Probabilistic Analysis of Bearing Capacity of Shallow Foundations Using Three-Dimensional Limit Analyses

Simões, João T.; Neves, Luís; Antão, A. N.; Guerra, Nuno

doi:10.1142/s0219876213420085

Cited by 26 publications

(15 citation statements)

References 21 publications

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“…These observations are consistent with previous works focusing on the same topic [22,23,41,13,28,9,27], which confirms that the combination of the Latin Hypercube sampling [34,36] with Sublim3d [45] is suitable to investigate the influence of soil heterogeneity in the bearing capacity of foundations [46];…”

Section: Discussionsupporting

confidence: 91%

Reliability assessment of shallow foundations on undrained soils considering soil spatial variability

Simões

Neves

Antão

et al. 2020

Computers and Geotechnics

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Structural design using partial safety factors aims at achieving an homogeneous safety level in geotechnical design without the use of more complex reliability analysis. In this work, the different Design Approaches proposed by Eurocode 7 for shallow foundations resting on the surface of undrained soils are compared in terms of the resulting reliability indices. The influence of both centered and eccentric loads, as well as homogeneous and heterogeneous isotropic and anisotropic distributions for the variability of soil properties were investigated in the reliability analysis.A finite element implementation of the upper bound theorem of limit analysis is combined with Latin Hypercube sampling to compute the probabilistic response of shallow foundations. Considering realistic probabilistic distributions for both permanent and live loads, First Order Reliability Method is used to calculate the reliability index of such structures designed according to the different Design Approaches present in Eurocode 7.The results obtained show that the Eurocode 7 leads to satisfactory reliability indices, but that significant differences between Design Approaches exist.

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Section: Discussionsupporting

confidence: 91%

Reliability assessment of shallow foundations on undrained soils considering soil spatial variability

Simões

Neves

Antão

et al. 2020

Computers and Geotechnics

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“…The comparison is shown in Table 1. The results obtained by both approaches are consistent; however, in the study by Simoes et al (2014), lower bearing capacity mean values and standard deviations were obtained. Certain parts of these differences can be explained by the fully three-dimensional mechanism considered in this paper and different covariance functions assumed in both studies.…”

Section: Numerical Accuracysupporting

confidence: 64%

“…Moreover, by using the algorithm proposed in this study, the same scenarios were examined as in the study by Simoes et al (2014), where the three dimensional spatial variability was considered for 8 m foundation section (the authors used random finite limit analysis). Note that in the study by Simoes et al (2014) plane strain conditions were assumed. Therefore, the obtained failure mechanism was not fully three-dimensional; however, due to its proportions 8.0 m over 1.0 m, this impact is not very significant.…”

Section: Numerical Accuracymentioning

confidence: 99%

On determining the undrained bearing capacity coefficients of variation for foundations embedded on spatially variable soil

Chwała

2020

Studia Geotechnica Et Mechanica

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AbstractThis paper presents an efficient method and its usage for the three-dimensional random bearing capacity evaluation for square and rectangular footings. One of the objectives of the study is to deliver graphs that can be used to easily estimate the approximated values of coefficients of variations of undrained bearing capacity. The numerical calculations were based on the proposed method that connects three-dimensional failure mechanism, simulated annealing optimization scheme and spatial averaging. The random field is used for describing the spatial variability of undrained shear strength. The proposed approach is in accordance with a constant covariance matrix concept, that results in a highly efficient tool for estimating the probabilistic characteristics of bearing capacity. As a result, numerous three-dimensional simulations were performed to create the graphs. The considered covariance matrix is a result of Vanmarcke’s spatial averaging discretization of a random field in the dissipation regions to the single random variables. The matrix describes mutual correlation between each dissipation region (or between those random variables). However, in the presented approach, the matrix was obtained for the expected value of undrained shear strength and keep constant during Monte Carlo simulations. The graphs were established in dimensionless coordinates that vary in the observable in practice ranges of parameters (i.e., values of fluctuation scales, foundation sizes and shapes). Examples of usage were given in the study to illustrate the application possibility of the graphs. Moreover, the comparison with the approach that uses individually determined covariance matrix is shown.

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“…Because the direct use of the finite difference code was computationally demanding, a metamodel was developed based on sparse polynomial chaos expansion combined with global sensitivity analysis. Simoes et al [35] used an upper bound formulation of finite element limit analysis (FELA) in order to check the influence of modelling strip foundations on spatially variable 3D soil with regard to the probability characteristics of structure bearing capacity. For these simulations, the Latin hypercube sampling technique was used, which allowed the limiting of a satisfactory number of simulations compared to the crude Monte Carlo technique.…”

Section: Introductionmentioning

confidence: 99%

“…The 3D modelling of a strip foundation located in spatially variable soil is also justified. As shown in [35], the modelling of a strip foundation in 2D can lead to much higher values of bearing capacity coefficients of variation than would result from a full 3D analysis. Thus, a 2D analysis of a strip footing may be a too conservative approach, which is of great importance when evaluating the probability of foundation failure.…”

Section: Introductionmentioning

confidence: 99%

3D bearing capacity probabilistic analyses of footings on spatially variable c–φ soil

Kawa

Puła

2019

Acta Geotech.

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The paper examines three-dimensional (3D) analyses of the load bearing capacity of square and strip footings on a spatially variable cohesive-frictional (c-u) soil. Embedded, rigid and smooth footings are considered. Cohesion and friction angle are modelled using random fields. The vertical scale of fluctuation (SOF) is based on earlier studies of natural soils. For the square footing problem, the horizontal SOF is the subject of a parametric study. For the strip footing, only one value of the horizontal SOF is assumed, and the parametric study concerns the modelled length of the foundation. To generate the fields of strength parameters, the Fourier series method is employed. For both problems analyzed, the influence of the parameters on the probabilistic characteristics of the bearing capacity of the soil is investigated. For the square footing problem, both the mean value of bearing capacity and its coefficient of variation increase with an increasing horizontal fluctuation scale, but they stabilize at higher values of SOF. For the strip footing problem, it appears that 2D modelling is a very conservative approach, and for the precise assessment of the probability of foundation failure, the footing should be modelled in 3D. Keywords FLAC3D Á Random field Á Reliability index Á Scale of fluctuation List of symbols Roman a Lower bound of bounded interval b Upper bound of bounded interval CoV Coefficient of variation c Cohesion

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Probabilistic Analysis of Bearing Capacity of Shallow Foundations Using Three-Dimensional Limit Analyses

Cited by 26 publications

References 21 publications

Reliability assessment of shallow foundations on undrained soils considering soil spatial variability

Reliability assessment of shallow foundations on undrained soils considering soil spatial variability

On determining the undrained bearing capacity coefficients of variation for foundations embedded on spatially variable soil

3D bearing capacity probabilistic analyses of footings on spatially variable c–φ soil

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