A stochastic approach to the problem of bearing capacity by the method of characteristics

Przewłócki, J.

doi:10.1016/j.compgeo.2005.06.001

Cited by 16 publications

(8 citation statements)

References 2 publications

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“…The probabilistic approaches allow one to consider the propagation of the uncertainties from the input parameters to the system responses. Most probabilistic analyses existing in literature consider the ultimate limit state of foundations resting on a soil mass [5][6][7][8][9][10][11][12]. To the best of the authors' knowledge, there are no probabilistic studies on the ultimate limit state of shallow foundations resting on rock masses.…”

Section: Introductionmentioning

confidence: 99%

Probabilistic analysis and design of strip foundations resting on rocks obeying Hoek–Brown failure criterion

Mao

Al-Bittar

Soubra

2012

International Journal of Rock Mechanics and Mining Sciences

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In this paper, a probabilistic analysis is presented to compute the probability density function (PDF) of the ultimate bearing capacity of a shallow strip footing resting on a rock mass. The rock is assumed to follow the modified Hoek-Brown failure criterion. Vertical and inclined loading cases are considered in the analysis. In this study, the deterministic models are based on the kinematic approach of the limit analysis theory. The polynomial chaos expansion (PCE) methodology is used for the probabilistic analysis. Four parameters related to the modified Hoek-Brown failure criterion are considered as random variables. These are the geological strength index (GSI), the uniaxial compressive strength of the intact rock (s c), the intact rock material constant (m i) and the disturbance coefficient (D). The results of the vertical load case have shown that (i) the variability of the ultimate bearing capacity increases with the increase in the coefficients of variation of the random variables; GSI and s c being of greater effect, (ii) the non-normality of the input variables has a significant effect on the shape of the PDF of the ultimate bearing capacity, (iii) a negative correlation between GSI and s c leads to less spread out PDF, (iv) the probabilistic footing breadth based on a reliability-based design (RBD) may be greater or smaller than the deterministic breadth depending on the values of the input statistical parameters. Finally, it was shown in the inclined load case that the variability of the ultimate bearing capacity decreases with the increase of the footing load inclination.

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Section: Introductionmentioning

confidence: 99%

Probabilistic analysis and design of strip foundations resting on rocks obeying Hoek–Brown failure criterion

Mao

Al-Bittar

Soubra

2012

International Journal of Rock Mechanics and Mining Sciences

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“…Au cours de la dernière décennie, la théorie de la fiabilité a été appliquée au problème de l'analyse et du dimensionnement des fondations superficielles par un certain nombre d'auteurs. Griffiths et Fenton (2001), Griffiths et al (2002), , 2003, Przewlocki (2005), Popescu et al (2005), La Bor derie et Breysse (2007), Soubra et Youssef Abdel Massih (2010) ont modélisé les paramètres incertains du sol par des processus aléatoires et ont étudié l'effet de la variabilité spatiale de ces paramètres sur le tassement ou la portance des fondations. La plupart de ces études ont considéré l'incertitude d'un seul paramètre (comme par exemple le module d'Young, la cohésion ou l'an gle de frottement interne du sol).…”

Section: Introductionunclassified

Analyse et dimensionnement fiabilistes des fondations superficielles filantes avec ou sans prise en compte des efforts sismiques pseudo-statiques

Massih¹,

Soubra²

2010

Rev. Fr. Geotech.

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Analyse et dimensionnement fiabil stes des fondations superficielles filantes avec ou sans prise en compte des efforts sismiques pseudo-statiques RésuméCet article présente une approche f i abiliste pour l'analyse et le dimensionnement d'une fondation superficielle filante, située ou non dans une zone sismique. Pour une fondation soumise à un chargement vertical centré et en l'absence d'effo rts sismiques, le mode de rupture par poinçonnement du sol est étudié. Cependant, pour une fondation chargée verticalement et située dans une zone sismique, les deux modes de rupture (i) poinçonnement du sol et (ii) glissement de la fondation sur le sol sous-jacent, sont considérés. Le chargement sismique est représenté par des forces pseudo-statiques. L'indice de fiabilité adopté est celui de Hasofer-Lind. Les variables aléatoires utilisées sont les propriétés de cisaillement du sol et le coefficient sismique. Il a été montré que la prise en compte d'une corrélation négative entre les propriétés mécaniques du sol augmente la fiabilité de la fondation et que la probabilité de défaillance est très sensible au coefficient de variation de l'angle de frottement interne et du coefficient sismique. Pour le cas d'une fondation située dans une zone sismique, un seul mode de rupture est prédominant dans le calcul de la probabilité de défaillance du système poinçonnement/glissement. Pour le dimensionnement, une procédure itérative est utilisée pour déterminer la largeur de la fondation pour une probabilité de défaillance cible.

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“…However, very few authors have investigated the reliability-based analysis and design of foundations. Some ͑Griffiths and Fenton 2001;Fenton and Griffiths 2002Griffiths et al 2002;Przewlocki 2005;Popescu et al 2005͒ modeled the uncertain parameters as random processes and examined the effect of the spatial variability of these parameters on the settlement or on the bearing capacity of foundations. Most of these studies considered the uncertainty of one single parameter ͑such as the soil elastic modulus, the cohesion, or the angle of internal friction of the soil͒.…”

Section: Introductionmentioning

confidence: 99%

Reliability-Based Analysis and Design of Strip Footings against Bearing Capacity Failure

Massih

Soubra

Low

2008

J. Geotech. Geoenviron. Eng.

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This paper presents a reliability-based approach for the analysis and design of a shallow strip footing subjected to a vertical load with or without pseudostatic seismic loading. Only the punching failure mode of the ultimate limit state is studied. The deterministic models are based on the upper-bound method of the limit analysis theory. The random variables used are the soil shear strength parameters and the horizontal seismic coefficient. The Hasofer-Lind reliability index and the failure probability are determined. A sensitivity analysis is also performed. The influence of the applied footing load on the reliability index and the corresponding design point is presented and discussed. It was shown that the negative correlation between the soil shear strength parameters highly increases the reliability of the foundation and that the failure probability is highly influenced by the coefficient of variation of the angle of internal friction of the soil and the horizontal seismic coefficient. For design, an iterative procedure is performed to determine the breadth of the footing for a target failure probability.

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A stochastic approach to the problem of bearing capacity by the method of characteristics

Cited by 16 publications

References 2 publications

Probabilistic analysis and design of strip foundations resting on rocks obeying Hoek–Brown failure criterion

Probabilistic analysis and design of strip foundations resting on rocks obeying Hoek–Brown failure criterion

Analyse et dimensionnement fiabilistes des fondations superficielles filantes avec ou sans prise en compte des efforts sismiques pseudo-statiques

Reliability-Based Analysis and Design of Strip Footings against Bearing Capacity Failure

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