A new method of meshing in discontinuous deformation analysis (DDA)

Simple item page
dc.contributor.advisorScheele, Friedrichen_ZA
dc.contributor.authorClatworthy, David Ellanden_ZA
dc.date.accessioned2016-01-02T04:18:51Z
dc.date.available2016-01-02T04:18:51Z
dc.date.issued1997en_ZA
dc.descriptionIncludes bibliography.en_ZA
dc.description.abstractDiscontinuous Deformation Analysis (DDA) is a discrete element method developed by Shi [1988] specifically for modelling blocky rock masses. The DDA method is based on the assumption that deformation and failure of such rock masses is primarily due to differential movements of rock blocks, rather than strain and fracture of intact rock material. Strains and stresses are assumed to be constant over the area of each rock block. Contact between blocks is modelled using penalty functions, with Coulomb's friction law controlling sliding along block boundaries. Tests show that while DDA is not well suited to dynamic simulations where the velocities of blocks become large, it can model rock masses to a reasonable degree of accuracy in static analyses. There are various analysis control parameters which have a marked effect on the solution, however, and the user should take care in choosing suitable values for these parameters. A method is proposed here, in which certain blocks can be sub-divided into Finite Element meshes in order to obtain a more accurate description of their deformation. The method takes advantage of the fact that both DDA and the Finite Element Method (FEM) use the principle of stationary potential energy to obtain the solution equations for block equilibrium. Both DDA blocks and FEM elements can therefore initially be treated as DDA blocks, using the standard DDA formulation, and then the solution equations for the FEM elements are converted into Finite Element format by a simple transformation procedure before solution. First and second order DDA blocks are considered in this report, along with their equivalents in FEM, the C0-linear and C0-quadratic triangular elements. The C0-linear elements are found to be too stiff in modelling bending deformation, due to the assumption of constant strain throughout the element. The C0-quadratic elements are able to accurately model bending, however. It is shown through tests that the performance of these FEM elements, formulated within the DDA method, is identical to that obtained using the corresponding elements in conventional Finite Element programs. The sub-meshing method therefore allows mixed-formulation analyses, with DDA blocks and FEM meshes interacting within a single system, while remaining efficient, and reasonably simple to incorporate into existing DDA program codes. It would also be possible to model material non-linearity and fracture using this method.en_ZA
dc.identifier.apacitationClatworthy, D. E. (1997). <i>A new method of meshing in discontinuous deformation analysis (DDA)</i>. (Thesis). University of Cape Town ,Faculty of Engineering & the Built Environment ,Department of Civil Engineering. Retrieved from http://hdl.handle.net/11427/16089en_ZA
dc.identifier.chicagocitationClatworthy, David Elland. <i>"A new method of meshing in discontinuous deformation analysis (DDA)."</i> Thesis., University of Cape Town ,Faculty of Engineering & the Built Environment ,Department of Civil Engineering, 1997. http://hdl.handle.net/11427/16089en_ZA
dc.identifier.citationClatworthy, D. 1997. A new method of meshing in discontinuous deformation analysis (DDA). University of Cape Town.en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Clatworthy, David Elland AB - Discontinuous Deformation Analysis (DDA) is a discrete element method developed by Shi [1988] specifically for modelling blocky rock masses. The DDA method is based on the assumption that deformation and failure of such rock masses is primarily due to differential movements of rock blocks, rather than strain and fracture of intact rock material. Strains and stresses are assumed to be constant over the area of each rock block. Contact between blocks is modelled using penalty functions, with Coulomb's friction law controlling sliding along block boundaries. Tests show that while DDA is not well suited to dynamic simulations where the velocities of blocks become large, it can model rock masses to a reasonable degree of accuracy in static analyses. There are various analysis control parameters which have a marked effect on the solution, however, and the user should take care in choosing suitable values for these parameters. A method is proposed here, in which certain blocks can be sub-divided into Finite Element meshes in order to obtain a more accurate description of their deformation. The method takes advantage of the fact that both DDA and the Finite Element Method (FEM) use the principle of stationary potential energy to obtain the solution equations for block equilibrium. Both DDA blocks and FEM elements can therefore initially be treated as DDA blocks, using the standard DDA formulation, and then the solution equations for the FEM elements are converted into Finite Element format by a simple transformation procedure before solution. First and second order DDA blocks are considered in this report, along with their equivalents in FEM, the C0-linear and C0-quadratic triangular elements. The C0-linear elements are found to be too stiff in modelling bending deformation, due to the assumption of constant strain throughout the element. The C0-quadratic elements are able to accurately model bending, however. It is shown through tests that the performance of these FEM elements, formulated within the DDA method, is identical to that obtained using the corresponding elements in conventional Finite Element programs. The sub-meshing method therefore allows mixed-formulation analyses, with DDA blocks and FEM meshes interacting within a single system, while remaining efficient, and reasonably simple to incorporate into existing DDA program codes. It would also be possible to model material non-linearity and fracture using this method. DA - 1997 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 1997 T1 - A new method of meshing in discontinuous deformation analysis (DDA) TI - A new method of meshing in discontinuous deformation analysis (DDA) UR - http://hdl.handle.net/11427/16089 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/16089
dc.identifier.vancouvercitationClatworthy DE. A new method of meshing in discontinuous deformation analysis (DDA). [Thesis]. University of Cape Town ,Faculty of Engineering & the Built Environment ,Department of Civil Engineering, 1997 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/16089en_ZA
dc.language.isoengen_ZA
dc.publisher.departmentDepartment of Civil Engineeringen_ZA
dc.publisher.facultyFaculty of Engineering and the Built Environment
dc.publisher.institutionUniversity of Cape Town
dc.subject.otherCivil Engineeringen_ZA
dc.titleA new method of meshing in discontinuous deformation analysis (DDA)en_ZA
dc.typeMaster Thesis
dc.type.qualificationlevelMasters
dc.type.qualificationnameMSc (Eng)en_ZA
uct.type.filetypeText
uct.type.filetypeImage
uct.type.publicationResearchen_ZA
uct.type.resourceThesisen_ZA
Files
Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
thesis_ebe_1997_clatworthy_david_elland.pdf
Size:
4.95 MB
Format:
Adobe Portable Document Format
Description:
Download
Collections
Masters