A Three-Dimensional Constitutive Model for Rocks Based on a Strain-Dependent Elastic Modulus
AbstractOur research group previously proposed a simple two-dimensional (2D) constitutive model for rocks to simulate not only the axial stress–axial strain relationship, but also the axial stress–lateral strain relationship, with few complicated equations. However, the failure envel...
| Main Authors: | , , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
GeoScienceWorld
2022-09-01
|
| Series: | Lithosphere |
| Online Access: | https://pubs.geoscienceworld.org/lithosphere/article/2021/Special%207/1409110/616571/A-Three-Dimensional-Constitutive-Model-for-Rocks |
| _version_ | 1798005822361436160 |
|---|---|
| author | Z. Li Y. Fujii J. Kodama D. Fukuda A. B. N. Dassanayake P. Sinkala |
| author_facet | Z. Li Y. Fujii J. Kodama D. Fukuda A. B. N. Dassanayake P. Sinkala |
| author_sort | Z. Li |
| collection | DOAJ |
| description |
AbstractOur research group previously proposed a simple two-dimensional (2D) constitutive model for rocks to simulate not only the axial stress–axial strain relationship, but also the axial stress–lateral strain relationship, with few complicated equations. However, the failure envelope that it predicted was linear, and it did not consider the effect of the intermediate principal stress (σ2). In the present study, the authors modify this simple 2D model to have a convex failure criterion. Then, the model is extended to a simple three-dimensional (3D) model that well approximates true triaxial stress–strain curves for real rocks under specific values of σ2 and σ3 and uses only four parameters. However, the predicted peak stress–σ2 relationship is linear. Finally, a modified 3D model was developed, which exhibited the true triaxial convex failure criterion. The equations in this model are simpler than the conventional true triaxial failure criteria. The proposed models can be implemented with a finite element method to improve the design of rock structures. |
| first_indexed | 2024-04-11T12:46:22Z |
| format | Article |
| id | doaj.art-5a1f6e92492f4c08b405226bccc43884 |
| institution | Directory Open Access Journal |
| issn | 1941-8264 1947-4253 |
| language | English |
| last_indexed | 2024-04-11T12:46:22Z |
| publishDate | 2022-09-01 |
| publisher | GeoScienceWorld |
| record_format | Article |
| series | Lithosphere |
| spelling | doaj.art-5a1f6e92492f4c08b405226bccc438842022-12-22T04:23:21ZengGeoScienceWorldLithosphere1941-82641947-42532022-09-012021Special 710.2113/2022/1409110A Three-Dimensional Constitutive Model for Rocks Based on a Strain-Dependent Elastic ModulusZ. Li0http://orcid.org/0000-0002-8764-0830Y. Fujii1J. Kodama2D. Fukuda3http://orcid.org/0000-0002-8320-5305A. B. N. Dassanayake4P. Sinkala51 Rock Mechanics Laboratory Division of Sustainable Resources Engineering Graduate School of Engineering Hokkaido University Sapporo 060-8628 Japan hokudai.ac.jp1 Rock Mechanics Laboratory Division of Sustainable Resources Engineering Graduate School of Engineering Hokkaido University Sapporo 060-8628 Japan hokudai.ac.jp1 Rock Mechanics Laboratory Division of Sustainable Resources Engineering Graduate School of Engineering Hokkaido University Sapporo 060-8628 Japan hokudai.ac.jp1 Rock Mechanics Laboratory Division of Sustainable Resources Engineering Graduate School of Engineering Hokkaido University Sapporo 060-8628 Japan hokudai.ac.jp2 Department of Earth Resources Engineering University of Moratuwa Moratuwa 10400 Sri Lanka mrt.ac.lk1 Rock Mechanics Laboratory Division of Sustainable Resources Engineering Graduate School of Engineering Hokkaido University Sapporo 060-8628 Japan hokudai.ac.jp AbstractOur research group previously proposed a simple two-dimensional (2D) constitutive model for rocks to simulate not only the axial stress–axial strain relationship, but also the axial stress–lateral strain relationship, with few complicated equations. However, the failure envelope that it predicted was linear, and it did not consider the effect of the intermediate principal stress (σ2). In the present study, the authors modify this simple 2D model to have a convex failure criterion. Then, the model is extended to a simple three-dimensional (3D) model that well approximates true triaxial stress–strain curves for real rocks under specific values of σ2 and σ3 and uses only four parameters. However, the predicted peak stress–σ2 relationship is linear. Finally, a modified 3D model was developed, which exhibited the true triaxial convex failure criterion. The equations in this model are simpler than the conventional true triaxial failure criteria. The proposed models can be implemented with a finite element method to improve the design of rock structures.https://pubs.geoscienceworld.org/lithosphere/article/2021/Special%207/1409110/616571/A-Three-Dimensional-Constitutive-Model-for-Rocks |
| spellingShingle | Z. Li Y. Fujii J. Kodama D. Fukuda A. B. N. Dassanayake P. Sinkala A Three-Dimensional Constitutive Model for Rocks Based on a Strain-Dependent Elastic Modulus Lithosphere |
| title | A Three-Dimensional Constitutive Model for Rocks Based on a Strain-Dependent Elastic Modulus |
| title_full | A Three-Dimensional Constitutive Model for Rocks Based on a Strain-Dependent Elastic Modulus |
| title_fullStr | A Three-Dimensional Constitutive Model for Rocks Based on a Strain-Dependent Elastic Modulus |
| title_full_unstemmed | A Three-Dimensional Constitutive Model for Rocks Based on a Strain-Dependent Elastic Modulus |
| title_short | A Three-Dimensional Constitutive Model for Rocks Based on a Strain-Dependent Elastic Modulus |
| title_sort | three dimensional constitutive model for rocks based on a strain dependent elastic modulus |
| url | https://pubs.geoscienceworld.org/lithosphere/article/2021/Special%207/1409110/616571/A-Three-Dimensional-Constitutive-Model-for-Rocks |
| work_keys_str_mv | AT zli athreedimensionalconstitutivemodelforrocksbasedonastraindependentelasticmodulus AT yfujii athreedimensionalconstitutivemodelforrocksbasedonastraindependentelasticmodulus AT jkodama athreedimensionalconstitutivemodelforrocksbasedonastraindependentelasticmodulus AT dfukuda athreedimensionalconstitutivemodelforrocksbasedonastraindependentelasticmodulus AT abndassanayake athreedimensionalconstitutivemodelforrocksbasedonastraindependentelasticmodulus AT psinkala athreedimensionalconstitutivemodelforrocksbasedonastraindependentelasticmodulus AT zli threedimensionalconstitutivemodelforrocksbasedonastraindependentelasticmodulus AT yfujii threedimensionalconstitutivemodelforrocksbasedonastraindependentelasticmodulus AT jkodama threedimensionalconstitutivemodelforrocksbasedonastraindependentelasticmodulus AT dfukuda threedimensionalconstitutivemodelforrocksbasedonastraindependentelasticmodulus AT abndassanayake threedimensionalconstitutivemodelforrocksbasedonastraindependentelasticmodulus AT psinkala threedimensionalconstitutivemodelforrocksbasedonastraindependentelasticmodulus |