Eine Plattform für die Wissenschaft: Bauingenieurwesen, Architektur und Urbanistik
Eine Plattform für die Wissenschaft: Bauingenieurwesen, Architektur und Urbanistik
A Non-parametric Discrete Fracture Network Model
https://orcid.org/0000-0003-1848-8465
Abstract A discrete fracture network (DFN) model based on non-parametric kernel density estimators (KDE) and directional-linear statistics is developed. The model provides a characterization of the fracture network with distributions of fracture orientation and size jointly. A solution to the Bertrand paradox is used for the calculation of disk sizes from trace lengths, the latter calculated from the intersection of disks and highwall faces by triangulation. A Poisson point process is applied for the generation of the model, with fractures assumed to be flat and circular in shape, the number of fractures per unit volume ($ P_{30} $) adjusted to match the experimental length of fractures per unit area ($ P_{21} $). Length censoring of traces due to the surface dimension is considered in the calculations by including semi-bounded traces, i.e., traces censored in one of their ends. Orientation and size biases are corrected with a weighting function in the random sampling. The truncation effect whereby no traces shorter than some cut-off length are recorded, is addressed by a randomized optimization algorithm. The joint fracture orientation-size distribution model developed is tested with trace maps of discontinuities measured from photogrammetric models of twelve highwall faces of quarry benches, with outstanding results. Computational advantages over traditional parametric fracture models are addressed.
Highlights Nonparametric directional-linear statistics has been used for the construction of DFN models. The mathematical analysis of this new approach is described in detail.A new link between distributions of disc size and pseudo-trace lengths is established. Relationships between means and variances for the distributions of trace length and disc size are discussed.Censoring bias is corrected by a mixed random variable and truncation bias is corrected by including semibounded traces and using a probabilistic filter.The nonparametric DFN model developed is applied to photogrammetric discontinuity data maps. Consistency of the results is assessed and thoroughly discussed.
A Non-parametric Discrete Fracture Network Model
https://orcid.org/0000-0003-1848-8465
Abstract A discrete fracture network (DFN) model based on non-parametric kernel density estimators (KDE) and directional-linear statistics is developed. The model provides a characterization of the fracture network with distributions of fracture orientation and size jointly. A solution to the Bertrand paradox is used for the calculation of disk sizes from trace lengths, the latter calculated from the intersection of disks and highwall faces by triangulation. A Poisson point process is applied for the generation of the model, with fractures assumed to be flat and circular in shape, the number of fractures per unit volume ($ P_{30} $) adjusted to match the experimental length of fractures per unit area ($ P_{21} $). Length censoring of traces due to the surface dimension is considered in the calculations by including semi-bounded traces, i.e., traces censored in one of their ends. Orientation and size biases are corrected with a weighting function in the random sampling. The truncation effect whereby no traces shorter than some cut-off length are recorded, is addressed by a randomized optimization algorithm. The joint fracture orientation-size distribution model developed is tested with trace maps of discontinuities measured from photogrammetric models of twelve highwall faces of quarry benches, with outstanding results. Computational advantages over traditional parametric fracture models are addressed.
Highlights Nonparametric directional-linear statistics has been used for the construction of DFN models. The mathematical analysis of this new approach is described in detail.A new link between distributions of disc size and pseudo-trace lengths is established. Relationships between means and variances for the distributions of trace length and disc size are discussed.Censoring bias is corrected by a mixed random variable and truncation bias is corrected by including semibounded traces and using a probabilistic filter.The nonparametric DFN model developed is applied to photogrammetric discontinuity data maps. Consistency of the results is assessed and thoroughly discussed.
A Non-parametric Discrete Fracture Network Model
https://orcid.org/0000-0003-1848-8465
Abstract A discrete fracture network (DFN) model based on non-parametric kernel density estimators (KDE) and directional-linear statistics is developed. The model provides a characterization of the fracture network with distributions of fracture orientation and size jointly. A solution to the Bertrand paradox is used for the calculation of disk sizes from trace lengths, the latter calculated from the intersection of disks and highwall faces by triangulation. A Poisson point process is applied for the generation of the model, with fractures assumed to be flat and circular in shape, the number of fractures per unit volume ($ P_{30} $) adjusted to match the experimental length of fractures per unit area ($ P_{21} $). Length censoring of traces due to the surface dimension is considered in the calculations by including semi-bounded traces, i.e., traces censored in one of their ends. Orientation and size biases are corrected with a weighting function in the random sampling. The truncation effect whereby no traces shorter than some cut-off length are recorded, is addressed by a randomized optimization algorithm. The joint fracture orientation-size distribution model developed is tested with trace maps of discontinuities measured from photogrammetric models of twelve highwall faces of quarry benches, with outstanding results. Computational advantages over traditional parametric fracture models are addressed.
Highlights Nonparametric directional-linear statistics has been used for the construction of DFN models. The mathematical analysis of this new approach is described in detail.A new link between distributions of disc size and pseudo-trace lengths is established. Relationships between means and variances for the distributions of trace length and disc size are discussed.Censoring bias is corrected by a mixed random variable and truncation bias is corrected by including semibounded traces and using a probabilistic filter.The nonparametric DFN model developed is applied to photogrammetric discontinuity data maps. Consistency of the results is assessed and thoroughly discussed.
A Non-parametric Discrete Fracture Network Model
Gómez, Santiago (Autor:in) / Sanchidrián, José A. (Autor:in) / Segarra, Pablo (Autor:in) / Bernardini, Maurizio (Autor:in)
2023
Aufsatz (Zeitschrift)
Elektronische Ressource
Englisch
BKL:
38.58
Geomechanik
/
56.20
Ingenieurgeologie, Bodenmechanik
/
38.58$jGeomechanik
/
56.20$jIngenieurgeologie$jBodenmechanik
RVK:
ELIB41
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