Seismic interference of two nearby horizontal strip anchors in layered soil

In the present analysis, an attempt is made to explore the seismic response of two nearby horizontal strip anchors embedded in non-homogenous c-? soil deposit at different depths. The analysis is performed by using two-dimensional finite-element software PLAXIS 2D. Each anchor carries equal static safe-working load without violating the ultimate uplift capacity under static condition. The soil is assumed to obey the Mohr?CCoulomb failure criterion. The behavior of single isolated anchor subjected to an earthquake loading is determined first to study the interference effect between two anchors. The horizontal acceleration response obtained from the Loma Prieta Gilroy Earthquake (1989) is considered as the input excitation in the analysis. A parametric study is performed by varying the clear spacing (S) between the anchors at different embedment ratios (??). The magnitude of vertical displacement, shear stress, and shear strain developed at different locations of the failure domain is determined for different clear spacings between the anchors.     

Bearing capacity tests of strip footings on reinforced layered soil

The ultimate bearing capacity of strip footings resting on subsoil consisting of a strong sand layer (reinforced/unreinforced) overlying a low bearing capacity sand deposit has been investigated. Three principal problems were analysed based on results obtained from the model tests as follows: (1) the effect of stratified subsoil on the foundations bearing capacity; (2) the effect of reinforcing the top layer with horizontal layers of geogrid reinforcement on the bearing capacity; (3) effect of reinforcing stratified subsoil (reinforced and unreinforced) on the settlement of the foundation. It has been observed that reinforcing the subsoil after replacing the top layer of soil with a well-graded soil is beneficial as the mobilization of soil-reinforcement frictional resistance will increase.     

Upper bound limit analysis for finding interference effect of two nearby strip footings on sand

The ultimate bearing capacity of two closely spaced strip footings, placed on a cohesionless medium and loaded simultaneously to failure at the same magnitude of failure load, was determined by using an upper bound limit analysis. A logarithmic spiral radial shear zone, comprising of a number of triangular rigid blocks, was assumed to exist around each footing edge. The equations of the logarithmic spiral arcs were based on angles φ_L and φ_R rather than soil friction angle φ; the values of φ_L and φ_R were gradually varied in between 0 and φ. The ultimate bearing capacity was found to become maximum corresponding to a certain critical spacing between the footings. For spacing greater than the critical, the bearing capacity was found to decrease continuously with increase in the spacing. The extent of the spacing corresponding to which the ultimate bearing capacity becomes either maximum or equal to that of a single isolated footing increases with increase in φ. The results compare reasonably well with the available theoretical and experimental data.     

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.     

Probabilistic analysis of strip footings resting on a spatially random soil using subset simulation approach

The failure probability of geotechnical structures with spatially varying soil properties is generally computed using Monte Carlo simulation (MCS) methodology. This approach is well known to be very time-consuming when dealing with small failure probabilities. One alternative to MCS is the subset simulation approach. This approach was mainly used in the literature in cases where the uncertain parameters are modelled by random variables. In this article, it is employed in the case where the uncertain parameters are modelled by random fields. This is illustrated through the probabilistic analysis at the serviceability limit state (SLS) of a strip footing resting on a soil with a spatially varying Young's modulus. The probabilistic numerical results have shown that the probability of exceeding a tolerable vertical displacement (P _e) calculated by subset simulation is very close to that computed by MCS methodology but with a significant reduction in the number of realisations. A parametric study to investigate the effect of the soil variability (coefficient of variation and the horizontal and vertical autocorrelation lengths of the Young's modulus) on P _e was presented and discussed. Finally, a reliability-based design of strip footings was presented. It allows one to obtain the probabilistic footing breadth for a given soil variability.     

Interference effect of two closely-spaced shallow strip foundations on geogrid-reinforced sand

Summary Geotextiles and geogrids are now being used extensively in many civil engineering construction works. This study presents some laboratory model test results for the ultimate bearing capacity of an isolated, and two closely-spaced, strip foundations resting on unreinforced sand, and sand reinforced with layers of geogrid. Based on the model test results, the variation of the group efficiency with the centre-to-centre spacing of the foundation has been determined.     

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。     

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.     

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.     

Probabilistic analysis of strip footings based on enhanced Kriging metamodeling

Two advanced Kriging metamodeling techniques were used to compute the failure probability of geotechnical structures involving spatially varying soil properties. These methods are based on a Kriging metamodel combined with a global sensitivity analysis that is called in literature Global Sensitivity Analysis-enhanced Surrogate (GSAS) modeling for reliability analysis. The GSAS methodology may be used in combination with either the Monte Carlo simulation (MCS) or importance sampling (IS) method. The resulting Kriging metamodeling techniques are called GSAS-MCS or GSAS-IS. The objective of these techniques is to reduce the number of calls of the mechanical model as compared with the classical Kriging-based metamodeling techniques (called AK-MCS and AK-IS) combining Kriging with MCS or IS. The soil uncertain parameters were assumed as non-Gaussian random fields. EOLE methodology was used to discretize these random fields. The mechanical models were based on numerical simulations. Some probabilistic numerical results are presented and discussed.     

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.     

Stochastic model for settlement: footings on cohesionless soil

In this paper, given an estimate of the bearing capacity of the soil, by treating settlement at a given load as a random variable and the evolution of settlement of footing on cohesionless soil with the increasing load as a stochastic process, a tri-level homogeneous Markov chain (TLHMC) model is proposed for prediction of settlement. Comparison of the predicted mean and bounds on settlements, obtained using TLHMC, with the respective field values obtained from literature shows that the stochastic evolution can be modelled using TLHMC with a correlation coefficient of 0.90. A methodology for reliability-based design of footings is also presented and its use is demonstrated through a numerical example.     

A note on the effect of mesh pattern on the lower-bound bearing capacity of embedded strip footings

This study deals with the prediction of the lower-bound bearing capacity of embedded smooth strip footings. The effect of mesh pattern on the result has been studied and a generalized mesh pattern has been proposed. The results obtained are compared with the computed solution using Meyerhof's bearing capacity equation.     

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.     

The influence of load inclination on the undrained bearing capacity of strip footings on slopes

The effect of inclined loading on the bearing capacity of foundations on horizontal ground surface is well established and both the exact solution and simpler empirical equations are available for the calculation of the failure loads. However, for footings on or near slopes complete solutions are available only for vertical loading. This paper investigates the influence of inclined loading on the horizontal and vertical failure loads. The finite element, upper bound plasticity and stress field methods are used to examine a wide range of geometries and soil properties. The methods are first validated against known solutions for two special cases and are subsequently employed to investigate the effect of the geometrical and material properties on the failure loads and the bearing capacity load interaction diagram. Based on this investigation an empirical equation is proposed for the load interaction diagram for undrained inclined loading of footings on or near slopes.     

Ultimate bearing capacity of equally spaced multiple strip footings on cohesionless soils without surcharge

The ultimate bearing capacity of a group of equally spaced multiple rough strip footings was determined due to the contribution of soil unit weight. The analysis was performed by using an upper bound theorem of limit analysis in combination with finite elements and linear programming. Along the interfaces of all the triangular elements, velocity discontinuities were considered. The value of ξ_γ was found to increase continuously with a decrease in S/B, where (i) ξ_γ is the ratio of the failure load of an interfering strip footing of a given width (B) to that of a single isolated strip footing having the same width and (ii) S is the clear spacing between any two adjacent footings. The effect of the variation of spacing on ξ_γ was found to be very extensive for small values of S/B; ξ_γ approaches infinity at S/B=0. In all the cases, the velocity discontinuities were found to exist generally in a zone only around the footing edge. Copyright © 2008 John Wiley & Sons, Ltd.     

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.     

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.     

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.     

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。