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Application of probabilistic methods in geomechanics
Suchomel, Radek ; Mašín, David (advisor) ; Šejnoha, Jiří (referee) ; Pruška, Jan (referee)
Three probabilistic methods of different complexity for slope stability calculations are in this work evaluated with respect to a well-documented case study of slope failure in Lodalen, Norway. A finite element method considering spatial random fields of uncorrelated parameters cohesion and friction angle is taken as a reference for comparison with two simpler methods based on Taylor series expansion, known as first-order-second-moment methods. It is shown that the FOSM method enhanced by a reduction of variance of input parameters due to spatial averaging along the potential failure surface leads to a significant improvement in predictions. This method is computationally inexpensive and can be used in combination with any existing finite element code, it is thus a useful approximate probabilistic method for geotechnical practice. Several limitations of the extended method for calculating probability of a slope failure are identified. An advanced hypoplastic constitutive model is used in probabilistic analyses of a typical geotech- nical problem, strip footing. The model, including horizontal and vertical correlation lengths, was calibrated using a set of experimental data on sand from horizontally stratified deposit. Some parameters followed normal, whereas other followed lognormal distributions....
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Application of probabilistic methods in numeric analyses of geotechnical problems
Suchomel, Radek
Two types of conventional methods are used for slope stability analysis in practise. The first type are analytical methods based on limit equilibrium (e.g. methods by Petterson, Bishop, Spencer etc.) The second type are a numerical methods based on finite elements analysis. From this sort the most frequently used is the φ-c reduction method. One of disadvantages of these methods is that analyzed geotechnical problem must be discretised into quasi-homogeneous parts that are characterized by constant value of mechanical properties. Detailed studies, for example El-Ramly et al. (2006), show that mechanical characteristics from one quasi-homogeneous part often have natural variability. This can be described with some type of statistical distribution. This observation is taken into account in random finite element method (for example Griffiths and Fenton (2004)). To study this method, program random field (Mašín 2006) was created. The program is able to generate random fields from parameters of statistical distribution of mechanical properties and map them onto finite element mesh. Next input parameter for creating the fields is correlation length that cha- racterises dependency of random variables on their distance in space. These random fields are used as input mechanical characteristic for the next step...
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Sources and evaluation of variability of mechanical properties of coarse-grained soils
Mayer, Petr ; Mašín, David (advisor) ; Suchomel, Radek (referee)
This thesis builds on the work of Dr. Radek Suchomel (2011), which dealt with the use of probabilstic methods in geomechanics and discusses the issues associated with inaccuracies in laboratory experiments. For this purpose it was necessary to design and prepare a set of laboratory experiments so as to obtain sufficient data for evaluation, calibrated, hypoplastic constitutive model, which is defined parameters φc, hs, n, ec0, ei0, ed0, α and β. On the basis of these parameters, the data was compared. For this purpose it was appropriate to 40 measuring the angle of repose, 40 triaxial tests and 40 oedometric tests on coarse-grained soil that was sand with missed fraction < 0.063 mm fraction and without fraction > 3 mm, which was classified as the same grain soil, poorly sorted. On this soil is managed successfully to evaluate fully the parameters for 38 samples. Two samples failed to calibrate only the parameters α and β. Test results and subsequent calibration of parameters hypoplastic constitutive model intended that observed variability affects the resulting values of eight parameters hypoplastic constitutive model, which is largely discussed, where there is a comparison with data of Suchomel (2011). With the help of coefficients of variation and standard deviations are concluded that some of...
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Application of probabilistic methods in geomechanics
Suchomel, Radek ; Mašín, David (advisor) ; Šejnoha, Jiří (referee) ; Pruška, Jan (referee)
Three probabilistic methods of different complexity for slope stability calculations are in this work evaluated with respect to a well-documented case study of slope failure in Lodalen, Norway. A finite element method considering spatial random fields of uncorrelated parameters cohesion and friction angle is taken as a reference for comparison with two simpler methods based on Taylor series expansion, known as first-order-second-moment methods. It is shown that the FOSM method enhanced by a reduction of variance of input parameters due to spatial averaging along the potential failure surface leads to a significant improvement in predictions. This method is computationally inexpensive and can be used in combination with any existing finite element code, it is thus a useful approximate probabilistic method for geotechnical practice. Several limitations of the extended method for calculating probability of a slope failure are identified. An advanced hypoplastic constitutive model is used in probabilistic analyses of a typical geotech- nical problem, strip footing. The model, including horizontal and vertical correlation lengths, was calibrated using a set of experimental data on sand from horizontally stratified deposit. Some parameters followed normal, whereas other followed lognormal distributions....
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Application of probabilistic methods in numeric analyses of geotechnical problems
Suchomel, Radek
Two types of conventional methods are used for slope stability analysis in practise. The first type are analytical methods based on limit equilibrium (e.g. methods by Petterson, Bishop, Spencer etc.) The second type are a numerical methods based on finite elements analysis. From this sort the most frequently used is the φ-c reduction method. One of disadvantages of these methods is that analyzed geotechnical problem must be discretised into quasi-homogeneous parts that are characterized by constant value of mechanical properties. Detailed studies, for example El-Ramly et al. (2006), show that mechanical characteristics from one quasi-homogeneous part often have natural variability. This can be described with some type of statistical distribution. This observation is taken into account in random finite element method (for example Griffiths and Fenton (2004)). To study this method, program random field (Mašín 2006) was created. The program is able to generate random fields from parameters of statistical distribution of mechanical properties and map them onto finite element mesh. Next input parameter for creating the fields is correlation length that cha- racterises dependency of random variables on their distance in space. These random fields are used as input mechanical characteristic for the next step...
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