Relationships Between Settlements of Circular and Square Bearing Plates/Footings and Deformation Zones Developing Beneath Them

ASTM Standards instruct experimenters to use circular or square bearing plates/footings having areas ranging between 0.073 and 0.456 m². In general, researchers and contractors perform loading bearing plate/footing tests using plates/footings which have dimensions exceeding the ones recommended by the Standards. This paper offers formulas describing relationships between settlements of square and circular plates/footings having areas ranging between 0.5 and 4.0 m² and deformation zones developing beneath them. The proposed formulas are verified by the results of field tests performed with circular and square plates or footings supported by cohesive soils.     

Behaviour of model footing on pond ash

This paper focuses on the effective utilization of pond ash, as foundation medium. A series of laboratory model tests have been carried out using square, rectangular and strip footings on pond ash. The effects of dry density, degree of saturation of pond ash, size and shape of footing on ultimate bearing capacity of shallow foundations are presented in this paper. Local shear failure of a square footing on pond ash at 37% moisture content (optimum moisture content) is observed up to the values of dry density 11.20 kN/m³ and general shear failure takes place at the values of dry density 11.48 kN/m³ and 11.70 kN/m³. Effects of degree of saturation on ultimate bearing capacity were studied. Experimental results show that degree of saturation significantly affects the ultimate bearing capacity of strip footing. The effect of footing length to width ratio (L/B), on increase in ultimate bearing capacity of pond ash, is insignificant for L/B ≥ 10 in case of rectangular footings. The effects of size of footing on ultimate bearing capacity for all shapes of footings viz., square, rectangular and strip footings are highlighted.     

Bearing capacity of two close strip footings on soft clay reinforced with geotextile

For many years ago, the beneficial effects of using reinforcement to improve the property of soil have been demonstrated. Over the last three decades, the use of polymeric reinforcement such as geotextile has increased in geotechnical engineering. Among the possible applications, earth reinforcement techniques have become useful and economical techniques to solve many problems in geotechnical engineering practice, such as improve the bearing capacity and settlement characteristics of the footing. This research presents the effect of geotextile inclusion on the bearing capacity of two close strip footings located at the surface of soft clay. A broad series of finite element analysis were performed on two footings with width of 1 and 2 m using two-dimensional plane strain model using the computer code Plaxis (ver 8). Only one type of soft clay was used for the analysis, and the soil was represented by two yielding criteria including hardening soil model and Mohr–Coulomb model, while reinforcement was represented by elastic element, and at the interface between the reinforcements and soft clay, interface elements have been used. A wide range of boundary conditions, including unreinforced and reinforced cases, was analyzed by varying parameters such as number of geotextile layers, vertical spacing of layers, depth to topmost layer of geotextile, tensile stiffness of geotextile layers, and distance of between two footings. From numerical results, the bearing capacity ratio and the interference factor of the foundations have been estimated. On the basis of the analysis performed in this research, it can be concluded that there is a best distance between footings and optimum depth for topmost layer to achieve maximum bearing capacity for closely spaced strip footings. The bearing capacity was also found to increase with increasing number of reinforcement layers if the reinforcements were placed within a range of effective depths. In addition, the analysis indicated that increasing reinforcement stiffness beyond a threshold value does not result in a further increase in the bearing capacity.     

Analysis of square and rectangular footings subjected to eccentric-inclined load resting on reinforced sand

In the present paper, a method of analysis for calculating the pressure intensity corresponding to a given settlement for eccentrically and obliquely loaded square and rectangular footings resting on reinforced soil foundation has been presented. The process has been simplified by presenting non-dimensional charts for the various terms used in the analysis, which can be directly used by practicing engineers. An approximate method has been suggested to find out the ultimate bearing capacity of such footings on reinforced soil. The results have been validated with the model test results. The procedure has been made clear by giving an illustrative example.     

Two- and three-dimensional bearing-capacity solutions for footings on two-layered clays

In this paper, finite element analysis is used to predict the undrained bearing capacity of strip, square and circular footings resting on layered clays. The soil profile consists of two clay layers with different thicknesses and properties. The results are compared with previous solutions for strip footings on layered clays. The bearing-capacity behaviour is discussed and the bearing-capacity factors are given for various cases involving a range of layer thicknesses and properties of the two clay soil layers.     

Vertical and horizontal deformation of an inhomogeneous elastic half-space

Vertical and horizontal deformations of surface footings have been studied for an inhomogeneous elastic half-space in which the shear modulus increases with an arbitrary power of depth, n, and Poisson's ratio is constant. A general solution for displacements has been obtained first for point loads applied in vertical and horizontal directions. These are then used in obtaining closed-form solutions for displacements of uniformly loaded circular and rectangular footings. Finally, a numerical method is described that can be used to analyse a rigid footing of an arbitrary shape, and results for rigid rectangular footings are given.     

Bearing capacity of interfering multiple strip footings by using lower bound finite elements limit analysis

The ultimate bearing capacity of a number of multiple strip footings, identically spaced and equally loaded to failure at the same time, is computed by using the lower bound limit analysis in combination with finite elements. The efficiency factor (ξ_γ), due to the component of soil unit weight, is computed with respect to changes in the clear spacing (S) between the footings. It is noted that the failure load for a footing in the group becomes always greater than that of a single isolated footing. The values of ξ_γ for the smooth footings are found to be always lower than the rough footings. The values of ξ_γ are found to increase continuously with a decrease in the spacing between footings. As compared to the available theoretical and experimental results reported in literature, the present analysis provides generally a little lower values of ξ_γ.     

Reliability Based Assessment of Shallow Foundations Using Mathcad

A reliability based method was used to design and analyse shallow foundations using first-order Taylor series approximation. The computer program Mathcad was used to facilitate all mathematical and computional efforts. This method is an effective tool to assist the foundation designers and analyists to investigate how reliable their designs or analyses are in relation to the ultimate bearing capacity of the foundations. The approach presented in this paper provides a reliable alternative for design and analysis of shallow foundations, rather than the conventional design methods, which employs the assumptions of a specified saftey factor. Several examples were presented for design and analysis of strip footings embedded in sandy soil, and rectangular and square footings analysis embedded in clayey soils. The program input and output of each example are also presented and discussed.     

Interference effect of two nearby strip footings on layered soil: theory of elasticity approach

In recent times, rapid urbanisation coupled with scarcity of land forces several structures to come up ever closer to each other, which may sometime cause severe damage to the structures from both strength and serviceability point of view, and therefore, a need is felt to devise simplified methods to capture the effect of footing interference. In the present study, an attempt has been made to model the settlement behaviour of two strip footings placed in close spacing on layered soil deposit consisting of a strong top layer underlying a weak bottom layer. Theory of elasticity is employed to derive the governing differential equations and subsequently solved by the finite difference method. The perfectly rough strip footings are considered to be resting on the surface of two-layer soil system, and the soil is assumed to behave as linear elastic material under a range of static foundation load. The effect of various parameters such as the elastic moduli and thickness of two layers, clear spacing between the footings and footing load on the settlement behaviour of closely spaced footings has been determined. The variation of vertical normal stress at the interface of two different soil layers as well as at the base of the failure domain also forms an important part of this study. The results are presented in terms of settlement ratio (ξ_δ), and their variation is obtained with the change in clear spacing between two footings. The present theoretical investigation indicates that the settlement of closely spaced footings is found to be higher than that of single isolated footing, which further reduces with increase in the spacing between the footings.     

土钉墙地基承载力问题探讨

土钉墙墙底地基土的承载力验算是土钉墙支护设计的一项重要内容。国内的工程实践中,通常将土钉墙地基承载力与坑底土抗隆起验算合并考虑。针对具体案例,通过Plaxis3D有限元数值模拟,分析研究了土钉墙底部土体发生地基承载力失稳的破坏模式、破坏荷载以及土钉墙墙底应力分布特点等,探讨了依据我国相关规程进行土钉墙坑底隆起或地基承载力计算可能存在的问题。借鉴国外加筋土挡墙地基承载力计算的一般方法,将土钉墙作为荷载倾斜、偏心的刚性基础对待,利用荷载倾斜、偏心条件下传统刚性浅基础的地基承载力的Meyerhof解和Vesic解,对土钉墙地基承载力进行了计算和对比,通过对比发现,Meyerhof解更接近实际,据此,提出了土钉墙地基承载力计算的合理模式。     

破坏包络面理论在多基础系统中的应用研究

由多个分离基础组成的多基础系统是常用的海洋结构基础型式。基于破坏包络面理论,分析了砂土地基多基础系统的失效模式,建立了相应的承载力计算方法,并验证了计算方法的可行性。对比分析了单一基础和多基础系统不同荷载路径下的荷载安全系数,探讨了破坏包络面理论与分项系数法相结合的基础承载力计算方法。失效模式的分析表明,由于水平荷载的增大,四腿平台结构迎浪侧基础首先到达破坏包络线,其失效模式属于滑动失稳,但由于基础间的运动约束,其并不会出现真正的滑移破坏。随着水平荷载进一步地增大,迎浪侧基础承担的水平和竖向荷载不断减小,导致背浪侧基础受到不断增大的荷载。最终,背浪侧基础也到达破坏包络线,多基础系统失效。分析表明,荷载路径对基础的荷载安全系数有决定性的影响,计算基础的荷载安全系数需指明相应的荷载路径。鉴于破坏包络面的大小和形状取决于众多因素,基础设计时需采用特定工况下的破坏包络面进行承载力计算。     

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.     

Upper-bound multi-rigid-block solutions for bearing capacity of two-layered soils

The limit analysis method has been widely used in the stability analysis of geotechnical problems including the bearing capacity of foundations. Two main approaches have been followed in the limit analysis to improve the calculation of the bearing capacity of foundations. One approach is to combine limit analysis with the finite element method and linear/nonlinear programming. The other is to use a multi-rigid-block mechanism to obtain an upper-bound solution. In this paper, the multi-rigid-block upper-bound method with a modified failure mechanism from that of Florkiewicz [Florkiewicz A. Upper bound to bearing capacity of layered soils. Can Geotech J 1989;26(4):730–6.] was employed to calculate the bearing capacity of foundations. Attention was paid particularly to the bearing capacity of strip footings over a two-layered soil. In order to verify the effectiveness of the modified mechanism, comparisons were made with other well-known solutions. The results showed improvements over the best available multi-rigid-block upper-bound solutions given by Michalowski and Shi [Michalowski RL, Shi L. Bearing capacity of footings over two-layer foundation soils. J Geotech Eng ASCE 1995;121(5):421–8.], and fair consistence with the results from the finite element limit analysis in Shiau et al. [Shiau JS, Lyamin AV, Sloan SW. Bearing capacity of a sand layer on clay by finite element limit analysis. Can Geotech J 2003;40(5):900–15.].     

Centrifuge modeling of surface footings on a sand layer underlain by a rigid base

The results of centrifuge modeling of surface footings on a sand layer underlain by a rigid base are presented. The primary objective was to investigate the effect of sand layer thickness on the ultimate bearing capacity. The relative density of the sand layer and shapes of the model footings were also varied in the test program. The data indicate that prototype size footings are likely to experience local shear failure rather than general shear type failure. The observed values of the bearing capacity are compared with the predictions based on the Mandel and Salencon (1972) theory. It is concluded that theoretical predictions are conservative in relation to the experimental bearing capacity values, if appropriate values of mobilized angles of friction are used. This revised version was published online in July 2006 with corrections to the Cover Date.     

Finite element modelling of pressuremeter tests and footings on frozen soils

A finite element code is developed to model the structure-frozen soil/ice interaction using a time incrementing, fully implicit, iterative algorithm, and a constitutive model based on the concept that total strain tensor consists of an elastic and a creep component. The code is used to investigate the applicability and limitations of the power law as the creep model for frozen soil by simulating two pressuremeter tests. Two extended phenomenological models based on the generalized power law are used in axisymmetric finite element analyses to simulate two, long-term, stage-loaded pressuremeter tests, and comparison of results with test data indicates that one model demonstrates a better ability to approximate the actual response to subsequent load steps, under certain restrictions. Stress analyses demonstrate the ability of the constitutive model to show transient as well as subsequent quasi-stationary stress stages in creep analysis. Additional simulations of short-term pressuremeter tests on ice are performed to further illustrate some limitations of the power-law model. Examples for prediction of creep settlements on frozen geomaterials are demonstrated by considering the interaction of fully flexible circular footings and concrete cylindrical footings (of different embedment depths) with frozen sands.     

条形埋置基础固结分析计算图表

基于比奥固结理论,用有限元方法研究了有限饱和土层中条形埋置基础的固结沉降特性。仔细分析了影响固结度的3个参数：基础埋深与土层厚度的比值;土层厚度与基础宽度的比值;土骨架的泊松比。根据分析结果,提出了归一化无量纲时间,并给出了计算条形埋置基础固结度的计算图表。这些图表为基础设计提供了便捷准确的计算方法。运用文中图表计算固结度的最大误差不超过3 %。     

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.     

Simple superposition approach for dynamic analysis of piled embedded footings

The effectiveness and accuracy of the superposition method in assessing the dynamic stiffness and damping coefficients (impedance functions) of embedded footings supported by vertical piles in homogeneous viscoelastic soil is addressed. To this end, the impedances of piled embedded footings are compared to those obtained by superposing the impedance functions of the corresponding pile groups and embedded footings treated separately, with the magnitude of the relative average differences being around 10–30%. The results are presented in a set of dimensionless graphs and simple expressions that can be used to estimate the dynamic stiffness and damping of piled embedded footings, provided that the impedance functions of the two individual components are known. This is precisely the reason why the superposition approach studied here is appealing, because such impedance functions for both embedded footings and pile groups are available for a wide range of cases. How to estimate the kinematic response functions of the system when those of the individual components are known is also discussed. To address the problem, parametric analyses performed using a 3D frequency‐domain elastodynamic BEM‐FEM formulation are presented for different pile–soil stiffness contrasts, embedment depths, pile‐to‐pile separations and excitation frequencies. Vertical, horizontal, rocking, and cross‐coupled horizontal‐rocking impedance functions, together with translational and rotational kinematic response functions, are discussed. The results suggest that the superposition concept, in conjunction with a correction strategy as that presented herein, can be employed in geotechnical design. For kinematic effects, the response functions of the embedded footing are found to provide reasonable estimates of the system's behaviour. Copyright © 2011 John Wiley & Sons, Ltd.     

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 Factors of Ring Footings by Using the Method of Characteristics

Ring footings can be more effective and economical than circular footings. In spite of similarities between circular and ring footings, their behaviors are different in some respects such as bearing pressure distribution under the footing and settlement. But no exclusive theoretical prediction of ultimate bearing capacity has been reported for ring footings. In the present study, stress characteristics method is employed for coding the bearing capacity of ring footing with horizontal ground surface. In the calculations, friction at the contact between the soil and foundation is considered. In this research, the soil obeys the Mohr–Coulomb yield criterion and that is cohesive–frictional-weighted with applied surcharge pressure. The bearing capacity factors Nγ, Nq and Nc for ring footings were calculated by a written code based on the method of characteristics. Bearing capacity was determined for different conditions of soil and different ratio of radii in comparison with the principle of superposition results. The findings show that the principle of superposition is effective for determining the bearing capacity of a ring footing.