By using some elementary inequalities, authors in this paper makes further improvement for estimating the heights of Bézier curve and rational Bézier curve. And the termination criterion for subdivision of t...By using some elementary inequalities, authors in this paper makes further improvement for estimating the heights of Bézier curve and rational Bézier curve. And the termination criterion for subdivision of the rational Bézier curve is also improved. The conclusion of the extreme value problem is thus further confirmed.展开更多
Reliability-based design (RBD) is being adopted by geotechnical design codes worldwide, and it is therefore necessary that rock engineering practice evolves to embrace RBD. This paper examines the Hoek-Brown (H-B) str...Reliability-based design (RBD) is being adopted by geotechnical design codes worldwide, and it is therefore necessary that rock engineering practice evolves to embrace RBD. This paper examines the Hoek-Brown (H-B) strength criterion within the RBD framework, and presents three distinct analyses using a Bayesian approach. Firstly, a compilation of intact compressive strength test data for six rock types is used to examine uncertainty and variability in the estimated H-B parameters m and σc, and corresponding predicted axial strength. The results suggest that within- and between-rock type variabilities are so large that these parameters need to be determined from rock testing campaigns, rather than reference values being used. The second analysis uses an extensive set of compressive and tensile (both direct and indirect) strength data for a granodiorite, together with a new Bayesian regression model, to develop joint probability distributions of m and σc suitable for use in RBD. This analysis also shows how compressive and indirect tensile strength data may be robustly used to fit an H-B criterion. The third analysis uses the granodiorite data to investigate the important matter of developing characteristic strength criteria. Using definitions from Eurocode 7, a formal Bayesian interpretation of characteristic strength is proposed and used to analyse strength data to generate a characteristic criterion. These criteria are presented in terms of characteristic parameters mk and σck, the values of which are shown to depend on the testing regime used to obtain the strength data. The paper confirms that careful use of appropriate Bayesian statistical analysis allows the H-B criterion to be brought within the framework of RBD. It also reveals that testing guidelines such as the International Society for Rock Mechanics and Rock Engineering (ISRM) suggested methods will require modification in order to support RBD. Importantly, the need to fully understand the implications of uncertainty in nonlinear strength criteria is identified.展开更多
This paper explores the potential implications of recent thinking in relation to rock mass strength for future tunnelling projects in Brisbane,Australia,particularly as they are constructed within deep horizons where ...This paper explores the potential implications of recent thinking in relation to rock mass strength for future tunnelling projects in Brisbane,Australia,particularly as they are constructed within deep horizons where the in situ stress magnitudes is larger.Rock mass failure mechanisms for the current tunnels in Brisbane are generally discontinuity controlled and the potential for stress-induced failure is relatively rare.For the road tunnels which have been constructed in Brisbane over the last 12 years,the strength of the more massive rock masses for continuum analysis has been estimated by the application of the Hoek-Brown(H-B)failure criterion using the geological strength index(GSI)to determine the H-B parameters mb,s and a.Over the last few years,alternative approaches to estimating rock mass strength for‘massive to moderately jointed hard rock masses’have been proposed by others,which are built on the work completed by E.Hoek and E.T.Brown in this area over their joint careers.This paper explores one of these alternative approaches to estimating rock mass strength for one of the geological units(the Brisbane Tuff),which is often encountered in tunnelling projects in Brisbane.The potential implications of these strength forecasts for future tunnelling projects are discussed along with the additional work which will need to be undertaken to confirm the applicability of such alternative strength criteria for this rock mass.展开更多
文摘By using some elementary inequalities, authors in this paper makes further improvement for estimating the heights of Bézier curve and rational Bézier curve. And the termination criterion for subdivision of the rational Bézier curve is also improved. The conclusion of the extreme value problem is thus further confirmed.
文摘Reliability-based design (RBD) is being adopted by geotechnical design codes worldwide, and it is therefore necessary that rock engineering practice evolves to embrace RBD. This paper examines the Hoek-Brown (H-B) strength criterion within the RBD framework, and presents three distinct analyses using a Bayesian approach. Firstly, a compilation of intact compressive strength test data for six rock types is used to examine uncertainty and variability in the estimated H-B parameters m and σc, and corresponding predicted axial strength. The results suggest that within- and between-rock type variabilities are so large that these parameters need to be determined from rock testing campaigns, rather than reference values being used. The second analysis uses an extensive set of compressive and tensile (both direct and indirect) strength data for a granodiorite, together with a new Bayesian regression model, to develop joint probability distributions of m and σc suitable for use in RBD. This analysis also shows how compressive and indirect tensile strength data may be robustly used to fit an H-B criterion. The third analysis uses the granodiorite data to investigate the important matter of developing characteristic strength criteria. Using definitions from Eurocode 7, a formal Bayesian interpretation of characteristic strength is proposed and used to analyse strength data to generate a characteristic criterion. These criteria are presented in terms of characteristic parameters mk and σck, the values of which are shown to depend on the testing regime used to obtain the strength data. The paper confirms that careful use of appropriate Bayesian statistical analysis allows the H-B criterion to be brought within the framework of RBD. It also reveals that testing guidelines such as the International Society for Rock Mechanics and Rock Engineering (ISRM) suggested methods will require modification in order to support RBD. Importantly, the need to fully understand the implications of uncertainty in nonlinear strength criteria is identified.
文摘This paper explores the potential implications of recent thinking in relation to rock mass strength for future tunnelling projects in Brisbane,Australia,particularly as they are constructed within deep horizons where the in situ stress magnitudes is larger.Rock mass failure mechanisms for the current tunnels in Brisbane are generally discontinuity controlled and the potential for stress-induced failure is relatively rare.For the road tunnels which have been constructed in Brisbane over the last 12 years,the strength of the more massive rock masses for continuum analysis has been estimated by the application of the Hoek-Brown(H-B)failure criterion using the geological strength index(GSI)to determine the H-B parameters mb,s and a.Over the last few years,alternative approaches to estimating rock mass strength for‘massive to moderately jointed hard rock masses’have been proposed by others,which are built on the work completed by E.Hoek and E.T.Brown in this area over their joint careers.This paper explores one of these alternative approaches to estimating rock mass strength for one of the geological units(the Brisbane Tuff),which is often encountered in tunnelling projects in Brisbane.The potential implications of these strength forecasts for future tunnelling projects are discussed along with the additional work which will need to be undertaken to confirm the applicability of such alternative strength criteria for this rock mass.
