A Simple Limit Equilibrium Approach for Calculation of Ultimate Bearing Capacity of Shallow Foundations on Two-Layered Granular Soils

The bearing capacity of shallow foundations in a non-homogeneous soil profile has been a challenging task in geotechnical engineering. In this paper, a limit equilibrium method is used for calculating bearing capacity factors of shallow foundations constructed on a two-layered granular soil profile. The main objective has been to determine the ultimate bearing capacity computed from equivalent bearing capacity factors N_q and N_γ and comparing that with numerical analysis using finite element methods. It will be shown that the data obtained form the developed method are well comparable with those obtained from FE approach, specially when the difference between shear strength parameters of layers is low which is a practical case for sedimentary soil profiles and also for artificially compacted soils. A computer program has been developed to investigate the influence of various parameters on bearing capacity factors.     

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.     

Calculation of seismic bearing capacity of shallow strip foundations using the cell-based smoothed finite element method

This paper adopts an upper bound procedure using the cell-based smoothed finite element method (CS-FEM) to estimate the seismic bearing capacity of shallow strip footings, focussing on seismic soil-structure interactions. In simulations, soil behaviour is assumed as the Mohr–Coulomb material, and increment of plasticity deformation obeys the associated flow rule. The first step of the numerical procedure involves approximating the kinematically admissible displacement fields using the cell-based smoothed finite element method, while the second relates to the establishments of the optimization problem as the conic programming. The inclusion of seismic conditions in the simulations was made using the pseudo-static approach. Initially, three seismic bearing capacity factors were resolved for both smooth and rough foundations by including horizontal and vertical inertia forces caused by the soil weight, the superstructure and the surcharge in the analyses. All seismic bearing capacity components obtained are in excellent agreement with those obtained using the method of characteristics and other finite element analyses. Subsequently, the reduction coefficients that correlate static and seismic bearing capacity factors were computed to facilitate the seismic design of the foundation.

     

港口工程中非均质层状地基承载力计算方法

在深水码头、防浪堤等大型港口工程建设中常常会遇到构筑物下覆地基由非均质的层状土构成的情况。对于这类非均质层状地基,我国港口工程地基规范推荐采用Hansen 61公式、Hansen 69公式和Sokolovskii数值解法3种方法计算地基的极限承载能力。然而,工程实践中由这3种方法计算得出的地基极限承载力数值往往有较大的差别。考虑到规范的继承性,基于牛顿迭代法,针对3个理论计算公式编制了计算程序,根据长江口深水治理二期工程地质实测资料,运用该计算程序对该地区地基的极限承载能力进行了计算比较。计算结果表明,对于非均质层状地基,在相同地质条件、相同荷载条件下Sokolovskii数值解法得到的承载力数值最大,Hansen 69公式得到的承载力数值最小。     

力矩与水平荷载联合作用下裙板式基础破坏包络面研究

联合采用swipe加载模式、固定位移比与固定荷载比加载模式,对于裙板式浅基础在水平荷载与力矩荷载的复合加载条件下的承载性能进行比较系统的平面应变有限元分析,主要探讨了裙板式基础埋深、地基土不排水强度的非均质性对于基础破坏包络面的影响,揭示了地基在水平和力矩荷载的不同组合条件下的失稳破坏机制。同时,对于两种swipe加载模式的有效性进行了比较。计算结果表明：对于非均质土,当裙板式基础埋深与宽度之比大于0.3时,破坏包络面产生正方向倾斜;当埋深与宽度之比小于0.3时,基础的破坏包络面出现负方向倾斜。而在均质土中,基础的破坏包络面没有出现负方向倾斜。     

倾斜与偏心荷载作用下裙板式基础破坏包络面研究

联合采用Swipe加载模式与固定位移比加载模式,对裙板式浅基础在倾斜与偏心荷载两种加载条件下的承载性能进行了比较系统的平面应变有限元分析,主要探讨了裙板式基础埋深、地基土不排水强度的非均质性对基础在竖向荷载V与水平荷载H、竖向荷载V与弯矩M加载平面内的破坏包络面的影响,揭示了地基在不同荷载分量组合条件下的失稳破坏机制。结果表明,基础埋深与地基土强度的非均质性对于地基失稳模式有较大影响,但V-H和V-M平面内的破坏包络面形状具有较好的归一化特性,并分别建议了裙板式基础在倾斜和偏心荷载作用下的破坏包络面方程。     

Discrete element analysis for active and passive pressure distribution on retaining wall

Analysis based on Discrete Element Method (DEM) is presented for active and passive earth pressure distribution behind a retaining wall under different modes of wall movement. Soil mass in the present model is treated as comprising of blocks which are connected by elasto-plastic Winkler-springs. The solution of this method satisfies all equilibrium and compatibility conditions. Formulation of the method is briefly reviewed. Examples are shown to demonstrate the applicability of the method for analyses of earth pressure behind a gravity retaining wall. The DEM can be used to study the sliding patterns of backfill blocks which effect the earth pressure distribution behind the wall. Advantages of this method over the conventional limit equilibrium method are also discussed.     

Allowable Bearing Capacity of Shallow Foundations Based on Shear Wave Velocity

Firstly, the historical background is presented for the determination of ultimate bearing capacity of shallow foundations. The principles of plastic equilibrium used in the classical formulation of the ultimate bearing capacity are reviewed, followed by a discussion about the sources of approximations inherent in the classical theory. Secondly, based on a variety of case histories of site investigations, including extensive bore hole data, laboratory testing and geophysical prospecting, an empirical formulation is proposed for the determination of allowable bearing capacity of shallow foundations. The proposed expression corroborates consistently with the results of the classical theory and is proven to be reliable and safe, also from the view point of maximum allowable settlements. It consists of only two soil parameters, namely, the in-situ measured shear wave velocity, and the unit weight. The unit weight may be also determined with sufficient accuracy, by means of another empirical expression, using the P-wave velocity. It is indicated that once the shear and P-wave velocities are measured in-situ by an appropriate geophysical survey, the allowable bearing capacity is determined reliably through a single step operation. Such an approach, is considerably cost and time-saving, in practice.     

Application of a non-coaxial soil model in shallow foundations

The influence of a non-coaxial model for granular soils on shallow foundation analyses is investigated. The non-coaxial plasticity theory proposed by Rudnicki and Rice (J. Mech. Phys. Solids 1975, 23, 371–394) is integrated into a Drucker–Prager model with both perfect plasticity and strain hardening. This non-coaxial model is numerically implemented into the finite-element program ABAQUS using a substepping scheme with automatic error control. The influence of the non-coaxial model on footing settlement and bearing capacity is investigated under various loading and boundary conditions. Compared with the predictions using conventional coaxial models, the non-coaxial prediction results indicate that the settlement of a footing increases significantly when the non-coaxial component of plastic strain rate is taken into consideration, although ultimate footing bearing capacities are not affected significantly. The non-coaxial model has a different effect on footing settlements under different loading and boundary conditions. In general, the discrepancies between coaxial and non-coaxial predictions increase with increasing rotation of principal stresses of the soil mass beneath a footing. It can be concluded that if the non-coaxial component of plastic strain rate is neglected in shallow foundation problems using the finite-element method, the results tend to be non-conservative when designs are dominated by settlement of footings.     

长短桩组合型复合地基优化设计方法研究

在软土地基上建造建(构)筑物需要进行地基处理,复合地基是一种行之有效的地基处理方式。工程上一般对地基浅层土的承载力要求较高,而深层只需满足下卧层强度要求即可。长短桩复合地基可做到浅层置换率高,深部置换率低,这样就合理地满足了软弱地基不同深度对承载力的要求。同时长短桩复合地基浅部置换率高,加固区复合地基模量大,深部置换率低,复合地基模量较低,正好适应浅部附加应力大,深部附加应力小的应力场,这样对减少软弱地基总沉降有利。本文探讨了长短桩复合地基优化设计方法,提出了长短桩复合地基优化设计数学模型,并利用复合形法求解优化设计数学模型,同时给出了优化设计计算算例,计算结果表明,此优化设计方法不仅可有效地保证长短桩复合地基设计方案技术上可靠,还可获得最佳的经济效益。     

Seismic bearing capacity of shallow foundations near rock slopes using the generalized Hoek–Brown criterion

The seismic bearing capacity of shallow foundations resting on a modified Hoek–Brown rock mass is investigated within the framework of the kinematic approach of limit analysis theory. The analysis focuses on evaluating the reduction in bearing capacity induced by seismic loading and by the proximity of a rock slope. A pseudo‐static approach is adopted to account for the earthquake effects for the seismic bearing capacity evaluations. At the rock material level, the closed‐form expressions previously obtained for the support functions of the rock failure criterion allow the implementation of different failure mechanisms families, and thus to derive rigorous upper bounds estimates of the load‐bearing capacity in both static and seismic conditions. The effects of geometrical, strength and loading parameters are assessed through a large number of parametric computations. Finally, design tables are presented for practical use in rock engineering. Copyright © 2010 John Wiley & Sons, Ltd.     

Experimental and numerical study of soil-reinforcement effects on the low-strain stiffness and bearing capacity of shallow foundations

This paper presents results of meticulous laboratory testing and numerical simulations on the effect of reinforcement on the low-strain stiffness and bearing capacity of shallow foundations on dry sand. The effect of the location and the number of reinforcement layers is studied in the laboratory, whereas numerical simulations are used to study the reinforcement-foundation interaction. Laboratory tests show an increase of 100, 200, and 275% not only in bearing capacity but also in low-strain stiffness (linear load–displacement behaviour) of a square foundation when one, two, and three layers of reinforcement are used, respectively. The specimen preparation technique is found to be crucial for the repeatability and reliability of the laboratory results (less than 5% variability). Numerical simulations demonstrate that if reinforcements are placed up to a depth of one footing width (B) below the foundation, better re-distribution of the load to deeper layers is achieved, thus reducing the stresses and strains underneath the foundation. Numerical simulations and experimental results clearly identify a critical zone between 0.3 and 0.5B, where maximum benefits not only on the bearing capacity but also on the low-strain stiffness of the foundation are obtained. Therefore, soil reinforcement can also be used to reduce low-strain vibrations of foundations.     

Pseudo-static Seismic Bearing Capacity of Shallow Foundations in Unsaturated Soils Employing Limit Equilibrium Method

There exist many structures founded on unsaturated soil deposits. Shear strength augmentation due to the evolution of the matric suction within the unsaturated porous media enhances the bearing capacity of the overlying foundation. This paper presents the evaluation of the pseudo-static seismic bearing capacity of the shallow foundations resting on unsaturated soil deposits using limit equilibrium method. Adopting the Coulomb failure mechanism and Bishop effective stress concept, the bearing capacity equations are solved. The distribution of the matric suction beneath the footing is assumed to be linear. The results of the bearing capacity evaluation are validated against some experimental data found in literature for the static condition. For the seismic loading consideration, the pseudo-static method is utilized. The dual effect of the earthquake acceleration vertical component is thoroughly discussed and a suction transition point is introduced in which the minimum bearing capacity is observed to bear the same value for both upward and downward directions. The increase in the matric suction throughout the soil deposit leads to the increase in the soil shear strength, thus posing more resisting forces as well as higher ultimate bearing capacity. The offered solution is deemed a consistent and useful tool for the accurate prediction of the seismic bearing capacity of shallow footings resting on unsaturated soil deposits.

     

http://www.sciencedirect.com/science/article/pii/S1674987114001625

Rock masses are commonly used as the underlying layer of important structures such as bridges, dams and transportation constructions. The success of a foundation design for such structures mainly depends on the accuracy of estimating the bearing capacity of rock beneath them. Several traditional numerical approaches are proposed for the estimation of the bearing capacity of foundations resting on rock masses to avoid performing elaborate and expensive experimental studies. Despite this fact, there still exists a serious need to develop more robust predictive models. This paper proposes new nonlinear prediction models for the ultimate bearing capacity of shallow foundations resting on non-fractured rock masses using a novel evolutionary computational approach, called linear genetic programming. A comprehensive set of rock socket, centrifuge rock socket, plate load and large-scaled footing load test results is used to develop the models. In order to verify the validity of the models, the sensitivity analysis is conducted and discussed. The results indicate that the proposed models accurately characterize the bearing capacity of shallow foundations. The correlation coefficients between the experimental and predicted bearing capacity values are equal to 0.95 and 0.96 for the best LGP models. Moreover, the derived models reach a notably better prediction performance than the traditional equations.     

软土地基上静压预制桩承载力的工后增大效应

分析了软土地基上预制桩承载力的时效性机理，介绍了几种研究承载力时效性的经验回归公式，结合工程说明应充分认识承载力时效性的科学性和利用这种规律潜在的巨大经济效益。     

New approaches to determine the ultimate bearing capacity of shallow foundations based on artificial neural networks and ant colony optimization

In this study, two different approaches are proposed to determine the ultimate bearing capacity of shallow foundations on granular soil. Firstly, an artificial neural network (ANN) model is proposed to predict the ultimate bearing capacity. The performance of the proposed neural model is compared with results of the Adaptive Neuro Fuzzy Inference System, Fuzzy Inference System and ANN, which are taken in literature. It is clearly seen that the performance of the ANN model in our study is better than that of the other prediction methods. Secondly, an improved Meyerhof formula is proposed for the computation of the ultimate bearing capacity by using a parallel ant colony optimization algorithm. The results achieved from the proposed formula are compared with those obtained from the Meyerhof, Hansen and Vesic computation formulas. Simulation results showed that the improved Meyerhof formula gave more accurate results than the other theoretical computation formulas. In conclusion, the improved Meyerhof formula could be successfully used for calculating the ultimate bearing capacity of shallow foundations.     

非均质各向异性黏土光滑条基承载力上限解

黏土地基中土体强度的非均质和各向异性是比较突出的现象。在已有工作的基础上,根据目前常用的不排水条件下饱和黏土非均质和各向异性强度模型,采用已被证实计算光滑条基极限承载力相当高效的多块体离散模式,编制了考虑强度非均质和各向异性时黏土地基上光滑条基地基承载力计算的多块体上限解计算程序,实现了非均质各向异性黏土地基上光滑条基地基极限承载力的多块体上限解法。为验证多块体上限解法的应用情况,将计算结果与已有的上限解、滑移线解等做了广泛的对比发现,该处计算非均质和各向异性黏土地基上光滑条基极限承载力的上限方法是相当有效的。为方便应用,基于多块体上限方法给出了非均质和各向异性条件下地基承载力系数 的计算曲线。探讨了 随土体强度非均质和各向异性的变化规律。通过分析非均质条件对地基破坏面的影响,揭示了非均质对地基承载力影响的内在原因。     

软黏土中张紧式吸力锚循环承载力简化计算方法

张紧式吸力锚是一种重要的深水浮式平台基础。深水环境中,海底浅层沉积物多为饱和软黏土。软黏土中平均荷载与循环荷载共同作用下吸力锚的循环承载力对其设计至关重要。根据最佳系泊点受倾斜荷载作用下吸力锚的破坏模式,假设不同破坏区土体具有相同的平均剪应力,且平均剪应力与循环剪切强度比等于吸力锚所受静荷载与静荷载和循环荷载之和的比值。结合室内土性试验获得的饱和软黏土样不固结不排水归一化循环剪切强度随归一化平均剪应力的变化关系曲线,建立了破坏区土体不排水循环剪切强度的确定方法。对不同破坏区土体阻力进行分析,按照水平应力具有连续性这一特点,构建了上部滑动楔体破坏区与深部平面流动破坏区交界深度的计算方法,进而提出了计算吸力锚循环承载力的简化极限平衡方法。采用该方法对竖向和水平破坏模式吸力锚循环承载力模型试验结果进行了预测,预测与试验结果基本吻合,最小和最大偏差分别为0.79 %和16.08 %,平均偏差为5.74 %,可较好地反映吸力锚循环承载力随循环破坏次数增加而减小的变化关系,验证了该方法的可行性。     

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.     

Load‐displacement and bearing capacity of foundations on granular soils using a multi‐surface kinematic constitutive soil model

A finite element approach based on an advanced multi‐surface kinematic constitutive model is used to evaluate the bearing capacity of footings resting on granular soils. Unlike simple elastic‐perfectly plastic models, often applied to granular foundation problems, the present model realistically accounts for stress dependency of the friction angle, strain softening–hardening and non‐associativity. After the model and its implementation into a finite element code are briefly discussed, the numerical difficulty due to the singularity at the footing edge is addressed. The bearing capacity factor N_γ is then calculated for different granular materials. The effect of footing size, shape, relative density and roughness on the ultimate bearing capacity are studied and the computed results compare very favourably with the general experimental trends. In addition, it is shown that the finite element solution can clearly represent counteracting mechanisms of progressive failure which have an important effect on the bearing capacity of granular foundations. Copyright © 2006 John Wiley & Sons, Ltd.