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.     

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.     

Bearing capacity factor, <Emphasis Type="Italic">N</Emphasis><Subscript><Emphasis Type="Italic">γ</Emphasis></Subscript>, for unsaturated soils by ZEL method

Bearing capacity of foundations is often determined for saturated state of the soil, regarding its simple and conservative results. This assumption, however, results in very uneconomic and overconservative design for a wide range of climates in the world. In this paper, plasticity equations were employed and extended for unsaturated soils to establish a theoretical approach to investigate the bearing capacity of unsaturated soils. It is achieved by combining the concept of effective stress and plasticity equations in terms of effective stress in unsaturated soils. The advantage of Bishop’s (4) effective stress concept was employed to simplify the equations. The equations were then transformed onto the zero extension lines directions to generalize this method for both associative and non-associative problems by which both stress and velocity field can be determined for unsaturated soils. A computer code was also developed to solve the relatively complex plasticity equations for a wide range of soil friction angles and matric suctions to compute the corresponding bearing capacity factor, N _γ , for strip foundations with smooth and rough base. This factor seems to be one of the major contributors in the bearing capacity of shallow foundations. The results have been presented in design charts and theoretical equations.     

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.     

Determination of partial factors for the verification of the bearing capacity of shallow foundations under open channels

The limit state design method has been introduced into the design criteria for geotechnical structures. The current paper attempts to apply the reliability-based design method, at Level II, to the bearing capacity of the foundations of open channels from the viewpoint of the limit state design. To examine the applicability of the proposed procedure for practical structures, the reliability index is computed for evaluating the stability of the foundations of existing open channels designed by the conventional method. The conventional design procedure makes excessively safe side design. We applied the FORM to the existing open channels designed by the conventional design procedure, and consequently, large values of reliability index, 3 and 5 were obtained for clayey and sandy soils, respectively. Finally, the partial factors for the soil parameters have been determined, corresponding to the target reliability indices β _t =1, 3 and 4.     

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.     

Bearing capacity computation for a ring foundation using the stress characteristics method

The stress characteristics method (SCM) has been used to compute the bearing capacity of smooth and rough ring foundations. Two different failure mechanisms for a smooth footing, and four different mechanisms for a rough footing have been considered. For a rough base, a curvilinear non-plastic wedge has been employed below the footing. The analysis incorporates the stress singularities at the inner as well as outer edges of the ring footing. Bearing capacity factors, N_c, N_q and N_γ are presented as a function of soil internal friction angle (ϕ) and the ratio (r_i/r_o) of inner to outer radii of the footing.     

Bearing capacity of strip foundations reinforced with geogrid sheets by using upper bound finite‐element limit analysis

By using the upper bound finite‐elements limit analysis, with an inclusion of single and two horizontal layers of reinforcements, the ultimate bearing capacity has been computed for a rigid strip footing placed over (i) fully granular, (ii) cohesive‐frictional, and (iii) fully cohesive soils. It is assumed that (i) the reinforcements are structurally strong so that no axial tension failure can occur, (ii) the reinforcement sheets have negligible resistance to bending, and (iii) the shear failure can take place between the reinforcement and soil mass. It is expected that the different approximations on which the analysis has been based would generally remain applicable for reinforcements in the form of geogrid sheets. A method has been proposed to incorporate the effect of the reinforcement in the analysis. The efficiency factors, η_c and η_γ, to be multiplied with N_c and N_γ , for finding the bearing capacity of reinforced foundations, have been established. The results have been obtained (i) for different values of ? in case of fully granular and cohesive‐frictional soils, and (ii) for different rates at which the cohesion increases with depth for a fully cohesive soil. The optimum positions of the reinforcements' layers have also been determined. The effect of the reinforcements' length on the results has also been analyzed. As compared to cohesive soils, the granular soils, especially with higher values of ?, cause a much greater increase in the bearing capacity. The results compare reasonably well with the available theoretical and experimental data from literature. Copyright © 2013 John Wiley & Sons, Ltd.     

Discrete element method for bearing capacity analysis

Analysis based on Discrete Element Method (DEM) is presented for estimating bearing capacity of foundations. Soil mass in the present model is treated as comprising of blocks which are connected by elasto-plastic Winkler-springs. By considering the conditions of compatibility, the boundary stresses on the failure surface and the ultimate bearing capacity of shallow foundations can be obtained. The computed boundary stresses from the present method satisfy equilibrium conditions and do not exceed the material strength. Formulation of the method is presented. Examples are shown to demonstrate the applicability of the method to the analysis of bearing capacity of shallow foundations. Effects of stiffness of Winkler-springs and mesh pattern on the computed results are investigated. The present method is shown to be a useful tool for analyzing bearing capacity of foundations with unusual geometry and loading conditions.     

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.

     

海上风机分段斜壁桶形基础的水平承载力计算方法

在部分浅海由于大型施工船舶无法进入,海上风电工程中传统的重力式基础或桩基础不再适用,为此提出了一种新型基础--分段斜壁桶形基础。基于极限平衡法对分段斜壁桶形基础的水平承载力进行了系统性研究,提出了水平承载力计算方法,并进一步考察了斜壁倾角、桶高、桶径、土性参数等对水平承载力的影响。计算表明,水平承载力随着上部桶壁倾角、下部桶壁倾角、地基反力比例系数、桶基顶部直径、桶基高度的增大而增大,随着海床深度的增加而减小。基于体积压缩率的概念,论证并推荐优先使用上部桶壁倾斜、下部桶壁直立的桶形基础构型。建议发展针对海床地基反力比例系数的准确确定方法。研究结果有助于对桶形基础进行优化设计。     

Bearing capacity of strip foundations with structural skirts

A modified bearing capacity equation is proposed for skirted strip foundations on dense sand. A series of tests on foundation models were carried out to study the factors that affect the bearing capacity of foundations with skirts. Several factors including foundation base friction, skirt depth, skirt side roughness, skirt stiffness and soil compressibility were studied and incorporated in the equation. The results obtained from the proposed equation were compared with the results obtained from Terzaghi, Meyerhof, Hansen and Vesic bearing capacity equations for foundations without skirt. Comparison shows that the use of structural skirts can improve the bearing capacity by a factor of 1.5 to 3.9 depending on the geometrical and structural properties of the skirts and foundation, soil characteristics and interface conditions of the soil-skirt-foundation system. This revised version was published online in July 2006 with corrections to the Cover Date.     

Upper bound solutions of bearing capacity of strip footing by pseudo-dynamic approach

This paper presents the pseudo-dynamic analysis of seismic bearing capacity of a strip footing using upper bound limit analysis. However, in the literature, the pseudo-static approach was frequently used by several researchers to compute the seismic bearing capacity factor theoretically, where the real dynamic nature of the earthquake accelerations cannot be considered. Under the seismic conditions, the values of the unit weight component of bearing capacity factor N _γE are determined for different magnitudes of soil friction angle, soil amplification and seismic acceleration coefficients both in the horizontal and vertical directions. The results obtained from the present study are shown both graphically as well as in the tabular form. It is observed that the bearing capacity factor N _γE decreases significantly with the increase in seismic accelerations and amplification. The results are thoroughly compared with the existing values in the literature and the significance of the present methodology for designing the shallow footing is discussed.     

Method for calculating the horizontal bearing capacity of segmentally-tapered bucket foundation of offshore wind turbinesEI北大核心CSCD

Because large construction ships cannot enter the shallow sea, traditional configuration foundations, such as gravity-type foundation and pile foundation, are not suited for offshore wind power project in shallow seas. Therefore, a new type of foundation-segmentally-tapered bucket foundation is proposed. Based on the limit equilibrium method, a systematic method is proposed to calculate the horizontal bearing capacity of the segmentally-tapered bucket foundation. The influences of obliquity of wall, foundation height, top diameter of bucket and soil parameters on the horizontal bearing capacity of the segmentally-tapered bucket foundation are analyzed. It is found that the horizontal bearing capacity increases with the increase of the wall obliquity, soil resistance, top diameter of bucket and foundation height, while decreases with the increase of the depth of seabed. Based on the concept of volume compression ratio, the bucket foundation with inclined upper section wall and vertical lower section wall is recommended and demonstrated. An accurate method is proposed to determine the proportional coefficient of soil resistance. The results are helpful in the optimization design of traditional bucket foundation.     

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.     

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.

     

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.     

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。     

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.     

Influence of random heterogeneity of the friction angle on bearing capacity factor Nγ

ABSTRACT

Probabilistic methods in geotechnical engineering have received a lot of attention during the last decade and different methodologies are used to capture the inherent variability of soil in different geotechnical engineering problems. In this paper, numerical simulations are conducted to obtain the bearing capacity factor, N_γ, for a purely frictional heterogenous soil where the friction angle is modelled as randomly distributed throughout the domain and the effect of its spatial variability on N_γ is investigated. A finite element method, based on the upper bound limit analysis was combined with random field theory and linear programming to develop a probabilistic analysis. Monte Carlo simulations were performed and the effect of the variability of the friction angle defined by statistical parameters on the bearing capacity factor was investigated. Results show that the mean bearing capacity factor N_γ of a footing on a spatially variable cohesionless soil is generally higher than the deterministic N_γ obtained from a constant mean value. Increasing the heterogeneity of the friction angle by an increase in the coefficient of variation generally increases this deviation. This can be explained by the nonlinearity of the relationship between N_γ and the friction angle.