Ultimate bearing capacity of strip footing resting on soil bed strengthened by wraparound geosynthetic reinforcement technique

In the recent past, the wraparound geosynthetic reinforcement technique has been recommended for constructing the geosynthetic-reinforced soil foundations. This paper presents the development of an analytical expression for estimating the ultimate bearing capacity of strip footing resting on soil bed reinforced with geosynthetic reinforcement having the wraparound ends. The wraparound ends of the geosynthetic reinforcement are considered to provide the shearing resistance at the soil-geosynthetic interface as well as the passive resistance due to confinement of soil by the geosynthetic reinforcement. The values of ultimate load-bearing capacity determined by using the developed analytical expression agree well with the model footing load test values as reported in the literature.     

土体软化条件下条形基础地基承载力数值模拟

为克服材料软化导致的有限元网格敏感性难题,提出了一个压力相关隐式梯度塑性模型来模拟土体软化条件下条形基础地基承载力。通过引入微应变作为附加运动学变量,推导了包含高阶广义应力的微力平衡和经典动量方程,并基于热力学第二定律,将附加的微力平衡转化为宏观等效塑性应变与微应变耦合的Helmholtz方程。进一步建立能耦合位移和微变量的有限元算法,并通过软化材料双轴压缩试验模拟,验证了该算法在应变局部化数值模拟中的适用性。将建立的方法用于条形基础地基承载力特性模拟,并通过与理想弹塑性模型计算结果对比表明,土体软化将导致地基承载能力降低,破坏模式表现为失稳区域变小且塑性应变幅值增大。     

Seismic bearing capacity of a strip footing on rock media

The bearing capacity factors for a rough strip footing placed on rock media, which is subjected to pseudo-static horizontal earthquake body forces, have been determined using the lower bound finite element limit analysis in conjunction with the power cone programming (PCP). The rock mass is assumed to follow the generalized Hoek-Brown (GHB) yield criterion. No assumption needs to be made to smoothen the GHB yield criterion and the convergence is found to achieve quite rapidly while performing the optimization with the usage of the PCP. While incorporating the variation in horizontal earthquake acceleration coefficient (k_h), the effect of changes in unit weight of rock mass (γ), ground surcharge pressure ($q_0$) and the associated GHB material shear strength parameters (geological strength index (GSI), yield parameter (m_i), uniaxial compressive strength (σ_ci)) on the bearing capacity factors has been thoroughly assessed. Non-dimensional charts have been developed for design purpose. The accuracy of the present analysis has been duly checked by comparing the obtained results with the different solutions reported in the literature. The failure patterns have also been examined in detail.     

复合加载情况下六自由度圆形基础失稳模式与 极限承载能力研究

海洋工程中结构物除了受到自身重力作用外,往往还受到海风、海浪、海流等的作用,使得海床土体中的基础一般受到集中力、弯矩和扭矩的联合作用,这一受力状态称为结构物基础的复合加载模式。详细研究复合加载模式下海床土体的失稳模式和极限承载能力,对海洋结构物的安全运行至关重要。以三维空间内圆形基础为研究对象,基于土体弹塑性极限平衡原理,利用非线性有限元分析软件ABAQUS,对空间六自由度圆形基础极限承载能力进行详细的数值分析。基于上述计算分析结果,揭示了单调加载情况下土体的失稳机理与极限承载能力,给出了复合加载模式下海床土体破坏包络面方程。给出的土体失稳模式和破坏包络面方程能够合理地评估复合加载模式下海床土体的极限承载能力。     

各向异性和非均质地基土上浅基础的极限承载力

应用塑性极限分析法上限定理及变分原理,确定非均质及各向异性地基土的极限承载力,导出了确定非均质和各向异性地基土极限承载力的基本公式。利用编制的计算机程序分析了土非均质和各向异性参数对承载力的影响。将结果与其他学者结果进行了比较,说明用本文提出的方法获得的承载力结果更为可靠。     

Ultimate bearing capacity of rigid footing under eccentric vertical load

In geotechnical engineering, the stability of rigid footings under eccentric vertical loads is an important issue. This is because the number of superstructure buildings has increased and the situation of structures being subjected to eccentric vertical loading is occurring more and more frequently. In this study, focus is placed on the ultimate bearing capacity of a footing against the eccentric load placed on two types of soil, namely, sandy soil and clayey soil, using a finite element analysis. For the sandy soil, the study newly introduces an interface element into the footing-soil system in order to properly evaluate the interaction between the footing and the soil, which greatly affects the failure mechanism of the footing-soil system. For the clayey soil, the study improves the analysis procedure by introducing a zero-tension analysis into the footing-soil system. Two friction conditions between the footing and the soils are considered; one models a perfectly rough condition and the other models a perfectly smooth condition. For a two-dimensional analysis of the footing-soil system, the rigid plastic finite element method (RPFEM) is applied to calculate the ultimate bearing capacity of the eccentrically loaded footing. The RPFEM is extended in this work to calculate not only the ultimate bearing capacity, but also the distribution of contact stress along the footing base. The study thoroughly investigates the effect of the eccentric vertical load on the ultimate bearing capacity in the normalized form of V/V_ult and e/B where e is the length of the eccentricity and B is the width of the footing. V_ult indicates the ultimate bearing capacity of the centric vertical load. The failure envelope in the plane of V/V_ult and M/BV_ult is further investigated under various conditions for the sandy and clayey soils. M is the moment load induced by the eccentric vertical load. This study examines the applicability of the failure envelope obtained for the eccentric vertical load to the cases where two variables, V and M, are independently prescribed. The obtained results are coincident and indicate the wide applicability of the failure envelope in the normalized V-M plane in practice. Finally, in a comparison with previous researches, the numerical data in the present study lead to the derivation of new equations for the failure envelopes of both sandy and clayey soils.     

Laboratory investigation of bearing capacity behaviour of strip footing on reinforced flyash slope

The paper presents the results of laboratory model tests on bearing capacity behaviour of a strip footing resting on the top of a geogrid reinforced flyash slope. A series of model footing tests covering a wide range of boundary conditions, including unreinforced cases were conducted by varying parameters such as location and depth of embedment of single geogrid layer, number of geogrid layers, location of footing relative to the slope crest, slope angles and width of footing. The results of the investigation indicate that both the pressure–settlement behaviour and the ultimate bearing capacity of footing resting on the top of a flyash slope can be enhanced by the presence of reinforcing layers. However the efficiency of flyash geogrid system increases with the increasing number of geogrid layers and edge distance of footing from the slope. Based on experimental results critical values of geogrid parameters for maximum reinforcing effects are established. Experimental results obtained from a series of model tests have been presented and discussed in the paper.     

Effect of interface adhesion factor on the bearing capacity of strip footing placed on cohesive soil overlying rock mass

The problem related to bearing capacity of footing either on pure soil or on pure rock mass has been investigated over the years. Currently, no study deals with the bearing capacity of strip footing on a cohesive soil layer overlying rock mass. Therefore, by implementing the lower bound finite element limit analysis in conjunction with the second-order cone programming and the power cone programming, the ultimate bearing capacity of a strip footing located on a cohesive soil overlying rock mass is determined in this study. By considering the different values of interface adhesion factor (α_cr) between the cohesive soil and rock mass, the ultimate bearing capacity of strip footing is expressed in terms of influence factor (I_f) for different values of cohesive soil layer cover ratio (T_cs/B). The failure of cohesive soil is modeled by using Mohr−Coulomb yield criterion, whereas Generalized Hoek−Brown yield criterion is utilized to model the rock mass at failure. The variations ofI_f with different magnitudes of α_cr are studied by considering the influence of the rock mass strength parameters of beneath rock mass layer. To examine stress distribution at different depths, failure patterns are also plotted.     

Centrifuge model tests on the behavior of strip footing on geotextile-reinforced slopes

This paper examines the stability of geotextile-reinforced slopes when subjected to a vertical load applied to a strip footing positioned close to the slope crest. Vertical spacing between geotextile reinforcement was varied while maintaining a constant slope angle, load position, soil density and geotextile type. Small-scale physical tests were conducted using a large beam centrifuge to simulate field prototype conditions. After the model was accelerated to 40g, a load was applied to the strip footing until slope failure occurred. Digital image analysis was performed, using photographs taken in-flight, to obtain slope displacements and strain distribution along the reinforcement layers at different loading pressures during the test and at failure. Stability analysis was also conducted and compared with centrifuge model test results. The vertical spacing between reinforcement layers has a significant impact on the stability of a reinforced slope when subjected to a vertical load. Less vertical distance between reinforcement layers allows the slope to tolerate much greater loads than layers spaced further apart. Distributions of peak strains in reinforcement layers due to the strip footing placed on the surface of the reinforced slope were found to extend up to mid-height of the slope and thereafter they were found to be negligible. Stability analysis of the centrifuge models was found to be consistent with the observed performance of geotextile-reinforced slopes subjected to loading applied to a strip footing near the crest.     

Comparison of bearing capacity of a strip footing on sand with geocell and with planar forms of geotextile reinforcement

Comprehensive results from laboratory model tests on strip footings supported on the geocell and planar reinforced sand beds with the same characteristics of geotextile are presented. The various parameters studied in this testing program include the reinforcement width, the number of planar layers of geotextile and height of the geocell below the footing base. Contrary to other researches, the performance of the geocell and planar reinforcement is investigated at the range of low to medium settlement level, similar to those of interest in practice. The results show that the efficiency of reinforcement was decreased by increasing the number of the planar reinforcement layers, the height of the geocell reinforcement and the reinforcement width. For the same mass of geotextile material used in the tests at the settlement level of 4%, the maximum improvement in bearing capacity (IF) and percentage reduction in footing settlement (PRS) were obtained as 2.73 and 63% with the provision of geocell, respectively, while these values compare with 1.88 and 47% for the equivalent planar reinforcement. On the whole, the results indicate that, for the same quantity of geotextile material, the geocell reinforcement system behaves much stiffer and carries greater loading and settles less than does the equivalent planar reinforcement system. Therefore, a specified improvement in bearing pressure and footing settlement can be achieved using a lesser quantity of geocell material compared to planar geotextile.     

考虑不排水抗剪强度空间变异性的条形基础极限承载力随机分析

目前有关抗剪强度参数随深度变化对地基稳定性影响的研究还不深入。为此,提出了考虑土体不排水抗剪强度均值和标准差随深度变化的地基稳定性随机分析方法。建立了表征不排水抗剪强度空间变异性的不平稳随机场模型,采用Karhunen-Loeve（KL）展开离散随机场。探讨了土体不排水抗剪强度参数空间变异性对地基极限承载力的影响规律,并比较了不排水抗剪强度参数平稳和不平稳随机场模型对地基稳定的影响。以不排水黏性地基稳定随机分析问题为例验证了所提方法的有效性。结果表明：考虑不排水抗剪强度参数空间变异性时,地基极限承载力均值和标准差随相关距离的增大而增大,地基极限承载力对竖直向相关距离更为敏感。地基极限承载力均值随不排水抗剪强度变异系数的增加而减小,标准差随变异系数的增加而增加。不排水抗剪强度变异性对地基失效概率有明显的影响,安全系数较大时,不排水抗剪强度相关距离越小,地基失效概率越小。与不排水抗剪强度参数的不平稳随机场相比,不排水抗剪强度的平稳随机场模型会高估地基极限承载力的变异性,在相同的安全度水平下,当地基的安全系数较低时,平稳随机场模型会导致对地基失效概率的低估;当地基安全系数较高时,平稳随机场模型会导致对地基失效概率的高估。     

Modified ultimate bearing capacity formula of strip footing on sandy soils considering strength non-linearity depending on stress level

Most of the contemporary ultimate bearing capacity (UBC) formulas assume a linear yield function in shear stress-normal stress space. However, experimental investigations have corroborated the non-linearity in the failure envelopes of sandy soils. This study focused on the assessment of the stress level effect on the UBC of surface strip footings ascribed to the soil unit weight (γ), footing size (B), and uniform surcharge load (q). The rigid plastic finite element method (RPFEM) was employed for the analysis. The analysis method was validated against the centrifuge test results from the published references in the case of various sandy soils with different relative densities. The RPFEM, using the mean confining stress dependence property of Toyoura sand, is utilized in non-linear finite element analysis of model sandy soil. The normalized ground failure domains in the case of the non-linear shear strength model are gleaned smaller than those in the case of the linear shear strength one. The numerical results are compared with the guidelines of the Architectural Institute of Japan (AIJ) and the Japan Road Association (JRA). The modification coefficients are ascertained for the frictional bearing capacity factor (N_γ) and surcharge bearing capacity factor (N_q), and a modified UBC formula is proposed. The performance of the proposed UBC formula is examined against the analysis results and various prevailing UBC guidelines.     

无黏性土斜坡地基承载力模型试验研究

采用缩尺模型试验对砂土斜坡地基的土压力分布、变形机制、破坏模式进行探索,并研究了斜坡坡角、基础尺寸、相对密度、基础形状对斜坡地基破坏形态及极限承载力的影响。结果表明：斜坡地基的破坏模式与Choudhury提出的破坏模式相近,破坏区域由不对称楔体、辐射向剪切区、被动楔体组成。斜坡地基的破坏区域长度随斜坡坡角、基础尺寸的增大而增大,但不随相对密度的变化而变化;而斜坡地基的极限承载力随斜坡坡角的增大而减小,随基础宽度、相对密度的增大而增大。对相同尺寸的基础而言,方形基础下的地基极限承载力和破坏区域长度均大于圆形基础。试验研究成果对斜坡地基变形特征、破坏形态和斜坡地基承载力影响因素的探究具有一定理论参考价值。     

Prediction of bearing capacity of circular footings on soft clay stabilized with granular soil

The shortage of available and suitable construction sites in city centres has led to the increased use of problematic areas, where the bearing capacity of the underlying deposits is very low. The reinforcement of these problematic soils with granular fill layers is one of the soil improvement techniques that are widely used. Problematic soil behaviour can be improved by totally or partially replacing the inadequate soils with layers of compacted granular fill. The study presented herein describes the use of artificial neural networks (ANNs), and the multi-linear regression model (MLR) to predict the bearing capacity of circular shallow footings supported by layers of compacted granular fill over natural clay soil. The data used in running the network models have been obtained from an extensive series of field tests, including large-scale footing diameters. The field tests were performed using seven different footing diameters, up to 0.90 m, and three different granular fill layer thicknesses. The results indicate that the use of granular fill layers over natural clay soil has a considerable effect on the bearing capacity characteristics and that the ANN model serves as a simple and reliable tool for predicting the bearing capacity of circular footings in stabilized natural clay soil.     

非均质地基上条形基础沉降的随机有限元分析

针对非均质地基土上条形基础弹性沉降计算的复杂性,建立了无量纲化有限元模型,处理了边界距离和弹性模量变异性问题。在确定性分析基础上,分别运用一阶Taylor展开式随机有限元(简称SFEM)和Monte-Carlo数值模拟随机有限元(简称RFEM)分析了土体弹性模量变异性对基础沉降的影响。结果表明,SFEM低估了基础沉降特征值受弹性模量变异性的影响程度。弹性模量变异系数越大,SFEM对基础沉降均值和标准差低估程度越显著,基础沉降均值随弹性模量空间相关距离逐渐减小。RFEM分析结果则呈现波动性但整体有不断增大趋势,因而基础沉降计算结果更为合理。     

合肥地区粘土地基承载力表建立方法的探讨

土的工程性质具有明显的区域性特点,如果简单地将来源于全国范围的地基承栽力经验表应用于某一特定地区,必然会带来地区适应性问题。根据合肥地区的地基场地分类,建立适用于该地区的地基承载力表,正是对全国规范的地基承载力表取消后的积极回应。本文以合肥地区33个工程场地的工程地质资料和地基承载力资料为依据,采用统计回归的方法,建立了地区性粘土地基的承载力表。     

Estimating the bearing capacity of single reinforced granular fill overlying clay

This paper develops an empirical design approach for estimating the footing pressure and settlement behavior of a circular footing on a geogrid reinforced granular fill overlying a weak clay soil by regression analysis. A power model has been developed with a high coefficient of determination R² with 0.959, according to the 398 training data obtained from in-situ tests. The empirical formulation has been evaluated for the validity of the regression model with 220 data which were not used in the derivation of the formulation and the mean absolute percentage error values have been demonstrated that the predictions were obtained with less than 10% error, on average. Additionally, the validity of the developed formulation has been confirmed with different plate load test results from literature, with an acceptable convergence.     

条形粗糙基础极限承载力求解与误差分析

利用滑移线法计算了粗糙条形基础极限承载力,计算时考虑了土的黏聚力c、内摩擦角φ和土体重度g的共同作用,避免了对破裂面形状的人为假定,并满足所有边界条件。将数值计算结果与其他学者的解答进行了对比,证明了解答的准确性。分析了地基承载力系数N_γ的影响因素,证实了N_γ除了与地基摩擦角φ有关外,还与超载比l有关。绘制了不同j值下N_γ随l的关系曲线,给出了N_γ的拟合公式,计算结果表明拟合公式的误差在±4%以内。最后对传统叠加方法计算承载力与精确解之间的误差进行了计算,总结了不同j值时误差e随l的变化规律,发现叠加计算结果比精确解小,且最大误差出现在l介于0.1~1之间。