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 code 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, memory 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 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.被簡(jiǎn)化的方程和完全的方程均被應(yīng)用于TeraDysac有限元分析軟件（Ravichandran，2005年）。然而，本文所示的樁與土相互作用問題僅僅模擬采用了簡(jiǎn)化的方程。與傳統(tǒng)的巖土工程研究實(shí)踐的代碼開發(fā)過程相比，TeraDysac是利用有限元的框架進(jìn)行開發(fā)的（Anatech公司，2001年）。這個(gè)框架代表了一個(gè)建立各種有限元的應(yīng)用程序的軟件組件的集合：如輸入/輸出服務(wù)、內(nèi)存管理和并行處理技術(shù)。通過收集這些軟件組件并集成到一個(gè)單一的工具包，這個(gè)框架能使應(yīng)用程序開發(fā)人員將這些組件應(yīng)用到許多不同的程序上。在這種情況下，有眾多的有限元方程可以用來求解非飽和土的動(dòng)力特性。這種帶有新特征的計(jì)算機(jī)代碼將有類似的商業(yè)軟件的功能，并可以很容易地供研究生和行業(yè)人員食使用。EXAMPLE: SOIL-PILE INTERACTION ANALYSIS 例：樁土相互作用分析The finite element mesh for the example problem 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 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 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 suction-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 interface 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 concentrated 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 history (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 stresses. The predicted responses using TeraDysac for unsaturated soil are discussed in the next section. 圖1所示的是例子的有限元網(wǎng)格，該結(jié)構(gòu)由一根單獨(dú)的柱組成，柱的上端承受著較大的質(zhì)量（上層建筑），下部則由樁基礎(chǔ)支撐。固體骨架的應(yīng)力-應(yīng)變特性是以一個(gè)基于邊界表面概念的彈塑性材料模型進(jìn)行分析。飽和土的邊界表面模型是由Dafalias和Herrman創(chuàng)建(Dafalias和Herrman, 1986)的。飽和土模型后來被MuraleetharanNedunuri修改（MuraleetharanNedunuri，1998年），他加入了諸如如破壞曲線（LC曲線）等的相關(guān)行為。此曲線由Alonso等人（Alanso等，1990）、Wheeler和Sivakumar (Wheeler和Sivakumar, 1995)提出。采用實(shí)驗(yàn)室測(cè)試的彈塑性材料模型參數(shù)標(biāo)準(zhǔn)（Vinayagam，2002）列于表1，相應(yīng)的相吸模型參數(shù)列于表2。以飽和度關(guān)系的相吸程度最為模型，此模型使用由van Genuchten（1980）提出土壤水特征曲線建立。 Timoshenko的梁理論用來解釋表示梁的性質(zhì)。結(jié)構(gòu)單元節(jié)點(diǎn)與固體節(jié)點(diǎn)相連接并與之一起移動(dòng)。在土層和結(jié)構(gòu)之間，沒有特定的界面單元能夠被用來測(cè)定氣體的進(jìn)出或垂直方向的相對(duì)運(yùn)動(dòng)。結(jié)構(gòu)單元由三個(gè)部分組成：上部結(jié)構(gòu)，橋墩和基礎(chǔ)。上部結(jié)構(gòu)等效為一個(gè)單獨(dú)的集中質(zhì)量單元作用于橋墩頂部。這個(gè)單元采用非常高的密度來反映上部結(jié)構(gòu)的質(zhì)量。假定此結(jié)構(gòu)彈性工作，結(jié)構(gòu)特性和彈性材料模型參數(shù)列于表3。在網(wǎng)格基礎(chǔ)上的加速度時(shí)程曲線（Kobe加速時(shí)程）如圖2所示。為網(wǎng)格計(jì)算原位應(yīng)力并把它作為初始應(yīng)力來進(jìn)行動(dòng)態(tài)分析。使用橫向的土壓力系數(shù)為0.5，計(jì)算出相應(yīng)的水平應(yīng)力。使用非飽和土的TeraDysac理論來預(yù)測(cè)的相應(yīng)的反應(yīng)將在下一節(jié)討論。圖1 示例的二維有限元網(wǎng)格圖2 基礎(chǔ)運(yùn)動(dòng)加速度隨時(shí)間變化曲線RESULTS AND DISCUSSION結(jié)果與討論Analyses were performed 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 slightly 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