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Numerical Study of Effect of Encasement on Stone Column Performance
护壁效应对“碎石桩性能”的数值分析

Majid Khabbazian, Stud. M. ASCE
Graduate Student and GSI Fellow, Dept. of Civil and Environmental Engineering, 301 DuPont Hall,
University of Delaware, Newark, DE 19716. E-mail: [e-mail]
纽瓦克，DE的19716，特拉华大学，301杜邦厅部，土木与环境工程系，研究生和GSI研究员Majid Khabbazian, Stud. M. ASCE。电子邮箱：[e-mail]
Christopher L. Meehan, A. M. ASCE
Assistant Professor, Dept. of Civil and Environmental Engineering, 301 DuPont Hall, University of
Delaware, Newark, DE 19716. E-mail: [e-mail]
纽瓦克，DE.的19716，美国特拉华州，大学部，301杜邦厅，土木及环境工程系，[e-mail]
Victor N. Kaliakin, M. ASCE
Associate Professor, Dept. of Civil and Environmental Engineering, 301 DuPont Hall, University of
Delaware, Newark, DE 19716. E-mail: [e-mail]
纽瓦克，DE的19716，美国特拉华州，大学部，301杜邦厅，土木及环境工程系，副教授。电子邮箱：[e-mail]

ABSTRACT
摘要
Encasing a stone column with a high-strength 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 comparison with conventional stone columns have not been studied in
detail. This paper describes three-dimensional 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 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 columns was then compared to that of fully encased columns and conventional stone columns.
用高强度土工合成材料包裹碎石柱，土工合成材料为碎石柱材料提供显著的横向约束，这样可以防止柱向着周围的软土地基发生侧向位移，从而增加柱子的承载能力。虽然这一技术已成功应用于实践中，受护壁作用的碎石桩的荷载传导机制和性能与传统的碎石桩相比，并没有被详细研究透。本文介绍在一个非常松软的粘土地基上使用ABAQUS软件的计算机程序模拟单个碎石桩，采用三位有限元分析法分析其有无包装效应。为了更深层次的了解传统的碎石桩和被土工合成材料包裹的碎石桩中的荷载传导机制，我们展开了更加全面的研究。在研究中，用部分被土工合成材料包裹的碎石桩分别与完全被包裹的碎石桩和传统的碎石桩进行比较。

INTRODUCTION
说明
Stone columns have been increasingly used for ground improvement, especially for
structures that can tolerate some settlement such as road embankments, storage tanks,
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 attributed 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.
碎石桩已经被越来越多的用于地基的改善工程，特别是能承受一些沉降的结构，例如，公路路堤、存储仓库、低层建筑以及受到较轻荷载的基础等。这种地基的改良形式也通常被称为碎石桩。碎石柱的广泛使用，是因为它成功地证明了自身在提高承载能力，降低整体沉降和不均匀沉降，增加沉降的时间速率，减少砂土地基液化可能性方面的能力。
Stone columns under compressive 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 common failure mode for stone columns is bulging (Madhav and Miura 1994).
碎石桩在压力作用下，会产生一些破坏模式，如膨胀破坏模式 （Hughes等人。1975年），一般的剪切破坏（Madhav和Vitkar 1978年），滑移破坏（Aboshi 等人 1979）。然而，在软土地基中，碎石桩最常见的破坏模式是膨胀破坏（Madhav和Miura1994年）。
In very soft soils, due to the lack of required lateral confining pressure, the use of
stone columns can be problematic. In these situations, to provide the required lateral confining 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 prevents 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-carrying capacity of a single stone column in soft clay. Murugesan and Rajagopal (2006, 2007) performed model tests and numerical analyses to study the behavior of a single geosynthetic-encased stone column with a limited zone of soil influence (a tributary approach to column group behavior). In the numerical analyses, Murugesan and
Rajagopal (2006) performed axisymmetric analyses and assumed continuum elements
for the geosynthetic without considering the behavior of the interface between
different materials (this paper addresses this phenomenon by using interface elements
in the numerical model). Lee et al. Lee et al. (2007) investigated the failure mechanism and load carrying capacity of individual geogrid 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 geotextile that is used for column confinement.
在非常松软的软土地基上，由于所需的侧向围压不足，碎石桩的使用可能会出现问题。在这种情况下，给碎石桩包裹一层适当的土工合成材料，可以提供必要的侧向围压，提高碎石桩的承载能力。使用一种高强度土工合成材料，不但可以增加了碎石桩的强度，而且还可以防止碎石桩向着周围松软地基发生侧向位移。Sharma等人（2004）进行测试，以探讨软土地基上的单一碎石桩的膨胀和承重能力对土工格栅的加固效果。 Murugesan和Rajagopal（2006年，2007年） 进行模型试验和数值分析，以研究在一个限定区域内的单个被土工合成材料包裹的碎石桩的性能影响（研究群桩效应的其他途径）。在数值分析的时候，Murugesan 和Rajagopal(2006)进行轴对称分析并假定构件与包裹的土工合成材料的连续性，而不考虑不同材料的交界面的影响（本文解决了在数学模型中使用界面单元的这一现象）。 Lee等人采用模型试验的方法调查研究被土工材料包裹的碎石桩破坏机制和单个土工格栅的负荷能力。Alexiew等人(2005)描述了用土木布包裹碎石桩的设计原则、技术方法和程序步骤，并强调了用于约束碎石桩的土工布的拉伸模量的重要性。
This paper describes 3D finite element analyses that were carried out to simulate
the behavior of a single geosynthetic-encased stone column (GESC) in soft clay using
the computer program ABAQUS (Hibbitt et al. 2007). To compare the performance 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 understand 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 fully encased columns and CSCs.
本文介绍了使用 ABAQUS软件的计算机程序采用三维有限元分析法进行模拟在软土地基上的单一土工合成材料包裹的碎石桩（GESC）的性能（Hibbitt等人。2007年）。采用比较分析法比较传统碎石桩（CSC）与被土工合成材料包裹的碎石桩（GESC）的性能，这种方法也被用于分析裸露碎石桩基的分析。本文介绍一项全面的研究的结果，以便更好地了解传统碎石桩和被土工合成材料包裹的碎石桩的荷载传导机制。对采用部分被土工合成材料包裹的碎石桩比完全包裹的碎石桩更合适的可能性进行调查，结果比较显示，更加倾向于完全包裹的碎石桩和传统的碎石桩。

NUMERICAL ANALYSES
数值分析
Finite element analyses were performed using the program ABAQUS (Hibbitt et al.
2007). 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 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 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
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 0.4 m the overall radius 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 circumferential boundary of the soft soil zone.On the planes of symmetry, normal
displacement is restricted.
有限元分析采用ABAQUS软件的程序（Hibbitt等人。2007年）。一个目的区域含有两个对称面，它只需要研究在在这个区域四分之一范围内的系统反应的数学模型。图一显示了在分析时使用的一个典型的有限元网格。在所有的数值 他们演奏了分析，软土层的厚度和碎石桩的长度被假定为5米，这是土工材料包裹碎石桩系统的一个合理的安装长度土工材料包裹碎石桩系统（美国联邦公路管理局，2006年）。另外还假设了土壤和桩都埋在刚性垫层以下。在选择碎石桩周围的软土地基的侧向延伸范围，这样在垂直边界条件的影响的计算结果可以降到最低。如图一所示，当碎石桩的半径为0.4米时，圆柱整体半径为2.0米。在有限元网格的底部边界上，在z轴方向位移设为零。在软土区圆周边界的x轴和y轴方向上设置为零。在对称面上，一般情况下位移将受到一定限制。
The finite-element mesh used in the numerical simulations was developed using 6-node linear triangular prism elements for both the stone column and soft soil. The
stone column is modeled using a linear elastic-perfectly plastic model with Mohr–
Coulomb failure criterion. The Mohr–Coulomb model is defined by 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. The 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).
在数学模拟中采用的有限元网格法发展为同时可在碎石桩和软土地基中使用的6节点线性三棱柱构件。这种碎石桩使用来源于莫尔-库仑破坏准则的线性理想弹塑性模型。莫尔-库仑模型是指由5个参数：摩擦角（φ），有效内聚力（c'），剪胀角（ψ），有效的杨氏弹性模量（E）和泊松比（ν）。在数值分析中使用的参数总结于表1。莫尔-库仑参数用于数值分析类似于其他国家的研究人员使用的典型值。（例如Guetif等人2007年，Ambily和Gandhi 2007年）

FIG. 1. Typical finite-element mesh used in the analyses
图一：在分析中使用的典型有限元网格
The soft soil was modeled as a modified Cam Clay material. Five material parameters were used in the model, 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 parameters used correspond to those obtained for experimental data on soft Bangkok clay (Balasubramian and Chaudhry 1978). These parameters are provided in Table 1.
典型的有限元网格中，软土被建模为一个可滑动粘土改性材料。在这个模型使用五个材料参数，即斜线斜率（κ），原始坡度巩固线的斜率（λ），在单位压力下孔隙比（e），临界状态线的坡度（M）和泊松比（ν）。修改后的可滑移粘土参数相当于采用曼谷软粘土进行实验获得的数据（Balasubramian 和 Chaudhry 1978年）。这些参数在表1中列出。
The geosynthetic was modeled using 4-node quadrilateral, reduced 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 isotropic 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 numerical results, and knowing that the encasement does not carry vertical (compressive) load, the longitudinal elastic modulus of the encasement was decreased to 1% of the circumferential elastic modulus. It should be mentioned that further decreases in the longitudinal elastic modulus had no effect on the numerical results.
土工合成材料是用模拟的4节点四边形，减少整合的薄膜构件。该土工合成材料被假定为是一个正交的线弹性材料，假设泊松比为0.3。一个综合性研究的数据结果表明，采用各向同性的线弹性材料可以去包裹碎石桩可以提高柱的承载能力高达10％，严重影响侧向膨胀的形状（Khabbazian等。2008）。为了不对数据结果产生大的影响，而且已经知道包裹的材料不能承受竖向（压力）荷载，包裹材料的纵向弹性模量减少到径向弹性模量的1%。值得一提的是进一步减小纵向弹性模量，对数值结果的基本没有什么影响。
Alexiew (2005) documented that design values of tensile modulus (J) between
2000-4000 kN/m were required for the geosynthetic used to encase stone columns on
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 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（2005）写到，在不同的项目中，当拉伸模量设计值(J)在2000-4000千牛顿/米之间时，需要用土工合成材料来包裹碎石桩。因此，在数值分析的时候常采用一个切向的弹性模量值3000千牛顿/米。这个土工合成材料的切向弹性模量(E)由公式J=Et得到，其中t是土工合成材料的厚度，这是假设所有的数值为5mm情况下分析完成的。
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 Mohr-Coulomb 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 0.5 (μ=2/3tanφ) (FHWA, 2006), where φ is the friction 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.
界面元素构件含有两个参数，其特点是采用土工合成材料和碎石桩之间，以及土工合成材料和周围的软土地基之间的相互作用的模型。界面元素采用无内聚力的Mohr-Coulomb破坏准则。土工合成材料和碎石桩之间的滑动摩擦系数（μ）取为0.5（μ=2/3tanφ）（美国联邦公路管理局，2006年），其中φ是碎石桩材料摩擦角。对于土工合成材料和软土地基之间的摩擦作用，μ被假定为0.3（μ=0.7tanφ） （Abu-Farsakhl等人，2007年），其中φ是软土地基的摩擦角。
In order to compare 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 0.3.
为了比较被土工合成材料包裹的碎石桩（GESC）与传统碎石桩（CSC）的性能差异，常在裸露碎石桩上采用平行比较分析。在这种情况下，如土工合成材料和软土地基之间的相互作用，碎石桩和软土地基之间的滑动摩擦系数取0.3。

Table 1. Material Parameters

表一：材料参数
项目
模型
φ(deg)
C
(kPa)
Ψ(deg.)
E
(Mpa)
ν
κ
λ
M
e
碎石桩
莫尔-库伦
40
1
0
60
0.3
0.3

松软地基
改良的滑移粘土

0.2
0.2
0.2
1.00
2.00
土工合成材料
线弹性

600
0.3
0.3
0.3

NUMERICAL RESULTS
数值结果
In order to determine the stress-displacement 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 stress-displacement curve to be drawn accordingly.
为了确定在被土工合成材料包裹的碎石桩顶部的应力与位移之间的关系，土壤结点与碎石桩顶部受到的竖向沉降相一致。在竖向沉降期间，记录碎石桩顶部平均合应力，可以相应的画出应力-位移曲线。
Fig. 2 shows the stress-displacement 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 common serviceability criteria), 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.
图2分别显示了GESC和CSC应力-位移反应，相应的参数在表1中列出。从图2中，可以看到在一个非常小竖向沉降之后，被合成材料包裹的碎石桩顶部的竖向应力始终大于传统碎石桩，同时增加附加沉降量。例如，当沉降量为25mm（一种常用的适用性标准值）时，被土工合成材料包裹的碎石桩顶部的可变竖向应力比传统碎石桩大了3.8倍。当沉降量为50mm时这个比例变为5.4。
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 1.2 m(1.5D), after which lateral bulging becomes negligible. For the GESC, the maximum value of lateral displacement 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 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.
图3显示了沉降量为50mm时，被土工合成材料包裹的碎石桩和传统碎石桩的横向膨胀量。可以看出，在传统碎石桩中，横向膨胀的最大值发生在1.2米的深度