The paper deals with the formulation of failure criterion for an in-plane loaded masonry. Using micro-mechanics approach the strength estimation for masonry microstructure with constituents obeying the Drucker-Prager criterion is determined numerically. The procedure invokes lower bound analysis: for assumed stress fields constructed within masonry periodic cell critical load is obtained as a solution of constrained optimization problem. The analysis is carried out for many different loading conditions at different orientations of bed joints. The performance of the approach is verified against solutions obtained for corresponding layered and block microstructures, which provides the upper and lower strength bounds for masonry microstructure, respectively. Subsequently, a phenomenological anisotropic strength criterion for masonry microstructure is proposed. The criterion has a form of conjunction of Jaeger critical plane condition and Tsai-Wu criterion. The model proposed is identified based on the fitting of numerical results obtained from the microstructural analysis. Identified criterion is then verified against results obtained for different loading orientations. It appears that strength of masonry microstructure can be satisfactorily described by the criterion proposed.
The paper deals with reliability analysis of square footing on soil with strength anisotropy. The strength of the soil has been described with identified anisotropic strength criterion dedicated to geomaterials with layered microstructure. The analysis assumes dip angle α and azimuth angle β which define direction of lamination of the structure to be random variables with given probability density functions. Bearing capacity being a function of these variables is approximated based on results of deterministic simulations obtained for variety of orientations. The weighted regression method by Kaymaz and McMahon within the framework of Response Surface Method is used for the approximation. As a result of analysis, global factor of safety that corresponds to assumed value of probability of failure is determined. The value of the safety factor denotes the ratio between the value of the design load and the mean value of bearing capacity which is needed to reduce the probability of failure to the acceptable level. The procedure of calculating the factor has been presented for two different cases. In the first case, no information about lamination direction of the soil has been provided and thus all the orientations are assumed to be equally probable (uniform distribution). In the second case, statistical information including mean, variance and assumed probability distribution for both α and β angle is known. For the latter case, using results obtained for few different values of mean of angle α, also the influence of strength anisotropy on the value of global factor of safety is shown.
The paper deals with evaluation of bearing capacity of strip foundation on random purely cohesive soil. The approach proposed combines random field theory in the form of random layers with classical limit analysis and Monte Carlo simulation. For given realization of random the bearing capacity of strip footing is evaluated by employing the kinematic approach of yield design theory. The results in the form of histograms for both bearing capacity of footing as well as optimal depth of failure mechanism are obtained for different thickness of random layers. For zero and infinite thickness of random layer the values of depth of failure mechanism as well as bearing capacity assessment are derived in a closed form. Finally based on a sequence of Monte Carlo simulations the bearing capacity of strip footing corresponding to a certain probability of failure is estimated. While the mean value of the foundation bearing capacity increases with the thickness of the random layers, the ultimate load corresponding to a certain probability of failure appears to be a decreasing function of random layers thickness.
In the present paper, a three-dimensional problem of bearing capacity of square footing on random soil medium is analyzed. The random fields of strength parameters c and φ are generated using LAS procedure (Local Average Subdivision, Fenton and Vanmarcke 1990). The procedure used is re-implemented by the authors in Mathematica environment in order to combine it with commercial program. Since the procedure is still tested the random filed has been assumed as one-dimensional: the strength properties of soil are random in vertical direction only.
Individual realizations of bearing capacity boundary-problem with strength parameters of medium defined the above procedure are solved using FLAC3D Software. The analysis is performed for two qualitatively different cases, namely for the purely cohesive and cohesive-frictional soils. For the latter case the friction angle and cohesion have been assumed as independent random variables. For these two cases the random square footing bearing capacity results have been obtained for the range of fluctuation scales from 0.5 m to 10 m. Each time 1000 Monte Carlo realizations have been performed. The obtained results allow not only the mean and variance but also the probability density function to be estimated. An example of application of this function for reliability calculation has been presented in the final part of the paper.
The paper deals with application of CPTu test results for the probabilistic modeling of dumping grounds. The statistical measures use results from 42 CPT test points located in the lignite mine dumping ground from the region of Central Europe. Both the tip resistance qc as well as local friction fs are tested. Based on the mean values and standard deviations of measured quantities the specific zones in the dumping site profile are distinguished. For three main zones standard deviations of linearly de-trended functions, distributions of normalized de-trended values for qc and fs are examined. Also the vertical scales of fluctuation for both measured quantities are estimated. The obtained result shows that lignite mine dumping site can be successfully described with the Random Field Theory. Additional use of fs values introduces supplementary statistical information.
The paper presents the identification methodology of anisotropic criteria based on triaxial test results. The considered material is varved clay – a sedimentary soil occurring in central Poland which is characterized by the so-called “layered microstructure”. The strength examination outcomes were identified by standard triaxial tests. The results include the estimated peak strength obtained for a wide range of orientations and confining pressures. Two models were chosen as potentially adequate for the description of the tested material, namely Pariseau and its conjunction with the Jaeger weakness plane. Material constants were obtained by fitting the model to the experimental results. The identification procedure is based on the least squares method. The optimal values of parameters are searched for between specified bounds by sequentially decreasing the distance between points and reducing the length of the searched range. For both considered models the optimal parameters have been obtained. The comparison of theoretical and experimental results as well as the assessment of the suitability of selected criteria for the specified range of confining pressures are presented.