A discrete numerical method for brittle rocks using mathematical programming

Meng, J; Huang, J; Yao, C; Sheng, D

A discrete numerical method for brittle rocks using mathematical programming

Meng, J Huang, J Yao, C Sheng, D

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Publisher:: SPRINGER HEIDELBERG
Publication Type:: Journal Article
Citation:: Acta Geotechnica, 2018, 13, (2), pp. 283-302
Issue Date:: 2018-04-01

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Field	Value	Language
dc.contributor.author	Meng, J
dc.contributor.author	Huang, J
dc.contributor.author	Yao, C
dc.contributor.author	Sheng, D https://orcid.org/0000-0002-1665-6931
dc.date.accessioned	2022-09-01T04:39:16Z
dc.date.available	2022-09-01T04:39:16Z
dc.date.issued	2018-04-01
dc.identifier.citation	Acta Geotechnica, 2018, 13, (2), pp. 283-302
dc.identifier.issn	1861-1125
dc.identifier.issn	1861-1133
dc.identifier.uri	http://hdl.handle.net/10453/161178
dc.description.abstract	A computational formulation of discrete simulations of damage and failure in brittle rocks using mathematical programming methods is proposed. The variational formulations are developed in two and three dimensions. These formulations naturally lead to second-order cone programs and can conveniently be solved using off-the-shelf mathematical programming solvers. Pure static formulations are derived so that no artificial damping parameters are required. The rock is represented by rigid blocks, with interfaces between blocks modelled by zero-thickness springs based on the rigid-body–spring network method. A modified Mohr–Coulomb failure criterion is proposed to model the failure of the interfaces. When the interface’ strength limits are reached, a microscopic crack forms and its strength is irreversibly lost. The microscopic elastic properties of the springs are related to the observed elastic behaviour of rocks with the developed empirical equations. The program is first validated with three simple tests. Then, numerical uniaxial and biaxial compression tests and the Brazilian tests are conducted. Furthermore, the proposed approach is employed to study the rock crack propagation and coalescence using cracked Brazilian disc test. The results are in good agreements with reported experimental data, which shows its potential in modelling mechanical behaviour of brittle rocks.
dc.language	English
dc.publisher	SPRINGER HEIDELBERG
dc.relation.ispartof	Acta Geotechnica
dc.relation.isbasedon	10.1007/s11440-017-0583-8
dc.rights	info:eu-repo/semantics/restrictedAccess
dc.subject	0905 Civil Engineering
dc.subject.classification	Geological & Geomatics Engineering
dc.title	A discrete numerical method for brittle rocks using mathematical programming
dc.type	Journal Article
utslib.citation.volume	13
utslib.for	0905 Civil Engineering
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology/School of Civil and Environmental Engineering
utslib.copyright.status	in_progress	*
dc.date.updated	2022-09-01T04:39:12Z
pubs.issue	2
pubs.publication-status	Published
pubs.volume	13
utslib.citation.issue	2

Abstract:

A computational formulation of discrete simulations of damage and failure in brittle rocks using mathematical programming methods is proposed. The variational formulations are developed in two and three dimensions. These formulations naturally lead to second-order cone programs and can conveniently be solved using off-the-shelf mathematical programming solvers. Pure static formulations are derived so that no artificial damping parameters are required. The rock is represented by rigid blocks, with interfaces between blocks modelled by zero-thickness springs based on the rigid-body–spring network method. A modified Mohr–Coulomb failure criterion is proposed to model the failure of the interfaces. When the interface’ strength limits are reached, a microscopic crack forms and its strength is irreversibly lost. The microscopic elastic properties of the springs are related to the observed elastic behaviour of rocks with the developed empirical equations. The program is first validated with three simple tests. Then, numerical uniaxial and biaxial compression tests and the Brazilian tests are conducted. Furthermore, the proposed approach is employed to study the rock crack propagation and coalescence using cracked Brazilian disc test. The results are in good agreements with reported experimental data, which shows its potential in modelling mechanical behaviour of brittle rocks.

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http://hdl.handle.net/10453/161178