A homogenization method for estimating the bearing capacity of soils reinforced by columns

The ultimate bearing capacity problem of a strip foundation resting on a soil reinforced by a group of regularly spaced columns is investigated in the situation when both the native soil and reinforcing material are purely cohesive. Making use of the yield design homogenization approach, it is shown that such a problem may be dealt with as a plane strain yield design problem, provided that the reinforced soil macroscopic strength condition has been previously determined. Lower and upper bound estimates for such a macroscopic criterion are obtained, thus giving evidence of the reinforced soil strong anisotropy. Performing the upper bound kinematic approach on the homogenized bearing capacity problem, by using the classical Prandtl's failure mechanism, makes it then possible to derive analytical upper bound estimates for the reinforced foundation bearing capacity, as a function of the reinforced soil parameters (volume fraction and cohesion ratio), as well as of the relative extension of the reinforced area. It is shown in particular that such an estimate is closer to the exact value of the ultimate bearing capacity, than that derived from a direct analysis which implicitly assumes that the reinforced soil is an isotropic material. Copyright © 2005 John Wiley & Sons, Ltd.     

Experimental Investigation on the Bearing Capacity of Stone Columns with Granular Blankets

Using stone columns is an efficient method to increase the bearing capacity of soft soils. This has led to an increased interest in further developing and improving the method. In addition, granular blankets are used to increase the bearing capacity of the stone columns. In this research, the bearing capacity of stone columns, granular blankets, and a combination of both methods in reinforced and unreinforced modes was examined using large-scale laboratory tests. A scale factor of 1–10 is used for the geometry of the models, and the stone columns are a floating type that are 60 mm in diameter and 350 mm in length. These columns are either reinforced with vertical encasement of a geotextile or they are unreinforced. The granular blankets are either reinforced by using a biaxial geogrid or they are unreinforced with 40 and 75 mm thicknesses. In general, 16 large experimental tests have been carried out. Results indicate that using all these variations (granular blankets, stone columns, and a combination of both) improves bearing capacity. Using geogrid as the reinforcement of granular blankets and geotextile as stone-column encasement increases the efficiency of granular blankets and stone columns significantly. The maximum bearing capacity was obtained when reinforced granular blankets and reinforced stone columns were combined. The stress-concentration ratio and bearing capacity increased as geotextile encasement was used in the stone columns.     

A plane strain yield design approach to stability analysis of a column‐reinforced soil foundation under inclined loading

The ultimate bearing capacity problem of column‐reinforced foundations under inclined loading is investigated within the framework of static and kinematic approaches of yield design theory. The configuration of a native soft clayey soil reinforced by either a group of purely cohesive columns (lime‐column technique) or a group of purely frictional columns (stone‐column technique) is analyzed under plane strain conditions. First, lower bound estimates are derived for the ultimate bearing capacity by considering statically admissible piecewise linear stress distributions that comply with the local strength conditions of the constitutive materials. The problem is then handled by means of the yield design kinematic approach of limit analysis through the implementation of several failure mechanisms, allowing the formulation of upper bound estimates for the ultimate bearing capacity. A series of finite element limit load solutions obtained from numerical elastoplastic simulations suggests that the predictions derived from the kinematic approach appear to be more accurate than the estimates obtained from the static approach. Comparison with available results obtained in the context of yield design homogenization demonstrates the accuracy of the proposed direct analysis, which may therefore be viewed as complementary approach to homogenization‐based approaches when a small number of columns is involved. Copyright © 2016 John Wiley & Sons, Ltd.     

土工格栅加筋土地基平板载荷试验研究

在近年来的岩土工程实践中,土工合成材料加筋土技术得到越来越广泛的应用。采用平板载荷板试验方法,进行了多组加筋砂土地基模型试验,监测和分析了不同加筋材料（双向格栅与四向格栅）和加筋层数对土工格栅加筋土地基承载特性的影响。研究结果表明：土工格栅加筋土地基与无筋地基相比,承载性能得到改善,双层加筋明显优于单层加筋;土工格栅加筋限制了浅层地基的侧向变形,相同荷载下地基沉降减小,可恢复变形增大;模型试验中测得加筋材料应变和拉力很小,与土工格栅强度相比,拉伸模量对加筋土地基承载力的贡献更大。     

Bearing capacity tests of strip footings on reinforced layered soil

The ultimate bearing capacity of strip footings resting on subsoil consisting of a strong sand layer (reinforced/unreinforced) overlying a low bearing capacity sand deposit has been investigated. Three principal problems were analysed based on results obtained from the model tests as follows: (1) the effect of stratified subsoil on the foundations bearing capacity; (2) the effect of reinforcing the top layer with horizontal layers of geogrid reinforcement on the bearing capacity; (3) effect of reinforcing stratified subsoil (reinforced and unreinforced) on the settlement of the foundation. It has been observed that reinforcing the subsoil after replacing the top layer of soil with a well-graded soil is beneficial as the mobilization of soil-reinforcement frictional resistance will increase.     

Experimental Study of Bearing Capacity of Granular Soils,Reinforced with Innovative Grid-Anchor System

The pull-out resistance of reinforcing elements is one of the most significant factors in increasing the bearing capacity of geosynthetic reinforced soils. In this research a new reinforcing element that includes elements (anchors) attached to ordinary geogrid for increasing the pull-out resistance of reinforcements is introduced. Reinforcement therefore consists of geogrid and anchors with cubic elements that attached to the geogrid, named (by the authors) Grid-Anchor. A total of 45 load tests were performed to investigate the bearing capacity of square footing on sand reinforced with this system. The effect of depth of the first reinforcement layer, the vertical spacing, the number and width of reinforcement layers, the distance that anchors are effective, effect of relative density, low strain stiffness and stiffness after local shear were investigated. Laboratory tests showed that when a single layer of reinforcement is used there is an optimum reinforcement embedment depth for which the bearing capacity is the greatest. There also appeared to be an optimum vertical spacing of reinforcing layers for multi-layer reinforced sand. The bearing capacity was also found to increase with increasing number of reinforcement layer, if the reinforcement were placed within a range of effective depth. The effect of soil density also is investigated. Finally the results were compared with the bearing capacity of footings on non-reinforced sand and sand reinforced with ordinary geogrid and the advantages of the Grid-Anchor were highlighted. Test results indicated that the use of Grid-Anchor to reinforce the sand increased the ultimate bearing capacity of shallow square footing by a factor of 3.0 and 1.8 times compared to that for un-reinforced soil and soil reinforced with ordinary geogrid, respectively.     

Failure modes and bearing capacity of strip footings on soft ground reinforced by floating stone columns

This study evaluates the failure modes and the bearing capacity of soft ground reinforced by a group of floating stone columns. A finite difference method was adopted to analyze the performance of reinforced ground under strip footings subjected to a vertical load. The investigation was carried out by varying the aspect ratio of the reinforced zone, the area replacement ratio, and the surface surcharge. General shear failure of the reinforced ground was investigated numerically without the surcharge. The results show the existence of an effective length of the columns for the bearing capacity factors N _c and N _γ. When certain surcharge was applied, the failure mode of the reinforced ground changed from the general shear failure to the block failure. The aspect ratio of the reinforced zone and the area replacement ratio also contributed to this failure mode transition. A counterintuitive trend of the bearing capacity factor N _q can be justified with a shift in the critical failure mode. An upper-bound limit method based on the general shear failure mode was presented, and the results agree well with those of the previous studies of reinforced ground. Equivalent properties based on the area-weighted average of the stone columns and clay parameters were used to convert the individual column model to an equivalent area model. The numerical model produced reasonable equivalent properties. Finally, a theoretical method based on the comparison of the analytical equations for different failure modes was developed for engineering design. Good agreement was found between the theoretical and numerical results for the critical failure mode and its corresponding bearing capacity factors.     

振冲碎石桩地基有限元分析的复合模型研究

从振冲碎石桩的变形、受力机制出发,提出相应的假设条件,利用弹性力学和Biot固结理论建立了可以考虑固结问题的振冲碎石桩复合的平面有限元分析弹性复合模型,并编制相应的有限元分析程序APOSE。通过算例考证了APOSE的可靠性和有效性,APOSE程序可以用于分析研究振冲碎石桩地基、砂井地基等类似复合地基沉降变形和固结问题。     

Stone Columns with Vertical Circumferential Nails: Laboratory Model Study

This paper presents results from a series of laboratory plate load tests carried out in unit cell tanks to investigate the improvement in stiffness, load carrying capacity and resistance to bulging of stone columns installed in soft soils. A new method of reinforcing the stone columns with vertical nails installed along the circumference of the stone column is suggested for improving the performance of these columns. Tests were carried out with two types of loading (1) the entire area in the unit cell tank loaded, to estimate the stiffness of improved ground and (2) only the stone column loaded, to estimate the limiting axial capacity. It is found that stone columns reinforced with vertical nails along the circumference have much higher load carrying capacity and undergo lesser compression and lesser lateral bulging as compared to conventional stone columns. The benefit of vertical circumferential nails increases with increase in the diameter, number and depth of embedment of the nails. The improvement in the performance of stone column was found to be more significant, even with lower area ratio. It is found that reinforcing stone column with vertical circumferential nails at the top portion to a depth equal to three times the diameter of stone columns, will be adequate to prevent the column from excessive bulging and to improve its load carrying capacity substantially.     

坡顶加载时黏性土坡土钉加固前后的离心模型试验比较研究

为研究坡顶加载条件下黏性土坡的承载特性和变形规律,进行了素土坡和土钉加固土坡的加载离心模型试验。测量了土坡的承载和变形过程。通过对比两种土坡的承载特性和变性规律,土钉的加固作用体现在：限制了土坡向坡面方向的位移,使土坡的承载能力得到了明显提高;在加固土坡内形成的土钉影响区域改善了加载底板边缘处的薄弱程度;增大了土坡中上部土体的竖向压缩变形,减小了剪切变形,增强了土坡的稳定性。土坡上部土钉的加固效果随着坡顶荷载的增大而越明显;土坡中下部土与土钉的相互作用越靠近坡面越强     

Axial stress–strain relation of encapsulated granular column

The axial stress–strain relations of embedded granular columns encapsulated with flexible reinforcement were evaluated using an analytical procedure based on the cavity expansion method. This proposed method has firstly been verified through an experimental triaxial test on a reinforced sand specimen. A normalized relation was established between the volumetric change and the axial strain of soil to enable the analysis of granular material behavior under a continuous increase in lateral pressure. The analytical results show that the reinforced granular columns embedded in clay behave differently from granular columns subjected only to a constant confining pressure. It is found that reinforcing a column with a sleeve at the top portion will be adequate to prevent the column from bulging and also improve its load carrying capacity. The optimum skirting length that a sleeve can deter a granular column from bulging depends on the characteristics of the in situ soil and the stiffness and yield strength of the sleeve.     

Improvement of soft clay using installation of geosynthetic-encased stone columns: numerical study

The use of geosynthetic-encased stone columns as a method for soft soil treatment is extensively used to increase the bearing capacity and reduce the settlement of raft foundations and the foundation of structures like embankments. Pre-strain is an effect occurring in the encasement during stone column installation due to the compaction of the stone material. The present study uses the finite element program Plaxis to perform a numerical analysis of the soft clay bed reinforced by geosynthetic-encased stone columns. An idealization is proposed for simulation of installation of geosynthetic-encased stone columns in soft clay based on the unit-cell concept. In the analyses, initially, the validity of the analysis of the single column-reinforced soil in the unit-cell model was performed through comparison with the group columns. Then, by considering a unit-cell model, the finite element analyses were carried out to evaluate the stiffness of the reinforced ground to estimate the settlement. The results of the analyses show that the improved stiffness of the encased stone column is not only due to the confining pressure offered by the geosynthetic after loading, but the initial strain of the geosynthetic that occurred during installation also contributes to the enhancement of the stiffness of the stone column and the reduction of the settlement.     

Finite element implementation of a homogenized constitutive law for stone column-reinforced foundation soils,with application to the design of structures

Making use of the homogenization method for periodic media, developed in the context of elastoplasticity, a simplified constitutive law is proposed for a stone column-reinforced soil, regarded as a homogeneous but anisotropic medium. The closed-form expressions derived for such a constitutive law allow for its implementation into a f.e.m-based numerical procedure. The computational code so obtained is then applied to simulating the response of a foundation soil reinforced by a group of floating columns, expressed in terms of load–settlement curves drawn up to the ultimate bearing capacity.     

包裹碎石桩承载特性试验研究

为了研究包裹碎石桩的承载机制,开展了室内模型试验,对不同套筒长度和刚度的包裹碎石桩承载力、端阻力、变形和破坏情况等进行了分析。试验中利用自制的桩体径向变形测量仪监测了桩体的径向变形情况。试验结果表明：当桩体支承在坚硬土层时,全长包裹碎石桩有效提高碎石桩的承载力和刚度,且采用弹性模量较大的土工材料套筒,包裹碎石桩的极限承载力和刚度也较大,部分包裹碎石桩（包裹长度为0.6倍桩长）相对于碎石桩优势不明显。这是因为部分包裹碎石桩和全长包裹的承载特性、变形特点和破坏模式均存在差异。全长包裹碎石桩传递至桩底端的荷载大于部分包裹碎石桩和碎石桩的。与部分包裹碎石桩和碎石桩比较,全长包裹碎石桩桩身变形分布较为均匀,同一应力作用下,桩身最大径向变形量较小。此外,全长包裹碎石桩刺入顶部褥垫层发生破坏,而部分包裹碎石桩发生鼓胀破坏。     

A State-of-the-Art Review of Stone/Sand-Column Reinforced Clay Systems

This paper presents a state-of-the-art review of published research papers and reports that focus on the modeling, testing, and analysis of soft clays that are reinforced with sand/stone columns in relation to bearing capacity and settlement considerations. The review is presented in chronological order to shed light on the development of this field of research in the last 40+ years. The objective of the study is to assemble published results from field, laboratory, and numerical investigations of sand/stone columns in clay in one resource to provide future researchers and designers with easy access to information and data. The majority of the reviewed papers include an experimental component that is based on field or laboratory scale tests (1-g, triaxial, or centrifuge) conducted on clay specimens reinforced with partially or fully penetrating, encased or ordinary, stone or sand columns that were installed as single columns or as column groups. Some papers included numerical experiments that were based on finite element models, while others presented analytical solutions for modeling the response of the composite system. A compilation of the important findings from physical, numerical, and analytical models in addition to a summary table that facilitates access to information from various research efforts are presented in the paper.     

An analytical model of the strip footing reinforced with geogrid

The ultimate bearing capacity of a strip footing on soil reinforced with geogrids has been studied analytically. The reinforcing mechanism of the soil bearing on lateral surfaces and shearing over soils through the apertures of the grids was considered. The passive resistance against transverse ribs of geogrid was calculated using the Prandtl mechanism. The proposed equation incorporated the traditional Nγ factors, unit weight of soil, soil shear strength angle, footing width, and the geometry of the geogrid. The accuracy of theoretical predictions was verified by the experimental and analytical results from the existing literatures. The mean bias of the theoretical model was found to be about 10%.     

水平加筋地基极限承载力的极限上限分析法

水平加筋是广泛应用的软土地基处理方法之一,而水平加筋地基极限承载力的确定是其地基处理设计的重要依据。因此,首先结合条形基础下水平加筋地基的工程特点,在探讨其承载机制和破坏特点的基础上,考虑破坏间断面上筋材与地基土体的变形协调,构建出反映加筋参数变化影响的可变破坏模式及机动允许速度场;然后,在此基础上,通过重点研究筋材的能量耗散分析方法,并引入上限极限分析理论,建立出条形基础下水平加筋地基极限承载力分析模型,再引入序列二次规划优化分析理论,建立出条形基础下水平加筋地基极限承载力确定方法,它能充分反映加筋设计参数对地基破坏模式及承载力的影响;最后,通过试验结果与该方法及现有同类分析模型结果的比较分析,表明了该模型与方法的合理性与可行性。     

循环荷载及静载下土工格室加筋路堤模型试验研究

为探究土工格室加筋路堤在循环荷载及静载下的各种性能,利用美国GCTS公司的USTX-2000加载装置进行加载,通过改变加筋层数、格室高度,格室焊距对土工格室加筋路堤进行一系列模型试验。对各种工况下加筋路堤极限承载力、长期循环荷载及固定振次循环荷载后极限承载力的变化进行研究。试验表明,土工格室加筋能显著提高地基极限承载力并能显著减小坡顶和坡中临界破坏时的法向累积变形,在加筋间距一定的情况下,加筋层数增加和格室高度增大均可不同程度提高极限承载力并减小临界破坏时坡顶法向累积变形,格室焊距的减小也可在一定程度提高极限承载力,格室焊距对边坡法向变形影响不大;长期循环荷载下固定间距加筋层数对路堤竖向累积沉降量影响不大,而对边坡坡顶法向累积变形有一定影响,格室高度增大和格室焊距减小均可不同程度减小路堤竖向累积沉降量和坡面法向累积变形;越靠近加载点处,路堤土压力值受加筋影响越显著,加筋提高了土体刚度和密实度,使加筋路堤土压力值较无筋路堤明显增大;对于无筋路堤,改变动载幅值和振次均导致振后极限承载力有不同程度的降低,而对于加筋路堤,当动载幅值≥30 kPa或动载振次≥1 000时,振后极限承载力均有不同程度的提高。     

加筋地基承载力研究现状

基于目前国内外文献对加筋地基承载力的研究成果,总结了加筋地基承载力的影响因素及其影响规律,并基于已有文献的研究成果得到了最优加筋参数的建议取值范围。对目前加筋地基的破坏模式及承载力计算公式进行了总结,并讨论了各承载力计算公式的区别与联系及优劣性。提出加筋地基承载力计算公式应基于准确的破坏模式与加筋机理。加筋地基的破坏模式与破坏模式类型定量化判断标准、加筋机理、原型实验等应成为加筋地基承载力未来的研究重点。      

条形基础加筋砂土地基极限承载力计算

基于传统的极限平衡条分法,利用临界滑动场法计算了条形基础的加筋地基极限承载力。假定土体处于极限平衡状态时,土体与筋材间存在均匀的摩擦力,通过建立土体条块极限平衡方程,推导了地基承载力的递推关系式。首先,设定计算土体范围,并划分条块和离散状态点;其次,根据递推公式计算各个状态点的参数,并搜索临界滑面;最后,根据搜索出的滑面计算地基承载力。通过实例比较进一步验证了计算结果的可靠性,并分析了首层筋带埋深、铺设层数和长度对地基承载力和滑面位置的影响。研究结果表明：地基承载力随着筋带埋深的增加先增大后减小;随着层数和长度的增加先逐渐增大,最后趋于稳定;滑面位置的变化规律主要是垂直影响深度和水平影响范围增大或减小。该方法原理简单、易于编程,为条形基础加筋地基承载力的计算提供了一种新思路,是临界滑动场法在地基承载力计算中的推广应用。