For decades, Lychrel numbers have been studied on many bases. Their existence has been proven in base 2, 11 or 17. This paper presents a probabilistic proof of the existence of Lychrel number in base 10 and provides s...For decades, Lychrel numbers have been studied on many bases. Their existence has been proven in base 2, 11 or 17. This paper presents a probabilistic proof of the existence of Lychrel number in base 10 and provides some properties which enable a mathematical extraction of new Lychrel numbers from existing ones. This probabilistic approach has the advantage of being extendable to other bases. The results show that palindromes can also be Lychrel numbers.展开更多
Rock slope stability is of great concern along highway routes as stability problems on cut slopes may cause fatal events as well as loss of property.In rock slope engineering,stability evaluations are commonly perform...Rock slope stability is of great concern along highway routes as stability problems on cut slopes may cause fatal events as well as loss of property.In rock slope engineering,stability evaluations are commonly performed by means of analytical or numerical analyses,principally considering the factor of safety concept.As a matter of fact,the probabilistic assessment of slope stability is progressively getting popularity due to difficulties in assigning the most appropriate values to design parameters in analytical or numerical methods.Additionally,the effect of heterogeneities in rock masses and discontinuities on the analysis results is minimized through the probabilistic concept.In this study,slope stability of high and steep sedimentary rock cut slopes along a state highway in AdilcevazBitlis(Turkey) was evaluated on the basis of probabilistic approach using the Slope Stability Probability Classification(SSPC) system.The probabilistic assessment indicates major slope stability problems because of discontinuity controlled and discontinuity orientation independent mass movements.Almost all studied cut slopes suffer from orientation-independent stability problems with very low stability probabilities.Additionally,the probability of planar and toppling failures issignificantly high with respect to the SSPC system.The stability problems along the investigated rock slopes were also verified by field reconnaissance.Remedial measures such as slope re-design and reinforcement at the studied locations should be taken to prevent hazardous events along the highway.On the other hand,the probabilistic approach may be a useful tool during rock slope engineering to overcome numerous uncertainties when probabilistic and analytic results are compared.展开更多
In open pit mining,uncontrolled block instabilities have serious social,economic and regulatory consequences,such as casualties,disruption of operation and increased regulation difficulties.For this reason,bench face ...In open pit mining,uncontrolled block instabilities have serious social,economic and regulatory consequences,such as casualties,disruption of operation and increased regulation difficulties.For this reason,bench face angle,as one of the controlling parameters associated with block instabilities,should be carefully designed for sustainable mining.This study introduces a discrete fracture network(DFN)-based probabilistic block theory approach for the fast design of the bench face angle.A major advantage is the explicit incorporation of discontinuity size and spatial distribution in the procedure of key blocks testing.The proposed approach was applied to a granite mine in China.First,DFN models were generated from a multi-step modeling procedure to simulate the complex structural characteristics of pit slopes.Then,a modified key blocks searching method was applied to the slope faces modeled,and a cumulative probability of failure was obtained for each sector.Finally,a bench face angle was determined commensurate with an acceptable risk level of stability.The simulation results have shown that the number of hazardous traces exposed on the slope face can be significantly reduced when the suggested bench face angle is adopted,indicating an extremely low risk of uncontrolled block instabilities.展开更多
Rock fall accidents in mountainous cliff areas have significant consequences for human life and transportation.This study aimed to evaluate the rockfall hazard in the Cap Aokas cliff region located along the northeast...Rock fall accidents in mountainous cliff areas have significant consequences for human life and transportation.This study aimed to evaluate the rockfall hazard in the Cap Aokas cliff region located along the northeast coast of Algeria by identifying the key factors contributing to rockfall occurrence.We employed a combination of kinematic analysis,Matterocking method,and 3D trajectory simulations to determine zones that are susceptible to rockfall mobilization.By using a probabilistic and structural approach in conjunction with photogrammetry,we identified the controlling factors.The kinematic analysis revealed the presence of five discontinuity families,which indicated both plane and wedge failure modes.The 3D trajectory simulations demonstrated that the falling blocks followed the stream direction.We then validated the susceptibility maps generated from the analysis using aerial photos and historical rockfall events.The findings of this study enhance our understanding of rockfall phenomena and provide valuable insights for the development of effective strategies to mitigate rockfall hazards.展开更多
This paper presents an interval effective independence method for optimal sensor placement, which contains uncertain structural information. To overcome the lack of insufficient statistic description of uncertain para...This paper presents an interval effective independence method for optimal sensor placement, which contains uncertain structural information. To overcome the lack of insufficient statistic description of uncertain parameters, this paper treats uncertainties as non-probability intervals. Based on the iterative process of classical effective independence method, the proposed study considers the eliminating steps with uncertain cases. Therefore, this method with Fisher information matrix is extended to interval numbers, which could conform to actual engineering. As long as we know the bounds of uncertainties, the interval Fisher information matrix could be obtained conveniently by interval analysis technology. Moreover, due to the definition and calculation of the interval relationship, the possibilities of eliminating candidate sensors in each iterative process and the final layout of sensor placement are both presented in this paper. Finally, two numerical examples, including a five-storey shear structure and a truss structure are proposed respectively in this paper. Compared with Monte Carlo simulation, both of them can indicate the veracity of the interval effective independence method.展开更多
文摘For decades, Lychrel numbers have been studied on many bases. Their existence has been proven in base 2, 11 or 17. This paper presents a probabilistic proof of the existence of Lychrel number in base 10 and provides some properties which enable a mathematical extraction of new Lychrel numbers from existing ones. This probabilistic approach has the advantage of being extendable to other bases. The results show that palindromes can also be Lychrel numbers.
基金financially supported by the Scientific Research Projects Office of YüzüncüYil University(YYU-BAP,Project Number 2012-FBEYL48)
文摘Rock slope stability is of great concern along highway routes as stability problems on cut slopes may cause fatal events as well as loss of property.In rock slope engineering,stability evaluations are commonly performed by means of analytical or numerical analyses,principally considering the factor of safety concept.As a matter of fact,the probabilistic assessment of slope stability is progressively getting popularity due to difficulties in assigning the most appropriate values to design parameters in analytical or numerical methods.Additionally,the effect of heterogeneities in rock masses and discontinuities on the analysis results is minimized through the probabilistic concept.In this study,slope stability of high and steep sedimentary rock cut slopes along a state highway in AdilcevazBitlis(Turkey) was evaluated on the basis of probabilistic approach using the Slope Stability Probability Classification(SSPC) system.The probabilistic assessment indicates major slope stability problems because of discontinuity controlled and discontinuity orientation independent mass movements.Almost all studied cut slopes suffer from orientation-independent stability problems with very low stability probabilities.Additionally,the probability of planar and toppling failures issignificantly high with respect to the SSPC system.The stability problems along the investigated rock slopes were also verified by field reconnaissance.Remedial measures such as slope re-design and reinforcement at the studied locations should be taken to prevent hazardous events along the highway.On the other hand,the probabilistic approach may be a useful tool during rock slope engineering to overcome numerous uncertainties when probabilistic and analytic results are compared.
基金financially supported by the National Natural Science Foundation of China(Grant Nos.42102313 and 52104125)the Fundamental Research Funds for the Central Universities(Grant No.B240201094).
文摘In open pit mining,uncontrolled block instabilities have serious social,economic and regulatory consequences,such as casualties,disruption of operation and increased regulation difficulties.For this reason,bench face angle,as one of the controlling parameters associated with block instabilities,should be carefully designed for sustainable mining.This study introduces a discrete fracture network(DFN)-based probabilistic block theory approach for the fast design of the bench face angle.A major advantage is the explicit incorporation of discontinuity size and spatial distribution in the procedure of key blocks testing.The proposed approach was applied to a granite mine in China.First,DFN models were generated from a multi-step modeling procedure to simulate the complex structural characteristics of pit slopes.Then,a modified key blocks searching method was applied to the slope faces modeled,and a cumulative probability of failure was obtained for each sector.Finally,a bench face angle was determined commensurate with an acceptable risk level of stability.The simulation results have shown that the number of hazardous traces exposed on the slope face can be significantly reduced when the suggested bench face angle is adopted,indicating an extremely low risk of uncontrolled block instabilities.
基金the support provided by the Laboratory of Applied Research in Engineering Geology, Geotechnics, Water Sciences, and Environment, Setif 1 University, Algeria
文摘Rock fall accidents in mountainous cliff areas have significant consequences for human life and transportation.This study aimed to evaluate the rockfall hazard in the Cap Aokas cliff region located along the northeast coast of Algeria by identifying the key factors contributing to rockfall occurrence.We employed a combination of kinematic analysis,Matterocking method,and 3D trajectory simulations to determine zones that are susceptible to rockfall mobilization.By using a probabilistic and structural approach in conjunction with photogrammetry,we identified the controlling factors.The kinematic analysis revealed the presence of five discontinuity families,which indicated both plane and wedge failure modes.The 3D trajectory simulations demonstrated that the falling blocks followed the stream direction.We then validated the susceptibility maps generated from the analysis using aerial photos and historical rockfall events.The findings of this study enhance our understanding of rockfall phenomena and provide valuable insights for the development of effective strategies to mitigate rockfall hazards.
基金supported by the National Natural Science Foundation of China(Grant No.11502278)
文摘This paper presents an interval effective independence method for optimal sensor placement, which contains uncertain structural information. To overcome the lack of insufficient statistic description of uncertain parameters, this paper treats uncertainties as non-probability intervals. Based on the iterative process of classical effective independence method, the proposed study considers the eliminating steps with uncertain cases. Therefore, this method with Fisher information matrix is extended to interval numbers, which could conform to actual engineering. As long as we know the bounds of uncertainties, the interval Fisher information matrix could be obtained conveniently by interval analysis technology. Moreover, due to the definition and calculation of the interval relationship, the possibilities of eliminating candidate sensors in each iterative process and the final layout of sensor placement are both presented in this paper. Finally, two numerical examples, including a five-storey shear structure and a truss structure are proposed respectively in this paper. Compared with Monte Carlo simulation, both of them can indicate the veracity of the interval effective independence method.
