Bearing capacity of square footings on reinforced layered soil

In the present study, an approximate method has been suggested to calculate the ultimate bearing capacity of a square footing resting on reinforced layered soil. The soil is reinforced with horizontal layers of reinforcement in the top layer of soil only. The pre requisite to the method is the ultimate bearing capacity of unreinforced layered soil, which can be determined from the methods already available in literature. The results have been validated with the model tests conducted on two layered soil compacted at different densities and the top layer reinforced with horizontal layers of geogrid reinforcement.     

Bearing capacity of rectangular footing on reinforced soil

In the present paper, a method of analysis for calculating the pressure intensity corresponding to a given settlement for a rectangular footing 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 empirical method has been suggested to find out the ultimate bearing capacity of footing on reinforced soil. The results have been validated with large-scale model tests also. The procedure has been made clear by giving an illustrative example. This revised version was published online in July 2006 with corrections to the Cover Date.     

Closely spaced rectangular footings on reinforced sand

In this paper, an analysis has been presented for calculating the pressure of an adjacent rectangular footing resting on reinforced sand for a given settlement. An approximate method has been suggested to compute the ultimate bearing capacity of adjacent footings resting on reinforced earth slab. The computation of normal force on the reinforcement area and estimation of interfacial friction coefficient at different layer levels are two essential steps in computation of pressure ratio. The process has been simplified by presenting suitable charts in non-dimensional form that can be directly used by practicing engineers.     

Seismic bearing capacity of shallow strip footings

Seismic bearing capacity of shallow strip footings in soil has been obtained in the form of pseudo-static seismic bearing capacity factors N_cd, N_qd and N_d, denoting the cohesion, surcharge and unit weight components, respectively, by an extensive numerical iteration technique. Limit equilibrium method of analysis with composite failure surface is assumed. The validity of the principle of superposition is examined. Effects of both the horizontal and vertical seismic acceleration coefficients have been found to always reduce the ultimate bearing capacity significantly. Results obtained by the present method of analysis are compared with the available results and are found to be the least in the seismic case.     

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.     

Pressure–settlement characteristics of rectangular footings on reinforced sand

A method has been proposed to obtain the pressure–settlement characteristics of rectangular footings resting on reinforced sand based on constitutive laws of soils. The confining effect of the reinforcement provided in the soil at different layers has been incorporated in the analysis by considering the equivalent stresses generated due to friction at the soil– reinforcement interface. The prerequisite of the method is the value of ultimate bearing capacity, which can be obtained from the approaches already available in literature. The value of settlement may be read directly from pressure–settlement curves for the given pressure intensity. Therefore, the rectangular footing resting on reinforced sand can be proportioned satisfying shear failure and settlement criteria.     

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.     

Numerical study of the bearing capacity for two interfering strip footings on sands

Current studies of bearing capacity for shallow foundations tend to rely on the hypothesis of an isolated footing. In practice a footing is never isolated; it is mostly in interaction with other footings. This paper focuses on a numerical study using the finite-difference code Fast Lagrangian Analysis of Continua (FLAC), to evaluate the bearing capacity for two interfering strip footings, subjected to centered vertical loads with smooth and rough interfaces. The soil is modeled by an elasto-plastic model with a Mohr–Coulomb yield criterion and associative flow rule. The interference effect is estimated by efficiency factors, defined as the ratio of the bearing capacity for a single footing in the presence of the other footing to that of the single isolated footing. The efficiency factors have been computed individually to estimate the effects of cohesion, surcharge, and soil weight using Terzaghi’s equation, both in a frictional soil with surcharge pressures and in a cohesive-frictional soil with surcharge pressures. The results have been compared with those available in the literature.     

复合加载情况下非均质地基上条形基础的极限承载力研究

复合加载情况下精确求解非均质地基上条形基础的极限承载力以及评价影响极限承载力的相关因素,具有很强的工程实用与理论参考价值。基于极限平衡原理,在Mohr-Coulomb破坏准则的基础上,将非均质地基上条形基础极限承载力问题等价为一个边界待定的泛函极值问题。利用变分原理得到与平衡方程相等价的积分约束条件以及相应的欧拉方程与横截条件。引入问题边界条件,利用VC++6.0编制了数值计算程序,求得了复合加载情况下非均质地基破坏时的滑裂面函数与破坏包络曲线。从理论上研究了土体内摩擦角、土体黏聚力、土层强度比与地下水位变化等因素对地基破坏包络曲线的影响。研究结果表明,其解答是地基极限承载力真实解的某一最小上限。     

Bearing capacity of ring footings on cohesionless soil under eccentric load

This paper presents a study on the bearing capacity of eccentrically-loaded rough ring footings resting over cohesionless soil. To this aim, a series of 3D numerical simulations were performed using the finite difference method. In order to consider the effect of load eccentricity, reduction factor method is applied. In this method, the ratio of an eccentrically-loaded bearing capacity to the bearing capacity of the same footing under vertical load is defined. Comparison between the results of the numerical simulations with those of analytical solutions and experimental data indicates good agreement. A mathematical expression is also introduced for eccentrically-loaded ring footings.     

Bearing capacity of strip and circular footings in sand using finite elements

Design of shallow foundations relies on bearing capacity values calculated using procedures that are based in part on solutions obtained using the method of characteristics, which assumes a soil following an associated flow rule. In this paper, we use the finite element method to determine the vertical bearing capacity of strip and circular footings resting on a sand layer. Analyses were performed using an elastic–perfectly plastic Mohr–Coulomb constitutive model. To investigate the effect of dilatancy angle on the footing bearing capacity, two series of analyses were performed, one using an associated flow rule and one using a non-associated flow rule. The study focuses on the values of the bearing capacity factors N_q and N_γ and of the shape factors s_q and s_γ for circular footings. Relationships for these factors that are valid for realistic pairs of friction angle and dilatancy angle values are also proposed.     

Bearing capacity of strip footings on spatially random soils using sparse polynomial chaos expansion

A probabilistic model is presented to compute the probability density function (PDF) of the ultimate bearing capacity of a strip footing resting on a spatially varying soil. The soil cohesion and friction angle were considered as two anisotropic cross‐correlated non‐Gaussian random fields. The deterministic model was based on numerical simulations. An efficient uncertainty propagation methodology that makes use of a non‐intrusive approach to build up a sparse polynomial chaos expansion for the system response was employed. The probabilistic numerical results were presented in the case of a weightless soil. Sobol indices have shown that the variability of the ultimate bearing capacity is mainly due to the soil cohesion. An increase in the coefficient of variation of a soil parameter (c or φ) increases its Sobol index, this increase being more significant for the friction angle. The negative correlation between the soil shear strength parameters decreases the response variability. The variability of the ultimate bearing capacity increases with the increase in the coefficients of variation of the random fields, the increase being more significant for the cohesion parameter. The decrease in the autocorrelation distances may lead to a smaller variability of the ultimate bearing capacity. Finally, the probabilistic mean value of the ultimate bearing capacity presents a minimum. This minimum is obtained in the isotropic case when the autocorrelation distance is nearly equal to the footing breadth. However, for the anisotropic case, this minimum is obtained at a given value of the ratio between the horizontal and vertical autocorrelation distances. Copyright © 2012 John Wiley & Sons, Ltd.     

ANN-based model for predicting the bearing capacity of strip footing on multi-layered cohesive soil

In reality, footings are most likely to be founded on multi-layered soils. The existing methods for predicting the bearing capacity of 4-layer up to 10-layer cohesive soil are inaccurate. This paper aims to develop a more accurate bearing capacity prediction method based on multiple regression methods and multi-layer perceptrons (MLPs), one type of artificial neural networks (ANNs). Predictions of bearing capacity from the developed multiple regression models and MLP in tractable equations form are obtained and compared with the value predicted using traditional methods. The results indicate ANNs are able to predict accurately the bearing capacity of strip footing and outperform the existing methods.     

Bearing capacity of two interfering footings

By using an upper bound limit analysis in conjunction with finite elements and linear programming, the ultimate bearing capacity of two interfering rough strip footings, resting on a cohesionless medium, was computed. Along all the interfaces of the chosen triangular elements, velocity discontinuities were employed. The plastic strains were incorporated using an associated flow rule. For different clear spacing (S) between the two footings, the efficiency factor (ξ_γ) was determined, where ξ_γ is defined as the ratio of the failure load for a strip footing of given width in the presence of the other footing to that of a single isolated strip footing having the same width. The value of ξ_γ at S/B = 0 becomes equal to 2.0, and the maximum ξ_γ occurs at S/B = S_cr/B. For S/B?S_cr/B, the ultimate failure load for a footing becomes almost half that of an isolated footing having width (2B + S), and the soil mass below and in between the two footings deforms mainly in the downward direction. In contrast, for S/B>S_cr/B, ground heave was noticed along both the sides of the footing. As compared to the available theories, the analysis provides generally lower values of ξ_γ for S/B>S_cr/B. Copyright © 2007 John Wiley & Sons, Ltd.     

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.     

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.     

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.     

Estimation of bearing capacity for multiple footings in sand

In the present study, the effects of multiple-footing configurations in sand on bearing capacity were investigated using field plate load tests and finite element analyses. Both strip and spread footings were considered in the finite element analyses. In each case, different footing distances were applied for the purposes of comparison among all of the results. From these results, it was observed that the load responses of multiple footings are similar to those of the single footing at distances greater than three times the footing width. Design equation and correlation parameters, necessary for quantifying the values of the bearing capacity ratio for the different multiple-footing configuration, were derived. Experimental test results from the literature were selected and used in verifying the proposed method.     

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.     

加筋膨胀土不同布筋型式三轴试验研究

基于三轴试验方法,对不同布筋方式的加筋膨胀土试样的强度特性和变形过程进行研究。室内三轴试验表明,非均匀加筋型式较适合低围压、变形小的加筋土体工程;高围压、大变形的加筋土体工程采用均匀布筋型式将会取得较好的效果。试样变形过程表明,加筋试样随着轴压的增加,将会形成多鼓状变形,并且中间土体最终变形将超过端部土体变形;该变形过程可较好地解释加筋挡土墙随着时间和外部荷载的作用出现中间部分突出的现象。试验结果对加筋土体施工将会起到一定的指导意义。