Effect of the Soil Spatial Variability on the Static and Dynamic Stability Analysis of a Lebanese Slope

The accidental topography and heterogeneous Lebanese geology in addition to the active seismicity have initiated the static and dynamic stability analysis of Lebanese slopes. In this paper, the stability of a sandy Lebanese slope situated at Mansourieh near Beirut is investigated using deterministic and probabilistic approaches. The characterization of the variability of the slope soil properties is done based on geological investigation, as well as geophysical (Resistivity and Ambient noise) and geotechnical tests performed on this slope. Three dimensional 3D static deterministic analyses is performed to determine the overall safety factor of the slope and to find the location of the critical failure surface. The deterministic model is based on numerical simulations using the finite difference code FLAC3D. Then, two-dimensional probabilistic analysis is carried out on the critical section obtained from the 3D model. In the probabilistic analysis, the soil properties are modeled using the random field theory. An efficient uncertainty propagation methodology based on the expansion optimal linear estimation EOLE method is used to discretize the random field. Concerning the dynamic analysis, it is implemented in order to determine the amplification at the top of slope, where the looseness of the soil there may amplify the earthquake acceleration. The results have shown a small safety factor as well as high amplification. The importance of using the probabilistic approach versus the deterministic one is also presented and discussed

Reliability-based analysis and design of foundations resting on a spatially random soil

International audienceThis paper presents the effect of the spatial variability of the soil shear strength parameters on the reliability analysis and design of a vertically loaded shallow strip footing against bearing failure. The deterministic model used is based on the upper-bound method of limit analysis. The Hasofer-Lind reliability index based on the most critical probabilistic failure surface is calculated for the assessment of the footing reliability. The random fields used in the analysis are the soil shear strength parameters. Normal and non-normal anisotropic random fields with or without cross correlation are considered. The two random fields are averaged along the potential slip lines of the failure mechanism. It was found that the assumption of negative cross correlation, soil heterogeneity and anisotropy regarding the autocorrelation distance gives a higher reliability index than the hypothesis of no cross correlation, homogeneous and isotropic soil respectively. These assumptions merely allow the reliability to be more accurately estimated and thus lead to an economic design. The failure probability was found more sensitive to the variability of the angle of internal friction than the cohesion. For design, an iterative procedure is performed to determine the breadth of the footing for a target failure probability

Analyse du comportement des fondations superficielles filantes par des approches fiabilistes

Le travail de cette thèse concerne l'étude du comportement des fondations superficielles filantes à l'état limite ultime et à l'état limite de service par des approches fiabilistes. Des modèles déterministes basés sur des mécanismes de ruine en analyse limite et des simulations numériques sous FLAC3D sont utilisés. La variabilité des propriétés du sol est modélisée soit par des variables aléatoires soit par des champs aléatoires. Les charges appliquées à la fondation sont considérées comme des variables aléatoires. Plusieurs configurations de chargement sont considérées : un chargement vertical centré, un chargement incliné et un chargement sismique. Le calcul de la fiabilité de la fondation est effectué à l'aide de l'indice de fiabilité de Hasofer-Lind. Il a été montré que l'indice de fiabilité déterminé en cherchant la ligne de glissement fiabiliste est plus critique que celui calculé pour la ligne de glissement déterministe. La corrélation négative entre les propriétés du sol augmente la fiabilité de la fondation. La probabilité de ruine est sensible aux incertitudes de l'angle de frottement interne du sol et de la charge horizontale appliquée. Pour le cas d'un chargement incliné ou sismique, un seul mode de rupture (soit le glissement de la fondation, soit le poinçonnement du sol) est prédominant dans le calcul de la probabilité de ruine du système. Un dimensionnement fiabiliste a été effectué pour déterminer la largeur de la fondation pour un indice de fiabilité cible. La variabilité spatiale du sol augmente la fiabilité de la fondation et aboutit à un dimensionnement plus économique. Pour un sol hétérogène, la valeur de la moyenne de la charge ultime calculée par des simulations de Monte Carlo est inférieure à la valeur déterministe obtenue pour un sol homogène. Pour l'état limite de service, il a été remarqué que pour les valeurs du facteur de sécurité communément utilisées dans la pratique, la fiabilité déterminée vis-à-vis de l'état limite ultime de portance est plus critique que celle obtenue vis-à-vis de l'état limite de service.NANTES-BU Sciences (441092104) / SudocSudocFranceF

Reliability-based analysis and design of obliquely loaded footings

International audienceThis paper presents a reliability-based approach for the analysis and design of a shallow strip footing subjected to an inclined load. The deterministic model used is based on the upper-bound method of limit analysis. Both the punching and sliding modes of failure are considered. The random variables used in the analysis are the soil shear strength parameters and the vertical and horizontal components of the footing load. The reliability index of each mode and the system failure probability were calculated. It was shown that for small values of the vertical component of the footing load, the sliding mode is dominant. When this vertical component increases, the punching mode becomes more critical. The hypothesis of uncorrelated shear strength parameters was found to be conservative in comparison to the one of negatively correlated variables. The coefficients of variation of only the angle of internal friction and the horizontal footing load have a significant effect on the system failure probability. For design, an iterative procedure is performed to determine the breadth of the footing for a target failure probability

Reliability-Based Analysis of Strip Footings Using Response Surface Methodology

International audienceA reliability-based analysis of a strip foundation subjected to a central vertical load is presented. Both the ultimate and the serviceability limit states are considered. Two deterministic models based on numerical simulations are used. The first one computes the ultimate bearing capacity of the foundation and the second one calculates the footing displacement due to an applied load. The response surface methodology is utilized for the assessment of the Hasofer–Lind reliability indexes. Only the soil shear strength parameters are considered as random variables while studying the ultimate limit state. Also, the randomness of only the soil elastic properties is taken into account in the serviceability limit state. The assumption of uncorrelated variables was found to be conservative in comparison to the one of negatively correlated variables. The failure probability of the ultimate limit state was highly influenced by the variability of the angle of internal friction. However, for the serviceability limit state, the accurate determination of the uncertainties of the Young’s modulus was found to be very important in obtaining reliable probabilistic results. Finally, the computation of the system failure probability involving both ultimate and serviceability limit states was presented and discussed

Bearing capacity of foundations resting on a spatially random soil

The paper presents the effect of the spatial variability of the soil properties on the ultimate bearing capacity of a vertically loaded shallow strip footing. The deterministic model used is based on numerical simulations using the Lagrangian explicit finite difference code FLAC3D. The cohesion and the angle of internal friction of the soil are modelled as non normal anisotropic random fields. The methodology used for the discretization of the random fields is based on the spectral representation method proposed by Yamazaki and Shinozuka (1988). The results have shown that the average bearing capacity of a spatially random soil is lower than the deterministic value obtained for a homogeneous soil. A critical case appears when the autocorrelation distances are equal to the footing breadth. The average value of the ultimate footing load is more sensitive to the horizontal autocorrelation distance than the vertical one. Finally, it has been shown that accounting for the spatial variability of the soil properties gives a higher reliability index of the foundation than the one obtained with the assumption of random variables

Bearing capacity of eccentrically and/or obliquely loaded strip footings over two-layer foundation soils by a kinematical approach

The aim of this paper is to determine the bearing capacity of a strip footing resting on a two-layer foundation soil sand/clay by a kinematical approach in limit analysis. Inclined and eccentric loading are considered in the analysis using translational and rotational failure mechanisms. Numerical results are presented and discussed

Dynamic slope stability analysis by a reliability-based approach

International audienceThe analysis of earth slopes situated in seismic areas has been extensively investigated in literature using deterministic approacheswhere average values of the input parameters are used and a global safety factor or a permanent displacement at the toe of the slope iscalculated. In these approaches, a decoupled analysis is usually performed in which a constant critical seismic acceleration is firstcalculated based on a pseudo-static representation of earthquake effects. Then, the permanent soil displacement is computed byintegration of the real acceleration record above the critical acceleration. A reliability-based approach for the seismic slope analysis isintroduced in this paper. This approach is more rational than the traditional deterministic methods since it enables to take into accountthe inherent uncertainty of the input variables. Furthermore, the deterministic model used in the reliability analysis is based on arigorous coupled analysis that simultaneously captures the fully non linear response of the soil and history of the real accelerationrecord. This model is based on numerical simulations using the dynamic option of the finite difference FLAC 3D software. The acceleration time history records used in this analysis is the one registered at the Lebanese Geophysical Center of the National Council for Scientific Research. The performance function used in the reliability analysis is defined with respect to the horizontal permanent displacement at the toe of the slope. The random variables considered in the analysis are the cohesion c and the shear modulus G of the soil since it was shown that these parameters have the most influence on slope displacements. The Stochastic Response Surface Methodology (SRSM) is utilized for the assessment of the probability distribution of the horizontal permanent displacement at the toe of the slope. The results have shown that the mean value of the permanent displacement is highly influenced by the coefficient of variation of the cohesion, the greater the scatter in c the higher the horizontal permanent displacement. Based on the probability distribution of the permanent displacement, the failure probability with respect to the exceedance of an allowable maximal permanent displacement was evaluated and discussed. At the end of the paper, a case study of a typical Lebanese slope is presented and analyzed to illustrate this approach

Damage of masonry structures relative to their properties: Development of ground movement fragility curves

International audienceThe objective of this paper is to study the effect of the properties of masonry buildings on the threshold values of the deflection ratio, which is used to assess the damage category of buildings. Based on the results obtained from a sensitivity analysis, fragility curves are drawn and used to develop a probabilistic approach to help assess the damage for different structure typologies due to ground settlement.The threshold values of the building deflection ratio are primarily empirical. The analytical method of Burland et al. (1977) was used to define analytical threshold values to assess the building damage in relation to the building properties: length L, height H, equivalent Young’s modulus E and equivalent shear modulus G. This paper starts with a comparison of various empirical and analytical threshold values of the deflection ratio. Next, a sensitivity analysis is performed using the analytical method of Burland et al. (1977) and modified by Saeidi et al. (2012) to take into account the anisotropic behaviour associated to the masonry mechanical properties and the existence of openings. The investigated parameters are the E/G and L/H ratios and the position of the neutral axis of the beam simulating the building. The results show a significant influence of the E/G and L/H ratios and suggest defining a range of the threshold deflection ratio associated to different damage categories for different building typologies. Fragility curves are then developed based on the definition of the building typologies. These fragility curves are a useful tool to estimate the probability of reaching each category of damage once the deflection ratio and the properties of the relative structure are determined. To improve their accuracy, several intervals of the properties of the buildings were used to develop these fragility curves. The choice of these intervals to draw the fragility curves was based on various bibliographic studies and numerical studies in the case of E/G and statistic studies in the case of L/H