土木工程畢業(yè)設計翻譯--護壁效應對“碎石樁性能”的數(shù)值分析

1、<p><b>　　附件C：譯文</b></p><p>　　Numerical Study of Effect of Encasement on Stone Column Performance</p><p>　　護壁效應對“碎石樁性能”的數(shù)值分析</p><p>　　Majid Khabbazian, Stud. M. ASCE

2、</p><p>　　Graduate Student and GSI Fellow, Dept. of Civil and Environmental Engineering, 301 DuPont Hall,</p><p>　　University of Delaware, Newark, DE 19716. E-mail: majid@udel.edu</p><

3、;p>　　紐瓦克，DE的19716，特拉華大學，301杜邦廳部，土木與環(huán)境工程系，研究生和GSI研究員Majid Khabbazian, Stud. M. ASCE。電子郵箱：majid@udel.edu</p><p>　　Christopher L. Meehan, A. M. ASCE</p><p>　　Assistant Professor, Dept. of Civil

4、and Environmental Engineering, 301 DuPont Hall, University of</p><p>　　Delaware, Newark, DE 19716. E-mail: cmeehan@udel.edu</p><p>　　紐瓦克，DE.的19716，美國特拉華州，大學部，301杜邦廳，土木及環(huán)境工程系，cmeehan@udel.edu<

5、/p><p>　　Victor N. Kaliakin, M. ASCE</p><p>　　Associate Professor, Dept. of Civil and Environmental Engineering, 301 DuPont Hall, University of</p><p>　　Delaware, Newark, DE 19716. E-m

6、ail: kaliakin@udel.edu</p><p>　　紐瓦克，DE的19716，美國特拉華州，大學部，301杜邦廳，土木及環(huán)境工程系，副教授。電子郵箱：kaliakin@udel.edu</p><p><b>　　ABSTRACT</b></p><p><b>　　摘要</b></p><

7、;p>　　Encasing a stone column with a high-strength geosynthetic provides the column</p><p>　　material with significant lateral confinement, which prevents lateral displacement of</p><p>　　the

8、column into potentially soft surrounding soil and consequently increases the</p><p>　　bearing capacity of the column. Although this technique has been successfully</p><p>　　applied in practice,

9、the load transfer mechanism of encased stone columns and their</p><p>　　performance in comparison with conventional stone columns have not been studied in</p><p>　　detail. This paper describes t

10、hree-dimensional finite element analyses that were</p><p>　　carried out to simulate the behavior of a single stone column with and without</p><p>　　encasement in a very soft clay soil using the

11、computer program ABAQUS. A comprehensive study was performed to better understand the mechanism of load transfer in conventional stone columns and geosynthetic encased stone columns. The performance of partially encased

12、columns was then compared to that of fully encased columns and conventional stone columns. </p><p>　　用高強度土工合成材料包裹碎石柱，土工合成材料為碎石柱材料提供顯著的橫向約束，這樣可以防止柱向著周圍的軟土地基發(fā)生側向位移，從而增加柱子的承載能力。雖然這一技術已成功應用于實踐中，受護壁作用的碎石樁的荷載傳導機制和

13、性能與傳統(tǒng)的碎石樁相比，并沒有被詳細研究透。本文介紹在一個非常松軟的粘土地基上使用ABAQUS軟件的計算機程序模擬單個碎石樁，采用三位有限元分析法分析其有無包裝效應。為了更深層次的了解傳統(tǒng)的碎石樁和被土工合成材料包裹的碎石樁中的荷載傳導機制，我們展開了更加全面的研究。在研究中，用部分被土工合成材料包裹的碎石樁分別與完全被包裹的碎石樁和傳統(tǒng)的碎石樁進行比較。</p><p>　　INTRODUCTION</p

14、><p><b>　　說明</b></p><p>　　Stone columns have been increasingly used for ground improvement, especially for</p><p>　　structures that can tolerate some settlement such as roa

15、d embankments, storage tanks,</p><p>　　low-rise buildings, lightly loaded foundations, etc. This form of ground improvement is also commonly referred to as granular piles. Extensive use of stone columns is a

16、ttributed to their proven successes in increasing bearing capacity, reducing total and differential settlements, increasing the time rate of settlement, and reducing the liquefaction potential of sands. </p><p

17、>　　碎石樁已經(jīng)被越來越多的用于地基的改善工程，特別是能承受一些沉降的結構，例如，公路路堤、存儲倉庫、低層建筑以及受到較輕荷載的基礎等。這種地基的改良形式也通常被稱為碎石樁。碎石柱的廣泛使用，是因為它成功地證明了自身在提高承載能力，降低整體沉降和不均勻沉降，增加沉降的時間速率，減少砂土地基液化可能性方面的能力。</p><p>　　Stone columns under compressive loads

18、experience failure modes such as bulging</p><p>　　(Hughes et al. 1975), general shear failure (Madhav and Vitkar 1978), and sliding(Aboshi et al. 1979). However, in soft clays the most common failure mode fo

19、r stone columns is bulging (Madhav and Miura 1994). </p><p>　　碎石樁在壓力作用下，會產(chǎn)生一些破壞模式，如膨脹破壞模式 （Hughes等人。1975年），一般的剪切破壞（Madhav和Vitkar 1978年），滑移破壞（Aboshi 等人 1979）。然而，在軟土地基中，碎石樁最常見的破壞模式是膨脹破壞（Madhav和Miura1994年）。<

20、/p><p>　　In very soft soils, due to the lack of required lateral confining pressure, the use of</p><p>　　stone columns can be problematic. In these situations, to provide the required lateral confi

21、ning pressure and to increase the bearing capacity, stone columns are encased by a suitable geosynthetic. Using a high-strength geosynthetic for confinement not only increases the strength of a stone column, but also pr

22、events lateral displacement of the column into the very soft surrounding soil. Sharma et al. (2004) conducted tests to investigate the effect of geogrid reinforcement on bulging and load-c</p><p>　　Rajagopal

23、 (2006) performed axisymmetric analyses and assumed continuum elements</p><p>　　for the geosynthetic without considering the behavior of the interface between</p><p>　　different materials (this

24、paper addresses this phenomenon by using interface elements</p><p>　　in the numerical model). Lee et al. Lee et al. (2007) investigated the failure mechanism and load carrying capacity of individual geogrid

25、encased stone columns by model tests. Alexiew et al. (2005) described the design principles, technologies, and procedures for geotextile encased stone columns and emphasized the importance of the tensile modulus of the g

26、eotextile that is used for column confinement. </p><p>　　在非常松軟的軟土地基上，由于所需的側向圍壓不足，碎石樁的使用可能會出現(xiàn)問題。在這種情況下，給碎石樁包裹一層適當?shù)耐凉ず铣刹牧?，可以提供必要的側向圍壓，提高碎石樁的承載能力。使用一種高強度土工合成材料，不但可以增加了碎石樁的強度，而且還可以防止碎石樁向著周圍松軟地基發(fā)生側向位移。Sharma等人（20

27、04）進行測試，以探討軟土地基上的單一碎石樁的膨脹和承重能力對土工格柵的加固效果。 Murugesan和Rajagopal（2006年，2007年） 進行模型試驗和數(shù)值分析，以研究在一個限定區(qū)域內(nèi)的單個被土工合成材料包裹的碎石樁的性能影響（研究群樁效應的其他途徑）。在數(shù)值分析的時候，Murugesan 和Rajagopal(2006)進行軸對稱分析并假定構件與包裹的土工合成材料的連續(xù)性，而不考慮不同材料的交界面的影響（本文解決了在數(shù)學模

28、型中使用界面單元的這一現(xiàn)象）。 Lee等人采用模型試驗的方法調(diào)查研究被土工材料包裹的碎石樁破壞機制和單個土工格柵的負荷能力。Alexiew等人(2005)描述了用土木布包裹碎石樁的設計原則、技術方法和程序步驟，并強調(diào)了用于約束碎石樁的土工布的拉伸模量的重要性。</p><p>　　This paper describes 3D finite element analyses that were carried o

29、ut to simulate</p><p>　　the behavior of a single geosynthetic-encased stone column (GESC) in soft clay using</p><p>　　the computer program ABAQUS (Hibbitt et al. 2007). To compare the performanc

30、e of the GESC with a conventional stone column (CSC), parallel analyses were also performed on a stone column without encasement. This paper describes the results of a comprehensive study that was performed to better und

31、erstand the load transfer mechanism of CSCs and GESCs. The possibility of using partially encased columns rather than fully encased columns is investigated, and the results are compared to those from full</p><

32、p>　　本文介紹了使用 ABAQUS軟件的計算機程序采用三維有限元分析法進行模擬在軟土地基上的單一土工合成材料包裹的碎石樁（GESC）的性能（Hibbitt等人。2007年）。采用比較分析法比較傳統(tǒng)碎石樁（CSC）與被土工合成材料包裹的碎石樁（GESC）的性能，這種方法也被用于分析裸露碎石樁基的分析。本文介紹一項全面的研究的結果，以便更好地了解傳統(tǒng)碎石樁和被土工合成材料包裹的碎石樁的荷載傳導機制。對采用部分被土工合成材料包裹的碎石

33、樁比完全包裹的碎石樁更合適的可能性進行調(diào)查，結果比較顯示，更加傾向于完全包裹的碎石樁和傳統(tǒng)的碎石樁。</p><p>　　NUMERICAL ANALYSES</p><p><b>　　數(shù)值分析</b></p><p>　　Finite element analyses were performed using the program ABA

34、QUS (Hibbitt et al.</p><p>　　2007). As the zone of interest has two planes of symmetry, it was only necessary to</p><p>　　numerically model the behavior of the system over a quarter of the domai

35、n. Fig. 1 shows a typical finite-element mesh used in the analyses. In all of the numerical analyses that were performed, the thickness of the soft soil and the length of the stone column were assumed to be 5 m, which is

36、 a reasonable length of installation for GESC systems (FHWA, 2006). It was also assumed that the soil and column were underlain by a rigid layer. The lateral extent of the soft soil around the stone column</p><

37、;p>　　was selected such that the effects of the vertical boundary conditions on the</p><p>　　calculated results were minimal. As shown in Fig. 1, when the radius of the stone column is 0.4 m the overall ra

38、dius of the cylinder is selected to be 2.0 m. At the bottom boundary of the finite-element mesh, the displacements are set to zero in the z direction. The displacements in the x and y directions are set to zero on the ci

39、rcumferential boundary of the soft soil zone.On the planes of symmetry, normal</p><p>　　displacement is restricted. </p><p>　　有限元分析采用ABAQUS軟件的程序（Hibbitt等人。2007年）。一個目的區(qū)域含有兩個對稱面，它只需要研究在在這個區(qū)域四分之一范圍

40、內(nèi)的系統(tǒng)反應的數(shù)學模型。圖一顯示了在分析時使用的一個典型的有限元網(wǎng)格。在所有的數(shù)值 他們演奏了分析，軟土層的厚度和碎石樁的長度被假定為5米，這是土工材料包裹碎石樁系統(tǒng)的一個合理的安裝長度土工材料包裹碎石樁系統(tǒng)（美國聯(lián)邦公路管理局，2006年）。另外還假設了土壤和樁都埋在剛性墊層以下。在選擇碎石樁周圍的軟土地基的側向延伸范圍，這樣在垂直邊界條件的影響的計算結果可以降到最低。如圖一所示，當碎石樁的半徑為0.4米時，圓柱整體半徑為2.0米。在

41、有限元網(wǎng)格的底部邊界上，在z軸方向位移設為零。在軟土區(qū)圓周邊界的x軸和y軸方向上設置為零。在對稱面上，一般情況下位移將受到一定限制。</p><p>　　The finite-element mesh used in the numerical simulations was developed using 6-node linear triangular prism elements for both the

42、stone column and soft soil. The</p><p>　　stone column is modeled using a linear elastic-perfectly plastic model with Mohr–</p><p>　　Coulomb failure criterion. The Mohr–Coulomb model is defined b

43、y five parameters:friction angle (φ)?, effective cohesion (c'), dilatancy angle (ψ), effective Young’s modulus (E), and Poisson’s ratio (ν). The parameters used in the numerical analyses are summarized in Table 1. Th

44、e Mohr-Coulomb parameters used in the numerical analyses are similar to the typical values used by other researchers (e.g. Guetif et al. 2007, Ambily and Gandhi 2007). </p><p>　　在數(shù)學模擬中采用的有限元網(wǎng)格法發(fā)展為同時可在碎石樁和軟土地

45、基中使用的6節(jié)點線性三棱柱構件。這種碎石樁使用來源于莫爾-庫侖破壞準則的線性理想彈塑性模型。莫爾-庫侖模型是指由5個參數(shù)：摩擦角（φ），有效內(nèi)聚力（c'），剪脹角（ψ），有效的楊氏彈性模量（E）和泊松比（ν）。在數(shù)值分析中使用的參數(shù)總結于表1。莫爾-庫侖參數(shù)用于數(shù)值分析類似于其他國家的研究人員使用的典型值。（例如Guetif等人2007年，Ambily和Gandhi 2007年）</p><p>　　FI

46、G. 1. Typical finite-element mesh used in the analyses</p><p>　　圖一：在分析中使用的典型有限元網(wǎng)格</p><p>　　The soft soil was modeled as a modified Cam Clay material. Five material parameters were used in the mo

47、del, namely the slope of the swelling line (κ), the slope of the virgin consolidation line (λ), the void ratio at unit pressure (e), slope of the critical state line (M), and Poisson’s ratio (ν). The modified Cam Clay pa

48、rameters used correspond to those obtained for experimental data on soft Bangkok clay (Balasubramian and Chaudhry 1978). These parameters are provided in Table 1.</p><p>　　典型的有限元網(wǎng)格中，軟土被建模為一個可滑動粘土改性材料。在這個模型使用

49、五個材料參數(shù)，即斜線斜率（κ），原始坡度鞏固線的斜率（λ），在單位壓力下孔隙比（e），臨界狀態(tài)線的坡度（M）和泊松比（ν）。修改后的可滑移粘土參數(shù)相當于采用曼谷軟粘土進行實驗獲得的數(shù)據(jù)（Balasubramian 和 Chaudhry 1978年）。這些參數(shù)在表1中列出。</p><p>　　The geosynthetic was modeled using 4-node quadrilateral, redu

50、ced integration membrane elements. The geosynthetic was assumed to be an orthotropic linear elastic material, with an assumed Poisson’s ratio of 0.3. A comprehensive study of numerical results showed that using an isotro

51、pic linear elastic material for encasement can increase the bearing capacity of column up to 10% and adversely affect the shape of lateral bulging (Khabbazian et al. 2008). In order not to adversely influence the numeri&

52、lt;/p><p>　　土工合成材料是用模擬的4節(jié)點四邊形，減少整合的薄膜構件。該土工合成材料被假定為是一個正交的線彈性材料，假設泊松比為0.3。一個綜合性研究的數(shù)據(jù)結果表明，采用各向同性的線彈性材料可以去包裹碎石樁可以提高柱的承載能力高達10％，嚴重影響側向膨脹的形狀（Khabbazian等。2008）。為了不對數(shù)據(jù)結果產(chǎn)生大的影響，而且已經(jīng)知道包裹的材料不能承受豎向（壓力）荷載，包裹材料的縱向彈性模量減少到徑向彈

53、性模量的1%。值得一提的是進一步減小縱向彈性模量，對數(shù)值結果的基本沒有什么影響。</p><p>　　Alexiew (2005) documented that design values of tensile modulus (J) between</p><p>　　2000-4000 kN/m were required for the geosynthetic used to e

54、ncase stone columns on</p><p>　　a number of different projects. Consequently, a circumferential elastic modulus of 3000 kN/m was used in the numerical analyses. The circumferential elastic modulus (E) of the

55、 geosynthetic was derived from the relationship J = Et, where t is the thickness of geosynthetic, which was assumed to be 5 mm for all of the numerical analyses performed.</p><p>　　Alexiew（2005）寫到，在不同的項目中，當拉

56、伸模量設計值(J)在2000-4000千牛頓/米之間時，需要用土工合成材料來包裹碎石樁。因此，在數(shù)值分析的時候常采用一個切向的彈性模量值3000千牛頓/米。這個土工合成材料的切向彈性模量(E)由公式J=Et得到，其中t是土工合成材料的厚度，這是假設所有的數(shù)值為5mm情況下分析完成的。</p><p>　　Interface elements, characterized by two sets of parame

57、ters, were used to model</p><p>　　interaction behavior between the geosynthetic and the stone column, and between the</p><p>　　geosynthetic and the surrounding soft soil. A Mohr-Coulomb failure

58、criterion with zero cohesion was used for the interface elements. The coefficient of sliding friction (μ) between the geosynthetic and the stone column was selected to be 0.5 (μ=2/3tanφ) (FHWA, 2006), where φ is the fric

59、tion angle of the column material. For interaction between the geosynthetic and the soft soil, μ was assumed to be 0.3 (μ=0.7tanφ) (Abu-Farsakhl, et al. 2007), where φ is the friction angle of the soft soil. </p>

60、<p>　　界面元素構件含有兩個參數(shù)，其特點是采用土工合成材料和碎石樁之間，以及土工合成材料和周圍的軟土地基之間的相互作用的模型。界面元素采用無內(nèi)聚力的Mohr-Coulomb破壞準則。土工合成材料和碎石樁之間的滑動摩擦系數(shù)（μ）取為0.5（μ=2/3tanφ）（美國聯(lián)邦公路管理局，2006年），其中φ是碎石樁材料摩擦角。對于土工合成材料和軟土地基之間的摩擦作用，μ被假定為0.3（μ=0.7tanφ） （Abu-Farsakh

61、l等人，2007年），其中φ是軟土地基的摩擦角。</p><p>　　In order to compare the performance of the GESC with a conventional stone</p><p>　　column (CSC), parallel analyses were also performed on a stone column without

62、</p><p>　　encasement. In this case, like interaction between the geosynthetic and soft soil, the coefficient of sliding friction between the stone column and the soft soil was selected to be 0.3. 為了比較被土

63、工合成材料包裹的碎石樁（GESC）與傳統(tǒng)碎石樁（CSC）的性能差異，常在裸露碎石樁上采用平行比較分析。在這種情況下，如土工合成材料和軟土地基之間的相互作用，碎石樁和軟土地基之間的滑動摩擦系數(shù)取0.3。</p><p>　　Table 1. Material Parameters </p><p><b>　　表一：材料參數(shù)</b></p><p&g

64、t;　　NUMERICAL RESULTS</p><p><b>　　數(shù)值結果</b></p><p>　　In order to determine the stress-displacement behavior on top of the geosynthetic</p><p>　　encased stone column, soil

65、 nodal points corresponding to the top of the column were</p><p>　　subjected to a series of vertical downward displacements. During these downward displacements, the average resultant stress on top of the co

66、lumn was recorded , allowing the stress-displacement curve to be drawn accordingly. </p><p>　　為了確定在被土工合成材料包裹的碎石樁頂部的應力與位移之間的關系，土壤結點與碎石樁頂部受到的豎向沉降相一致。在豎向沉降期間，記錄碎石樁頂部平均合應力，可以相應的畫出應力-位移曲線。</p><p>　　F

67、ig. 2 shows the stress-displacement response for both a GESC and CSC having</p><p>　　the parameters listed in Table 1. From Fig. 2, it can be seen that after a very small vertical settlement the mobilized ve

68、rtical stress on top of the encased column is always greater than the CSC and the difference increases with additional settlement. </p><p>　　For example, at a settlement of 25 mm (a common serviceability cri

69、teria), the mobilized vertical stress on top of the GESC is 3.8 times greater than that of CSC. This ratio becomes 5.4 for a settlement of 50 mm. </p><p>　　圖2分別顯示了GESC和CSC應力-位移反應，相應的參數(shù)在表1中列出。從圖2中，可以看到在一個非常小豎

70、向沉降之后，被合成材料包裹的碎石樁頂部的豎向應力始終大于傳統(tǒng)碎石樁，同時增加附加沉降量。例如，當沉降量為25mm（一種常用的適用性標準值）時，被土工合成材料包裹的碎石樁頂部的可變豎向應力比傳統(tǒng)碎石樁大了3.8倍。當沉降量為50mm時這個比例變?yōu)?.4。</p><p>　　The lateral bulging of the GESC and CSC at a settlement of 50 mm is sho

71、wn in</p><p>　　Fig. 3. It is observed that in the CSC, lateral bulging occurs up to depth of 1.2 m(1.5D), after which lateral bulging becomes negligible. For the GESC, the maximum value of lateral displaceme

72、nt is much less than that for the CSC. However, after a depth of 1D, the GESC experiences more lateral displacement than the CSC. This is attributed to mobilization of more load on top of the GESC (Fig. 2), and the subse

73、quent transmission of greater loads to higher depths in the case of the GESC. </p><p>　　This phenomenon is studied further and discussed in more detail in the following</p><p>　　sections. </p

74、><p>　　圖3顯示了沉降量為50mm時，被土工合成材料包裹的碎石樁和傳統(tǒng)碎石樁的橫向膨脹量?？梢钥闯?，在傳統(tǒng)碎石樁中，橫向膨脹的最大值發(fā)生在1.2米的深度 （1.5天），隨著深度降低橫向膨脹量減少。對于被土工合成材料包裹的碎石樁來說，最大側向位移值遠小于的傳統(tǒng)碎石樁。然而，在達到一定的深度以后，GESC發(fā)生的側向位移比CSC更大。這是由于在GESC中，能更多轉移頂部荷載（圖2），隨后傳遞到更深的地基土壤中。接下去

75、，這種現(xiàn)象還將做更深層次的、更詳細的研究和討論。</p><p>　　FIG. 2. Displacement vs. stress FIG. 3. Lateral bulging vs. </p><p>　　應力-位移曲線 depth at a vertical settlement of 50 mm</p>&

76、lt;p>　　豎向沉降量為50mm下的側向位移</p><p>　　Having found that the use of encasement can noticeably enhance the load-carrying capacity of CSCs (Fig. 2), it is instructive to more comprehensively study the loadtransfe

77、r mechanism of both CSCs and GESCs. Figs. 4a and 4b show contours of vertical displacement for both the CSC and GESC, respectively. In the CSC (Fig. 4a), vertical displacements are negligible (less than 5 mm) after a dep

78、th of 1D. This is caused by the lateral bulging failure mechanism of the CSC, which occurs in the top portion</p><p>　　經(jīng)發(fā)現(xiàn)，對傳統(tǒng)碎石樁進行包裹合成材料可以顯著的提高其承載能力（圖2），有利于更加全面的研究CSC和GESC的荷載傳遞機制。圖4a和4b分別顯示了CSC和GESC豎向沉降的等高線

79、。在CSC（圖4a）中，一定深度以后其豎向位移可以忽略不計（小于5毫米）。這是由于部分柱頂發(fā)生橫向膨脹破壞所造成的。實際上，在CSC中觀察發(fā)現(xiàn)豎向位移主要是因為在荷載作用下柱的橫向材料膨脹而不是因承受壓力產(chǎn)生的豎向沉降。然而，在GESC（圖4B）中，豎向位移沿著整個柱子分布。舉一個例子說明，豎向位移等于5毫米時，可以看到其發(fā)生的在5D的深度。當橫向膨脹受到約束時，GESC的性能表現(xiàn)（圖3）可以看成沿GESC垂直分布，由此改善碎石樁的性能

80、。</p><p>　　The distribution of vertical displacements along the length of the column (Fig. 4) can affect the relative vertical displacements between the soft soil and the column material in the case of CSCs

81、and between the soft soil and the geosynthetic in the case of GESCs. For the CSC at a vertical settlement of 25 mm, it can be seen (Fig. 5) that the value of relative displacement between On the other hand, for GESCs, th

82、e value of relative displacement between the soft soil and the geosynthetic not only</p><p>　　沿柱子縱向分布的垂直位移會影響CSC中軟土地基和柱子材料的相對垂直位移，以及GESC中的相對垂直位移（圖4）。對于CSC中在豎向沉降為25毫米時，可以看出（圖5），軟土地基和柱子材料的相對沉降量在2m深度以下將變得微不足道了。

83、另一方面，在GESCs中，軟土地基與土工合成材料之間的相對沉降量不僅沿著整個柱子長度增大而增大，而且在研究中發(fā)現(xiàn)其值遠大于CSC中的相對沉降量。觀察發(fā)現(xiàn)，無論是CSC還是GESC在相應的深度下的側向應力幾乎相同（圖6）。因為相對位移不同，它會嚴重影響表面摩擦力沿著柱子的分布形態(tài)，總的表面摩擦力大小也將沿著柱子產(chǎn)生變化（圖7）。</p><p>　　FIG. 4. Contours of vertical disp

84、lacements (a) CSC (b) GESC</p><p>　　圖4：豎向位移的等高線 （a）CSC（b）GESC</p><p>　　The end-bearing capacity of columns is another component that should be considered when the overall load-transfer behavior

85、of these systems is studied. To investigate the effects of column encasement on the end-bearing behavior, loadtransfer curves of a CSC and GESC at a vertical settlement of 25 mm are shown in Fig. 8. From Fig. 8, it can b

86、e seen that both the CSC and GESC are primarily endbearing columns, as 72% and 66% of the loads applied at the ground surface are transferred to the tip of t</p><p>　　在研究整個系統(tǒng)的荷載傳遞時，柱的端部承載力是必須考慮的一個方面?？捎蓤D8中畫出的

87、CSC和GESC在沉降量為25mm時曲線，看出對柱子包裹合成材料之后對端部承載力的影響和何在傳遞機制。從圖8中可以看出，無論是CSC和GESC的主要柱端承載力，分別為地表所受荷載的72%和66%傳遞到柱的頂部。如圖8所示，在給定的沉降量的情況下，GESC柱端傳遞荷載的大小要遠大于CSC中所傳遞的荷載，因為GESC中給柱子包裹土工合成材料使其強度和剛度變得更大。數(shù)值計算結果顯示，約65％的負荷增加， 包裹合成材料的碎石樁的增加的承載能力有

88、65%來源于其柱端承載力，另外的35%與表面摩擦力的增加。</p><p>　　FIG. 5. Relative vertical displacement FIG. 6. Lateral stresses vs. depth at a between soft soil and column vertical settlement of 25 mm</p>&l

89、t;p>　　圖5：軟土地基和柱之間的相對位 圖6：25毫米沉降量下側向應力與深度的關系</p><p>　　FIG. 7. Skin friction vs. depth at vertical FIG. 8. Load transfer curves for CSC and</p><p>　　settlement of 25 mm

90、 GESC at vertical settlement of 25 mm</p><p>　　圖7：25mm沉降量時表面摩擦力 圖8：25mm沉降量時CSC和GESC荷載 與深度的關系 傳遞曲線</p><p>　　INFLUENCE OF LENGTH OF ENCASEMENT</p><

91、p>　　碎石樁的合成材料包裹長度的影響分析</p><p>　　Fig. 3 and Fig. 4a clearly show that the failure mechanism of a typical CSC is lateral bulging, and that this type of failure occurs in the top portion of the column. As sho

92、wn in Fig. 3, below a depth of 1.5D, the lateral displacements are relatively negligible. Consequently, it may be possible to encase only the top portion of a stone</p><p>　　column to improve its performance

93、. This phenomenon has been previously explored by Murugesan and Rajagopal (2006, 2007), who performed both numerical and experimental analyses and found that the optimum length of encasement for stone columns is 2D from

94、numerical analyses and 4D from model tests. Previous attempts at encasement or strengthening the upper portion of stone columns using alternative approaches have also been tried: Aboshi et al. (1979) applied a steel skir

95、t to reinforce the top port</p><p>　　圖3和圖4a清楚地表明，一個典型的CSC的破壞機理是橫向脹破，而且這種類型的破壞發(fā)生在柱子頂部。如圖3所示，在1.5D深度以下，其側向位移相對較小。因此，它可能只在碎石樁的頂部進行土工材料的包裹，以提高其性能。這種現(xiàn)象已被Murugesan和Rajagopal（2006，2007）研究探明，他們同時進行理論分析和實驗分析，發(fā)現(xiàn)碎石樁包裹土

96、工合成材料的最佳長度分別為2D和4D。在早前的探索中，運用變換方法對碎石樁頂部進行包裹合成材料或者加固也曾被多次嘗試，Aboshi等人(1979)提出了用鋼制裙板約束碎石樁頂部。類似的，Sharma等人(2004)提出采用水平合成層板去約束碎石樁頂部。對于改善其性能，Juran 和 Riccobono (1991)已經(jīng)建議在碎石樁頂部采用混凝土中添加混合材料添加劑。</p><p>　　To investigat

97、e the influence of partial encasement on the load carrying capacity</p><p>　　and lateral bulging of stone columns, numerical analyses were carried out on columns</p><p>　　having varying length o

98、f encasement from 0.8 m (1D) to 4.0 m (5D). Fig. 9 shows the stress-displacement responses of a CSC and a series of partially encased columns. By comparing the load carrying capacity of the CSC with the partially encased

99、 columns, it can be seen that encasing the stone column even up to a depth of one diameter can significantly increase the bearing capacity of the column. Fig. 9 shows that the response of partially encased columns is rel

100、ated to the vertical settlements. For</p><p>　　為了調(diào)查部分包裹土工合成材料對碎石樁承載能力和側向膨脹的影響，在0.8m（1D）到4.0米（5D）之間不同長度的碎石樁進行數(shù)值分析。圖9顯示了CSC和部分包裹合成材料的碎石樁上的應力-位移反應。通過比較部分包裹合成材料的碎石樁和CSC的承載能力， 可以看出，被土工合成材料包裹的碎石樁即使到了一定的直徑也能顯著增加碎石樁