【正文】 y. In the CSC (Fig. 4a), vertical displacements are negligible (less than 5 mm) after a depth of 1D. This is caused by the lateral bulging failure mechanism of the CSC, which occurs in the top portion of the column. In fact, the vertical displacements that are observed in CSCs appear to be mostly due to lateral bulging of the column material rather than vertical settlements due to pression of the column material under load. However, in the GESC (Fig. 4b), vertical displacements are distributed all along the column. As an example, vertical displacements equal to 5 mm were observed to occur up to a depth of 5D. The constrained lateral bulging behavior of the GESC (Fig. 3) is the explanation for the distribution of vertical displacements along the GESC, and the resulting improved behavior of the column. 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 。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 。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 。 附件 C：譯文 C7 Table 1. Material Parameters 表一：材料參數(shù) 項目 模型 φ(deg) C (kPa) Ψ(deg.) E (Mpa) ν κ λ M e 碎石樁 莫爾 庫倫 40 1 0 60 松軟地基 改良的滑移粘土 土工合成材料 線彈性 600 NUMERICAL RESULTS 數(shù)值結果 In order to determine the stressdisplacement behavior on top of the geosynthetic encased stone column, soil nodal points corresponding to the top of the column were subjected to a series of vertical downward displacements. During these downward displacements, the average resultant stress on top of the column was recorded , allowing the stressdisplacement curve to be drawn accordingly. 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。 土工合成材料和 碎石樁之間的 滑動摩擦系數(shù)（ μ ）取為 （ μ=2/3tanφ ） （ 美國 聯(lián)邦公路管理局， 2020年），其中 φ 是 碎石樁 材料摩擦角。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。 2020）。這些參數(shù)在表 1中列出 。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。 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。 在有限元網(wǎng)格的底部邊界 上 ，在 z軸 方向位移 設 為零。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， 2020年）。 NUMERICAL ANALYSES 數(shù)值分析 Finite element analyses were performed using the program ABAQUS (Hibbitt et al. 2020). As the zone of interest has two planes of symmetry, it was only necessary to numerically model the behavior of the system over a quarter of the domain. Fig. 1 shows a typical finiteelement 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 a reasonable length of installation for GESC systems (FHWA, 2020). 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 was selected such that the effects of the vertical boundary conditions on the calculated results were minimal. As shown in Fig. 1, when the radius of the stone column is m the overall radius of the cylinder is selected to be m. At the bottom boundary of the finiteelement 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 circumferential boundary of the soft soil the planes of symmetry, normal displacement is restricted. 有限元分析采用 ABAQUS軟件的程序（ Hibbitt等 人 。 2020年） 。 在數(shù)值分析的時候， Murugesan 和Rajagopal(2020)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)學模型中 使用界面 單元的 這一現(xiàn)象） 。在這種情況下， 給碎石樁包裹一層適當?shù)耐凉ず铣刹牧?，可?提供必要的 側向 圍壓，提高 碎石樁的 承載能力 。 Stone columns under pressive loads experience failure modes such as bulging (Hughes et al. 1975), general shear failure (Madhav and Vitkar 1978), and sliding(Aboshi et al. 1979). However, in soft clays the most mon failure mode for stone columns is bulging (Madhav and Miura 1994). 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。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。電子郵箱： ABSTRACT 摘要 Encasing a stone column with a highstrength geosynthetic provides the column material with significant lateral confinement, which prevents lateral displacement of the column into potentially soft surrounding soil and consequently increases the bearing capacity of the column. Although this technique has been successfully applied in practice, the load transfer mechanism of encased stone columns and their performance in parison with conventional stone columns have not been studied in detail. This paper describes threedimensional finite element analyses that were carried out to simulate the behavior of a single stone column with and without encasement in a very soft clay soil using the puter program ABAQUS. A 指導教師評定成績 (五級制 )： 指導教師 簽字： 附件 C：譯文 C2 prehensive 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 columns was then pared to that of fully encased columns and conventional stone columns. 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。電子郵箱： Christopher L. Meehan, A. M. ASCE Assistant Professor, Dept. of Civil and Environmental Engineering, 301 DuPont Hall, University of Delaware, Newark, DE 19716. Email: 紐瓦克， 19716， 美國特拉華州，大學部， 301杜邦廳，土木及環(huán)境工程 系， Victor N. Kaliakin, M. ASCE Associate Professor, Dept. of Civil and Environmental Engineering, 301 DuPont Hall, University of Delaware, Newark, DE 19716. Email: 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。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。 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 。 In very soft soils, due to the lack of required lateral confin