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t projects. Consequently, a circumferential elastic modulus of 3000 kN/m was used in the numerical analyses. The circumferential elastic modulus (E) of the 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. Alexiew( 2020) 寫到 , 在 不同的項目 中, 當(dāng)拉伸模量設(shè)計值 (J)在 20204000千牛頓 /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(shè)所有的數(shù)值為 5mm情況下 分析完成的。 Interface elements, characterized by two sets of parameters, were used to model interaction behavior between the geosynthetic and the stone column, and between the geosynthetic and the surrounding soft soil. A MohrCoulomb failure 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 (μ=2/3tanφ) (FHWA, 2020), where φ is the friction angle of the column material. For interaction between the geosynthetic and the soft soil, μ was assumed to be (μ=) (AbuFarsakhl, et al. 2020), where φ is the friction angle of the soft soil. 界面元素 構(gòu)件含有 兩個參數(shù),其特點(diǎn)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 MohrCoulomb破壞準(zhǔn)則 。 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。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 ( μ= ) ( AbuFarsakhl等 人, 2020年),其中 φ 是軟土 地基的 摩擦角。 In order to pare the performance of the GESC with a conventional stone column (CSC), parallel analyses were also performed on a stone column without 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 . 為了比較 被土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 。 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(jié)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(yīng)力與位移之間的關(guān)系 ,土壤結(jié)點(diǎn) 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(yīng)力,可以相應(yīng)的畫出應(yīng)力 位移曲線。 Fig. 2 shows the stressdisplacement response for both a GESC and CSC having the parameters listed in Table 1. From Fig. 2, it can be seen that after a very small vertical settlement the mobilized vertical stress on top of the encased column is always greater than the CSC and the difference increases with additional settlement. For example, at a settlement of 25 mm (a mon serviceability criteria), the mobilized vertical stress on top of the GESC is times greater than that of CSC. This ratio bees for a settlement of 50 mm. 圖 2分別 顯示了 GESC和 CSC應(yīng)力 位移反應(yīng), 相應(yīng) 的參數(shù) 在 表 1中 列出 。 從圖 2中 ,可以看到 在 一個非常小 豎向沉降之 后 ,被合成材料 包裹 的碎石樁頂部的豎向應(yīng)力始終大于傳統(tǒng)碎石樁,同時增加 附加沉降 量 。例 如, 當(dāng) 沉降 量為 25mm(一種常 用的適用性標(biāo)準(zhǔn) 值 ) 時 , 被土工合成材料包裹的碎石樁頂部的可變豎向應(yīng)力比傳統(tǒng)碎石樁大了 。 當(dāng)沉降量為 50mm時這個比例變?yōu)?。 The lateral bulging of the GESC and CSC at a settlement of 50 mm is shown in Fig. 3. It is observed that in the CSC, lateral bulging occurs up to depth of m(), after which lateral bulging bees negligible. For the GESC, the maximum value of lateral displacement is much less than that for the CSC. However, after a depth of 1D, 附件 C:譯文 C8 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 subsequent transmission of greater loads to higher depths in the case of the GESC. This phenomenon is studied further and discussed in more detail in the following sections. 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 。 可以看出 , 在 傳統(tǒng)碎石樁中 ,橫向膨脹的 最大值 發(fā)生 在 ( 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(cè) 向位移值遠(yuǎn)小于的 傳統(tǒng)碎石樁 。然而, 在達(dá)到一定的深度以后 , GESC發(fā)生的側(cè)向位移比 CSC更大。 這是由于 在 GESC中,能更多轉(zhuǎn)移頂部荷載 (圖 2) ,隨后傳遞到更深的地基土壤中。 接下去,這種現(xiàn)象還將做更深層次的、更詳細(xì)的研究和討論。 FIG. 2. Displacement vs. stress FIG. 3. Lateral bulging vs. 應(yīng)力 位移曲線 depth at a vertical settlement of 50 mm 豎向沉降量為 50mm下的側(cè)向位移 Having found that the use of encasement can noticeably enhance the loadcarrying capacity of CSCs (Fig. 2), it is instructive to more prehensively study the loadtransfer 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 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(jìn)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(jī)制 。 圖 4a和