@phdthesis{Zhu,
  author    = {Zhu, Pengtao},
  title     = {The Variability of the Void Ratio of Sand and its Effect on Settlement and Infinite Slope Stability},
  doi       = {10.25643/bauhaus-universitaet.3741},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20180403-37411},
  school      = {Bauhaus-Universit{\"a}t Weimar},
  pages     = {164},
  abstract  = {The uncertainty of a soil property can significantly affect the physical behavior of soil, so as to influence geotechnical practice. The uncertainty can be expressed by its stochastic parameters, including the mean, the standard deviation, and the spatial correlation length. These stochastic parameters are regarded as constant value in most of the former studies. The main aim of this thesis is to prove whether they are depth-dependent, and to evaluate the effect of this depth-dependent character on both the settlement and the infinite slope stability during rainwater infiltration. A stochastic one-dimensional settlement simulation is carried out using random finite element method with the von Wolffersdorff hypoplastic model, so as to evaluate the effect of stress level on the stochastic parameters of void ratio related parameters of sand. It is found that these stochastic parameters are both stress-dependent and depth-dependent. The non-stationary random field, considering the depth-dependent character of these stochastic parameters, can be generated through the distortion of the stationary random field. The one-dimensional settlement analysis is carried out to evaluation the effect of the depth-dependent character of the stochastic parameters of void ratio on the strain. It is found that the depth-dependent character has low effect on the strain. The deterministic analysis of infinite slope stability during rainwater infiltration is simulated. The transient seepage is carried out using finite difference method, while the steady state seepage is simulated using the analytical solution. The saturated hydraulic conductivity (ks) is taken as the only variable. The results show that the depth-dependent ks has a significant influence on the stability of the slope when the negative flux is high. Without considering the depth-dependent character, can overestimate the factor of safety of the slope. A slope can fail if the depth-dependent character is considered, while it is stable if the depth-dependent character is neglected. The failure time of the slope with a greater depth-dependent ks is earlier during transient infiltration. Meanwhile, the stochastic infinite slope stability analysis during infiltration, is also carried out to highlight the effect of the depth-dependent character of the stochastic parameters of ks. The results show that: the probability of failure is significantly increased if the depth-dependent character of mean is considered, while, it is moderately reduced if the depth-dependent character of the standard deviation is accounted. If the depth-dependent character of both the mean and standard deviation of ks is considered, the depth-dependent mean value plays a dominant influence on the results. Furthermore, the depth-dependent character of the spatial correlation length can slightly reduce the probability of failure.},
  subject      = {Bodenunruhe},
  language  = {en}
}
@article{MosaviShokriMansoretal.,
  author    = {Mosavi, Amir Hosein and Shokri, Manouchehr and Mansor, Zulkefli and Qasem, Sultan Noman and Band, Shahab S. and Mohammadzadeh, Ardashir},
  title     = {Machine Learning for Modeling the Singular Multi-Pantograph Equations},
  series = {Entropy},
  volume    = {2020},
  journal   = {Entropy},
  number    = {volume 22, issue 9, article 1041},
  publisher = {MDPI},
  address   = {Basel},
  doi       = {10.3390/e22091041},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20210122-43436},
  pages     = {1 -- 18},
  abstract  = {In this study, a new approach to basis of intelligent systems and machine learning algorithms is introduced for solving singular multi-pantograph differential equations (SMDEs). For the first time, a type-2 fuzzy logic based approach is formulated to find an approximated solution. The rules of the suggested type-2 fuzzy logic system (T2-FLS) are optimized by the square root cubature Kalman filter (SCKF) such that the proposed fineness function to be minimized. Furthermore, the stability and boundedness of the estimation error is proved by novel approach on basis of Lyapunov theorem. The accuracy and robustness of the suggested algorithm is verified by several statistical examinations. It is shown that the suggested method results in an accurate solution with rapid convergence and a lower computational cost.},
  subject      = {Fuzzy-Regelung},
  language  = {en}
}