Prandtl Revisited - Grifths, D. V. & Fenton, G. A....

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Bearing capacity of spatially random soil: the undrained clay Prandtl problem revisited D. V. GRIFFITHS ± andG .A .FENTON { By merging elasto-plastic ®nite element analysis with ran- dom ®eld theory, an investigation has been performed into the bearing capacity of undrained clays with spatially vary- ing shear strength. The object of the investigation is to determine the extent to which variance and spatial correla- tion of the soil's undrained shear strength impact on the statistics of the bearing capacity. Throughout this study, bearing capacity results are expressed in terms of the bear- ing capacity factor, N c , in relation to the mean undrained strength. For low coef®cients of variation of shear strength, the expected value of the bearing capacity factor tends to the Prandtl solution of N c ² 5 : 14. For higher values of the coef®cient of variation, however, the expected value of the bearing capacity factor falls quite steeply. The spatial corre- lation length is also shown to be an important parameter that cannot be ignored. The results of Monte Carlo simula- tions on this non-linear problem are presented in the form of histograms, which enable the interpretation to be ex- pressed in a probabilistic context. Results obtained in this study help to explain the well-known requirement that bear- ing capacity calculations require relatively high factors of safety compared with other branches of geotechnical design. KEYWORDS: bearing capacity; limit state design/analysis; numer- ical modelling; plasticity; shear strength; statistical analysis En associant une analyse d'e Âle Âments ®nis e Âlasto-plastiques et une the Âorie du champ ale Âatoire, nous avons enque Ãte  sur la capacite  porteuse des argiles non draine Âes ayant une re Âsis- tance au cisaillement variant dans l'espace. Cette investiga- tion a pour but de de Âterminer les effets sur les statistiques de capacite  porteuse de la variance et de la corre Âlation spatiale de la re Âsistance au cisaillement non draine  du sol. Tout au long de cette e Âtude, nous exprimons les valeurs de capacite  porteuse en termes de facteur de capacite  porteuse, N c , par rapport au moyen de re Âsistance non draine Âe. Pour les coef®cients bas de variation de re Âsistance au cisaillement, la valeur attendue du facteur de capacite  porteuse tend a Á la solution de Prandt1 de N c ² 5 : 14. Cependant, pour des valeurs plus e Âleve Âes du coef®cient de variation, la valeur attendue du facteur de capacite  porteuse baisse de manie Áre assez marque Âe. Nous montrons e Âgalement que la longueur de la corre Âlation spatiale est un parame Átre important qui ne peut e Ãtre ne Âglige Â. Nous pre Âsentons les re Âsultats des simula- tions de Monte-Carlo sur ce proble Áme non line Âaire sous forme d'histogrammes, ce qui permet d'exprimer l'interpre Â- tation dans un contexte probabiliste. Les re Âsultats obtenus dans cette e Âtude aident a Á expliquer une ne Âcessite  bien connue : les calculs de capacite Â
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Prandtl Revisited - Grifths, D. V. & Fenton, G. A....

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