Stability of eccentrically loaded footings on slopes

The stability of eccentrically loaded strip footings on slopes was investigated using the method of finite element analysis based on the theory of elasto-plasticity. The analysis was done for two different soils involving three levels of slope angle, six footing locations, and two levels of load eccentricity plus central vertical loading. The strip footing analysed was a 3-ft (0.9 m) wide reinforced concrete footing embedded to a depth of 3 ft (0.9 m). The analysis focused on footing settlement, plastic yielding of soil, and ultimate bearing capacity. The results of analysis show that the influence of load eccentricity on footing pressure vs. footing centre settlement is negligibly small. However, the progressive soil yielding and ultimate bearing capacity are greatly affected by load eccentricity. Furthermore, the effect of load eccentricity differs considerably with the load location relative to the footing centre and slope crest. The ultimate bearing capacity for the eccentric load located on the slope side is significantly greater than that for the load located on the other side of the footing centre. For a 2(H): 1(V) slope in silty clay, the effect of slope on footing stability decreases with increasing footing location from slope crest as would be expected, and diminishes when the footing is located from the crest at about 5-times the footing width.     

有关砂土地基承载力数值解析问题的讨论

以砂土地基的极限承载力为对象,讨论了古典理论解与室内模型实验值之间的差异,并结合试验中所观察到的现象对其原因进行了简要的分析,最后,利用有限元解析对各种极限承载力的计算方法进行了客观地评价.砂土材料强度具有明显的各向异性以及软化特性,并与周围压力大小以及密度相关.另外,砂土地基的破坏呈渐进性,砂土的粒径大小影响它的承载力以及变形破坏.结果表明,只有考虑砂土以上的各种特性的数值解析方法才能合理地得到砂土地基的极限承载力.     

土钉加固黏性土坡加载的离心模型试验研究

进行了不同坡度土钉加固边坡坡顶加载的离心模型试验,观测了土坡的破坏过程并测量土坡的位移场,研究了土钉加固黏性土坡的承载力、变形和破坏规律以及坡角对其破坏规律的影响。试验结果表明,坡顶荷载的增加引起土坡变形的增加,变形的集中产生和发展导致滑裂面的形成并使土坡发生破坏。土钉变形规律受加载阶段和加载底板的综合影响,坡顶荷载越大,接近坡顶的土钉弯曲挠度越大,钉土间的相互作用越强。土坡的坡角越大,承载力越低,土体呈现出更显著的向坡面位移的趋势。     

Collapse of a Model Strip Footing on Dense Sand Under Vertical Eccentric Loads

The paper focuses on the behaviour of a model strip footing, resting on a saturated dense sandy soil, subjected to centred or eccentric vertical loading. Experimental tests, carried out on a small-scale physical model, are able to reproduce effective stress levels equivalent to those prevailing in prototype problems, thanks to the maintenance of a downward steady-state seepage in the soil. The test program consists of three series of tests, each corresponding to an imposed value of hydraulic gradient, and each involving five load eccentricities; one series, in particular, is carried out with still water. Relevant points of load–settlement curves are related to the evolution of soil-footing collapse mechanism, evidenced by the distortion of some vertical coloured sand strips. The collapse mechanism is formed either by one or two sliding surfaces, depending on both load eccentricities and hydraulic gradient values. Significant differences are shown to occur between centred and eccentric loading footing response. Shear strength parameters obtained from back-analyses carried out on load values recorded at the appearance of each sliding surface on the free soil surface, in both hypotheses of associated and non-associated flow rule validity, are adopted to draw, for each test, a theoretical collapse mechanism consisting, in plane strain, of a log-spiral line with adjacent-end tangents; the obtained theoretical sliding surfaces, in turn, are compared to the experimental ones, showing that these latter are either stress characteristic or zero-extension lines depending mainly on cumulative footing displacements and current effective stress level in the soil.     

基于非对称双侧破坏模式的临坡地基承载力上限分析

临坡地基已成为一种广泛的地基形式。针对临坡条形基础地基破坏模式的非对称性特点,首先引进双侧破坏模式的研究思路,重点考虑临坡地基基础两侧滑块大小和同一滑块几何形状的双重非对称性特征,构建了临坡条形基础地基非对称双侧破坏模式,为临坡地基承载力分析奠定了坚实基础;然后在此基础上,引进极限上限分析和优化理论,建立了临坡条形基础地基承载力分析的模型与方法,该方法不仅可考虑地基破坏模式,还可考虑基础与坡顶距离对临坡地基承载力的影响,而且还可较好地蜕化为平地地基承载力的分析;最后通过工程实例计算,并与现有相关分析方法进行对比分析,表明该方法的可行性与合理性以及普遍适用性。     

Bearing capacity of two interfering strip footings from lower bound finite elements limit analysis

A rigorous lower bound solution, with the usage of the finite elements limit analysis, has been obtained for finding the ultimate bearing capacity of two interfering strip footings placed on a sandy medium. Smooth as well as rough footing–soil interfaces are considered in the analysis. The failure load for an interfering footing becomes always greater than that for a single isolated footing. The effect of the interference on the failure load (i) for rough footings becomes greater than that for smooth footings, (ii) increases with an increase in ?, and (iii) becomes almost negligible beyond S/B > 3. Compared with various theoretical and experimental results reported in literature, the present analysis generally provides the lowest magnitude of the collapse load. Copyright © 2011 John Wiley & Sons, Ltd.     

钢板桩挡墙主动土压力分布的形状效应

采用有限元数值试验,研究帽型钢板桩的截面形状对墙后主动土压力分布规律的影响。首先,对室内缩尺模型试验进行数值模拟,对比实测数据验证数值模型的有效性;然后,建立钢板桩挡墙数值模型,模拟该挡墙在不同位移模式下土压力变化和分布的规律,与平板挡墙计算结果进行对比,分析钢板桩截面形状对土压力分布的影响,进一步探讨形状效应的可能影响因素及机制。分析结果表明,钢板桩的截面形状影响墙后主动土压力的分布形式,影响程度与位移模式有关;墙体平动和绕墙底转动情况下,钢板桩挡墙凸出部分的主动土压力值大于凹处,但墙体绕墙顶转动情况下差异不明显;主动土压力的形状效应由土拱效应引起,截面高宽比对其影响显著,墙土摩擦角影响有限。     

桩及桩板墙加固路基边坡的对比室内模型试验研究

设计了尺寸相似比为1:25的室内试验模型,对两组不同支护方式下预设滑面的边坡模型进行逐级水平推移式加载,对比分析了在横向荷载作用下抗滑桩及桩板式挡墙（后置式挡土板）两种支护结构的受力及变形特点（考虑深层滑坡）。研究发现:边坡-支护结构系统的破坏明显分为3个阶段,即滑体土压密阶段、支护结构主要变形阶段及支护结构失效阶段;距桩顶14cm的同一水平位置桩后土压力传递效率较低,与距加载板位置远近成反比,呈指数变化规律;抗滑桩仍是两种支护结构的主要受力构件,挡土板延长了模型破坏的主要变形阶段,加固效果显著;桩板支护结构较抗滑桩支护多承受一级荷载（0.5kN）,承载力提高了14.29%;挡土板优化了桩后土压力的分布形式,使作用在整个桩背侧土压力合力的作用点更靠近锚固端,有利于抵抗桩身的挠曲变形。本研究可为这两种边坡支护结构形式的选择提供参考。     

Experimental and analytical investigations on bearing capacity of strip footing in reinforced sand backfills and flexible retaining wall

This study focuses on the experimental and analytical investigations of small-scale physical model tests. For this purpose, a set of tests were conducted with and without reinforcement on the top of the backfill. The specimens were different in terms of parameters like the number of geotextile layers, the vertical distance between layers and the strip footing distance from the wall. Soil failure in the bearing capacity step and the backfill shear zones was analysed using particle image velocimetry methods. Bearing capacity of the strip footings was studied using analytical procedures. The results indicate that a reinforcing top zone of the flexible retaining structures may be more appropriate than unreinforced case. The ultimate bearing capacity and wall deflection can be significantly improved by increasing the number of reinforcement layers. When the three layers of reinforcement are used, there is an optimum vertical spacing of the layers at which the bearing capacity is the greatest (h/H?=?0.12, d/H?=?0.33 and u?=?B). The study shows that the analytical solution and the results from the experimental models are in good agreement.     

Nonlinear three-dimensional analysis of reinforced concrete piles subjected to horizontal loading

A three-dimensional finite element approach is proposed to predict the response of reinforced concrete piles to horizontal loading. This approach allows the nonlinear effects arising from the soil–pile interaction to be properly accounted for. In particular, the occurrence of plastic strains in the soil, concrete cracking and steel yielding in the pile as well as the occurrence of slip and gap at the soil–pile interface are reliably simulated using appropriate constitutive models. Another advantage of the present method is that it requires few material parameters as input data. In addition, these parameters can be readily obtained from conventional geotechnical and structural tests. The proposed approach is used to analyse the results from some loading tests documented in the literature concerning a large-diameter pile and a large-section rectangular pile (barrette) embedded in sandy soils. The theoretical results from these analyses are found to be in fairly good agreement with the experimental measurements available from the loading tests. Remarks of practical interest on the response of the structures considered to horizontal loading are also made.     

Influence of spatial variability of soil friction angle on sheet pile walls’ structural behaviour

The uncertainty in terms of soil characterisation is studied to assess its effect on the structural behaviour of extended structures as sheet pile walls. A finite element model is used. This integrates a numerical model of the soil–structure interaction together with a stochastic model that allows characterising the soil variability. The model serves in propagating the variability and the system parameter uncertainties. Discussion is mainly focused on two points: (1) testing the sensitivity of the structural behaviour of a sheet pile wall to different geotechnical parameters and (2) assessing the influence of spatial variability of soil properties on the structural behaviour by identifying the most sensitive geotechnical parameter and the most significant correlation length values. The findings showed that in assessing the sheet pile wall’s structural behaviour, there are spatial variability parameters that cannot be considered negligible. In this study, soil friction angle is found to be an important parameter.     

基于饱和-非饱和渗流理论的基坑防渗措施分析

应用饱和-非饱和渗流理论,对某临河基坑进行了渗流计算,评价了基坑的渗透稳定性,并确定了基坑的最佳防渗措施及相应的参数。计算结果表明：无防渗措施时,基坑坡面土体在渗透压力作用下是不稳定的,必须采取防渗措施。从便于施工的角度考虑,采用钢板桩防渗,其位置定在距基坑右边坡6.0 m处。钢板桩长度对渗流场影响显著,钢板桩应穿过粉砂层,这样才能起到较好的防渗效果,有利于基坑边坡的稳定;同时也不宜太长,太长不仅浪费材料,效果也不会更好,最佳长度应为15.4 m。     

Seismic Bearing Capacity of Strip Footings Located Close to the Crest of Geosynthetic Reinforced Soil Structures

This paper investigates the performance of geo-reinforced soil structures subjected to loading applied to strip footings positioned close to a slope crest. The kinematic theorem of limit analysis, which is based on the upper bound theory of plasticity, is applied for evaluating the ultimate bearing capacity within the framework of pseudo-static approach to account for earthquake effects. The mechanism considered in this analysis is a logarithmic spiral failure surface, which is assumed to start at the edge of the loaded area far from the slope, consistent with the observed failure mechanisms shown in the experimental tests reported in the literature. A parametric study is then carried out to investigate the influence of various parameters including the geosynthetic configuration, backfill soil friction angle, footing distances from the crest of the slope, slope angles and horizontal seismic coefficients. Attention is paid to the failure mechanism because its maximum depth is the depth at least to which the reinforcements must be placed. Results of the analyses are presented in the form of non-dimensional design charts for practical use. Finally, a simple procedure based on the assessment of earthquake-induced permanent displacements is shown for the design of footing resting on reinforced slopes subjected to earthquake.     

Modelling the settlement behaviour of a strip footing on sloping sandy fill under cyclic loading conditions

This paper investigates the settlement behaviour of a strip footing seating on the crest of an embankment and subjected to cyclic loading. The embankment fill is a dense sand and the issue is the gradual accumulation of settlement over a large number of load repetitions. Cyclic triaxial tests were first conducted to develop a consistent but simple material model for numerical implementation. Particular emphasis was placed on linking the stress-strain behaviour of an unload-reload cycle to the accumulation of permanent strain, with only five input parameters required to model the cyclic behaviour. The material model was implemented in a numerical analysis to compute the settlement behaviour obtained from model tests conducted by another researcher. It is pertinent to highlight that the same soil, compacted to same density at same moisture content, was used for both the cyclic triaxial tests and model tests. Reasonable to good agreement between the experimental and numerical results was achieved.     

Interference of Multiple Strip Footings on Sand Using Small Scale Model Tests

By using small scale model tests, the interference effect on the vertical load-deformation behavior of a number of equally spaced strip footings, placed on the surface of dry sand, was investigated. At any stage, all the footings were assumed to (i) carry exactly equal magnitude of load, and (ii) settle to the same extent. No tilt of the footing was permitted. The effect of clear spacing (s) among footings on the results was explored. A new experimental setup was proposed in which only one footing needs to be employed rather than a number of footings. The bearing capacity increases continuously with decrease in spacing among the footings. The interference effect becomes further prominent with increase in soil friction angle. In contrast to an increase in the bearing capacity, with decrease in spacing of footings, an increase in the footing settlement associated with the ultimate state of shear failure was observed. The present experimental observations were similar to those predicted by the available theory, based on the method of characteristics. As compared to the theory, the present experimental data, however, indicates much greater effect of interference especially for larger spacing among footings.     

Ultimate Bearing Capacity Prediction of Eccentrically Inclined Loaded Strip Footings

Extensive laboratory model tests have been carried out on a strip footing resting over dry sand bed subjected to eccentrically inclined load to determine the ultimate bearing capacity (Patra et al. in Int J Geotech Eng 6(3):343–352, 2012a.  https://doi.org/10.3328/IJGE.2012.06.03.343-352, Int J Geotech Eng 6(4):507–514, b.  https://doi.org/10.3328/IJGE.2012.06.04.507-514). Similarly, lower bound calculations based on finite element method were performed to compute the bearing capacity of a strip footing subjected to an eccentric and inclined load lying over a cohesionless soil with varying embedment depth and relative density (Krabbenhoft et al. in Int J Geomech ASCE, 2014.  https://doi.org/10.1061/(ASCE)GM.1943-5622.0000332). The load may be applied in two ways namely, towards the center line and away from the center line of the footing. Based on the results (both experimental and numerical analyses), a neural network model is developed to predict the reduction factor that will be used in computing the ultimate bearing capacity of an eccentrically inclined loaded strip footing. This reduction factor (RF) is the ratio of the ultimate bearing capacity of the footing subjected to an eccentrically inclined load to the ultimate bearing capacity of the footing subjected to a centric vertical load. A thorough sensitivity analysis is carried out to evaluate the parameters affecting the reduction factor. Based on the weights of the developed neural network model, a neural interpretation diagram is developed to find out whether the input parameters have direct or inverse effect on the output. A prediction model equation is framed with the trained weights of the neural network as the model parameters. The predictions from ANN, and those from other approaches, are compared with the results computed from both experimentation and FEM analyses. The ANN model results are found to be more accurate and well matched with other results.     

临近边坡的条形基础地基极限承载力数值分析

建筑物或构筑物基础临近边坡置放的情况在实际工程中十分普遍,但目前对于临近边坡基础的地基承载力及破坏模式尚缺乏深入研究。采用不连续布局优化（DLO）极限分析法建立数值模型,分析边坡几何尺寸、土体参数和基础位置对临坡条形基础的极限承载力和边坡破坏模式的影响,并对国内外现行规范推荐的计算方法进行评价。结果表明：极限承载力随边坡高度和边坡倾斜角的增大而减小,当坡高超过临界高度后,极限承载力将不受其影响;极限承载力随土体黏聚力和内摩擦角的增大而提高,滑动面随黏聚力的增大而变浅,随内摩擦角的增大而变深;极限承载力随基础与坡肩相对距离的增大而提高,当基础置放位置超过某临界距离后极限承载力不受边坡影响。在土体强度高、坡角较大时,《建筑地基基础设计规范》规定的临坡基础最小置放距离偏于危险,设计时仍需考虑边坡对承载力的减损作用;在土体强度较低、坡角较小时,规范规定值偏于保守。美国AASHTO规范对边坡地基极限承载力的取值在砂土边坡时较为可靠,但其仅适用于坡面破坏模式的情况;饱和黏土边坡的承载力曲线有悖于理论解,对临界距离的规定同样存在低估。     

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%.     

Bearing capacity of sandy soil treated by Kenaf fibre geotextile

Bio-based materials are widely used recently in order to introduce a more sustainable construction material. Kenaf is a type of bio-based material that can be easily obtained in a tropical country, which could be a potential material to be utilised as a geotextile material because it has good tensile strength. The geotextile could be used to improve the bearing capacity of a loose soil. This paper presents a series of small-scale physical modelling tests to investigate the bearing capacity performance of Kenaf fibre geotextile laid on and inside the sand layer. A rigid footing was used to replicate a strip footing during the loading test, and sand was prepared based on 50% of relative density in a rigid testing chamber for ground model preparation. In order to treat the soil, Kenaf fibre geotextile was laid at four difference locations which are on the soil surface and underneath the ground model surface at 50, 75 and 100 mm deep. It was found that the usage of the Kenaf fibre geotextile has improved the bearing capacity of the sandy soil up to 414.9% as compared to untreated soil. It was also found that the depth of the Kenaf fibre geotextile treated into the soil also affects the soil performance.     

Bearing Capacity of Embedded Strip Footings on Cohesionless Soil Under Vertical and Horizontal Loads

In the last decades a few attention was given to the evaluation of the bearing capacity of embedded footing under inclined loads on a frictional soil. This paper focuses on a numerical study using the finite-difference code Fast Lagrangian Analysis of Continua (FLAC), to evaluate the bearing capacity of embedded strip footing on a frictional soil. The soil is modeled by an elasto-plastic model with a Mohr–Coulomb yield criterion and associative flow rule; the effect of non-associativity of the soil on the bearing capacity is also investigated. The effect of the embedment is estimated though a depth factor, defined as a ratio of the bearing capacity of a strip footing at a depth D to that of a strip footing at the ground surface. The inclination effect is estimated by inclination factors, defined as the ratio of the limit vertical load for a footing under inclined loading to that of the vertically loaded footing. Both swipe and probe analyses were carried out to identify the vertical force–horizontal force (V–H) failure envelope. The results have been compared with those available in the literature.