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。     

砂-黏土双层地基极限承载力的数值研究

在实际工程中,常见天然的或通过人工换填形成的上部砂土、下部黏土的层状地基,目前关于这种双层地基极限承载力和破坏机制研究还不够深入。通过有限差分法建立双层地基数值模型,分析基底粗糙程度、砂土剪胀角和超载对地基破坏模式及极限承载力的影响,并根据有限差分法计算结果对强度加权平均法、应力扩散法和冲剪破坏法等现有实用计算方法的估算正确性进行评价。研究结果表明,基底粗糙程度对极限承载力的影响随着砂土内摩擦角的增大而减小;当剪胀角较小时,剪胀角变化对承载力的影响更为明显;当下层黏土强度较小时,超载的作用更明显。强度加权平均法由于低估破坏面影响深度导致砂土层权重较大,计算结果偏大;应力扩散法忽略了砂土剪切强度,在砂土层较厚时出现低估;冲剪破坏法由于可较为精确地计算砂土破坏面上抗剪强度和被动土压力,是3种实用方法中计算最准确的,当砂土厚度和黏土强度较大时,建议按太沙基经验公式对下卧黏土进行局部剪切破坏修正后确定极限承载力。     

空洞上方浅基础地基破坏模式与极限承载力分析

利用极限分析上限法求解地基极限承载力问题的关键在于构造合适的破坏模式。当地基下方存在空洞时,地基的破坏模式变得相当复杂。通过分析空洞存在时地基的受力特点及破坏形态,将地基破坏范围划分成为不同的刚性区和过渡区,构造了空洞上方条形基础地基的破坏模式。利用上限法,建立与破坏模式对应的速度场,推导了破坏模式不同区域内的耗散功率和外力功率,得到地基极限承载力的目标函数,并采用数学优化方法进行求解,获得了极限承载力的上限解。通过算例分析,讨论了空洞顶板厚度、空洞大小与地基极限承载力的关系,并与无空洞条件下地基极限承载力进行对比分析。结果表明,随着空洞顶板厚度增加,地基极限承载力增加,破坏模式也由地基与空洞之间扩散到地基两侧;空洞顶板厚度存在临界值,当超过此临界值时,空洞对地基极限承载力的影响可忽略。     

Bearing capacity of strip footings on <Emphasis Type="Italic">c</Emphasis>–<Emphasis Type="Italic">φ</Emphasis> soils with square voids

The presence of underground voids has an adverse influence on the performance of shallow foundations. In this study, the bearing capacity and failure mechanism of footings placed on cohesive-frictional soils with voids are evaluated using discontinuity layout optimization. By introducing a reduction coefficient, a set of design charts that can be directly applied to the classical bearing capacity formulation is presented. The results indicate that the undrained bearing capacity with voids is sensitive to soil weight and cohesion, as both the bearing capacity and stability issues exist in the problem. The failure mechanism is directly related to a variety of soil properties, the locations of single voids, and the horizontal distance between two voids. The presence of voids has a more dominant effect on c–φ soils compared to that on undrained soil. An interpretation of the critical and adverse locations for single-void and dual-void cases with various soil strengths is presented.     

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.     

非均质地基承载力及破坏模式的FLAC数值分析

利用基于Lagrangian显式差分的FLAC算法，通过数值计算，对黏结力随深度线性增长的非均质地基上条形基础和圆形基础的极限承载力及地基破坏模式进行了对比计算与系统分析。研究表明：（1）随着地基黏结力沿深度非均匀变化系数的增大，地基的破坏范围逐渐集中在地基表层和基础两侧：（2）即使地基的非均质程度较小，当将非均质地基近似地按均质地基考虑时，由此所估算的承载力可能过于保守；（3）地基承载力系数随黏结力沿深度非均匀变化系数的增大而非线性地增大。与数值解相比，skempton与Peck等近似公式均可能高估了非均质地基承载力。     

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.     

Reliability bearing capacity analysis of footings on cohesive soil slopes using RFEM

Reliability analysis of bearing capacity of a strip footing at the crest of a simple slope with cohesive soil was carried out using the random finite element method (RFEM). Analyses showed that the coefficient of variation and the spatial correlation length of soil cohesion can have a large influence on footing bearing capacity, particularly for slopes with large height to footing width ratios. The paper demonstrates cases where a footing satisfies a deterministic design factor of safety of 3 but the probability of design failure is unacceptably high. Isotropic and anisotropic spatial variability of the soil strength was also considered.     

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.     

关于偏心荷载下地基承载力的验算方法

针对偏心荷载作用下的地基承载力验算,以条形基础为例,介绍了Meyerhof提出的考虑荷载偏心的地基承载力计算方法,并通过与有限元上下限极限分析这一极限荷载精细数值计算方法的比较验证了其正确性和准确性。所考虑的地基既包括排水条件下的一般地基,也包括不排水强度随深度近似线性增大的饱和黏性土地基。依据有关机理深入分析了基础埋深对偏心荷载下地基承载力计算精度的影响,明确了可以考虑基础埋深有利作用的偏心距上限。进而采用本课题组所提出计算地基承载力的改进公式,通过计算并结合理论分析比较了国内规范验算方法与按Meyerhof方法的验算,表明采用后一方法更为合理。     

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。     

Developing artificial neural network models to predict allowable bearing capacity and elastic settlement of shallow foundation in Sharjah,United Arab Emirates

This research proposes the use of artificial neural network to predict the allowable bearing capacity and elastic settlement of shallow foundation on granular soils in Sharjah, United Arab Emirates. Data obtained from existing soil reports of 600 boreholes were used to train and validate the model. Three parameters (footing width, effective unit weight, and SPT blow count) are considered to have the most significant impact on the magnitude of allowable bearing capacity and elastic settlement of shallow foundations, and thus were used as the model inputs. Throughout the study, depth of footing was limited to 1.5 m below existing ground level and water table depth taken at the level of the footing. Performance comparison of the developed models (in terms of coefficient of determination, root mean square error, and mean absolute error) revealed that the developed artificial neural network models could be effectively used for predicting the allowable bearing capacity and elastic settlement. As such, the developed models can be used at the preliminary stage of estimating the allowable bearing capacity and settlements of shallow foundations on granular soils, instead of the conventional methods.     

Elasto-viscoplastic finite element study of the effect of degradation on bearing capacity of footing on clay ground

The bearing capacity of footing has been studied by both conventional and numerical methods by many researchers. However, degradation of the microstructure of material, that is, a change in the microstructure of the soil, has not been adequately taken into account. Degradation of microstructure causes strain softening of materials and it leads to strain localization such as shear bands and slip bands. From an engineering point of view the strain localization is crucial because it is a precursor of failure. In the present study, finite element analyses of the bearing capacity of a shallow foundation on homogeneous and inhomogeneous saturated clay strata have been conducted using an elasto-viscoplastic soil constitutive model of microstructure change. A series of analyses of footing on clay deposit with different microstructure parameters have been carried out. Numerical results show that strain localization can be predicted during the loading of rigid footing on highly structured soil and strain localization affects the footing–soil interaction. The effects of footing roughness on the failure mechanism are also discussed in the study.     

Seismic Bearing Capacity of Shallow Strip Footing with Coulomb Failure Mechanism using Limit Equilibrium Method

In this paper, an effort is made to evaluate the seismic bearing capacity of shallow strip footing resting on c–ф soil. The formulation is developed to get a single coefficient of bearing capacity for simultaneous resistance of weight, surcharge and cohesion. Limit equilibrium method in Pseudo-static approach with Coulomb mechanism is applied here to evaluate the seismic bearing capacity. The seismic bearing capacity of footing (q_uE) is expressed in terms of single coefficient N_γE. The effect of various parameters viz. angle of internal friction of soil (ф), angle of wall friction (δ), cohesion (c), ratio of depth to width of footing (d_f/B₀), seismic acceleration (k_h, k_v) are studied on the variation of seismic bearing capacity co-efficients.     

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。     

离心机中球形贯入仪贯入黏土特性

目前球形全流贯入被仪广泛应用于岩土离心试验中,以表征软弱黏土土样的抗剪性能。然而,在离心加速度作用下离心机试验中的球贯入仪比现场使用的标准球贯入仪有更大的加载杆与球的面积比a、更大的等效原型直径以及不一样的球-土摩擦系数,从而使得离心机球体会出现不一样的贯入特性,进而导致不一样的土体抗剪承载力校验系数。通过大变形有限元（large deformation finite element,简称LDFE）方法对中国常见离心机球形贯入仪贯入单层黏土进行分析,获得不同几何尺寸和摩擦系数下球形贯入仪的贯入特性。计算结果通过与有关解析解以及其他前人研究结论的对比分析,验证了有限元分析结果的合理性。通过大量参数分析表明,球摩擦系数对空腔的临界深度以及深层破坏深度的影响较小,面积比a对浅层和深层承载力系数以及达到深层破坏深度有显著的影响。根据数值模拟的结果,提出了不同面积比和摩擦系数下的极限间隙深度Hc、浅层和深层临界破坏模式深度Hd、不同摩擦系数和面积比情况下的深层承载力系数和浅层承载力校准系数的计算公式,从而能获得更精确的土体抗剪强度,为离心机中球形贯入仪的应用提供了理论依据。     

用极限分析法研究饱和地基承载力三维问题

基于土体的三维破坏模式,探讨了饱和地基的极限承载力随基础宽长比的变化规律。研究了基础的形状对极限承载力的影响;通过引入合理的能量安全系数ＦＳ值,进一步探讨了饱和地基三维稳定条件下的承载力设计值问题。     

圆形基础地基极限承载力计算

利用临界滑动场法计算了浅埋圆形基础的地基承载力,并提供了系数N、Nq和Nc的计算表格和曲线,同时分析了侧面土压力对N、Nq的影响。通过建立土体条块极限平衡方程,推导了计算地基承载力的递推关系式。首先,设定土体计算范围,并划分条块和设置状态点; 其次,根据递推公式和推力极值原理计算各个状态点的参数,并搜索临界滑面; 最后,根据搜索出的临界滑面计算地基承载力。通过与已有系数计算值或模型试验的比较,验证了该方法的合理性。研究结果表明:N、Nq和Nc与其他学者的计算值相近; 相同情况下侧面土压力越大系数N、Nq越小。该方法是临界滑动场法在地基承载力研究中的推广应用,原理简单、易于编程,可为深入研究圆形基础地基承载力的计算提供参考。     

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 rectangular footings in uniform clay with deep embedment

This letter is concerned with the undrained bearing capacity of rectangular footings with various aspect ratios and embedment ratios in uniform clay. It covers thin plate foundations with low aspect ratios and high embedment depth with embedment ratio up to 150. The work is based on small strain finite element analysis (FEA). After verification of the FEA model against existing solutions of the bearing capacity factors of rectangular footings, a series of FEA results are obtained. Based on the FEA results, a simple formulation is proposed to calculate the bearing capacity factor for rectangle footing with different aspect ratio in any embedment depth, extending the existing solutions to cover a wider ranges of footing aspect ratios and embedment ratios.