×

Maximum-entropy method for evaluating the slope stability of Earth dams. (English) Zbl 1302.74201

Summary: The slope stability is a very important problem in geotechnical engineering. This paper presents an approach for slope reliability analysis based on the maximum-entropy method. The key idea is to implement the maximum entropy principle in estimating the probability density function. The performance function is formulated by the Simplified Bishop’s method to estimate the slope failure probability. The maximum-entropy method is used to estimate the probability density function (PDF) of the performance function subject to the moment constraints. A numerical example is calculated and compared to the Monte Carlo simulation (MCS) and the Advanced First Order Second Moment Method (AFOSM). The results show the accuracy and efficiency of the proposed method. The proposed method should be valuable for performing probabilistic analyses.

MSC:

74S30 Other numerical methods in solid mechanics (MSC2010)
74L10 Soil and rock mechanics
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] DOI: 10.1139/t76-024 · doi:10.1139/t76-024
[2] DOI: 10.1061/(ASCE)0733-9410(1994)120:12(2180) · doi:10.1061/(ASCE)0733-9410(1994)120:12(2180)
[3] DOI: 10.1061/(ASCE)1090-0241(1999)125:4(301) · doi:10.1061/(ASCE)1090-0241(1999)125:4(301)
[4] DOI: 10.1139/t97-032 · doi:10.1139/t97-032
[5] DOI: 10.1016/0167-4730(87)90002-6 · doi:10.1016/0167-4730(87)90002-6
[6] DOI: 10.1061/(ASCE)1090-0241(2006)132:11(1444) · doi:10.1061/(ASCE)1090-0241(2006)132:11(1444)
[7] DOI: 10.1061/(ASCE)0733-9410(1996)122:7(517) · doi:10.1061/(ASCE)0733-9410(1996)122:7(517)
[8] DOI: 10.1016/S0045-7825(02)00287-6 · Zbl 1101.74377 · doi:10.1016/S0045-7825(02)00287-6
[9] Li, Overtopping risk analysis using LHS-MC method (in Chinese), J. Hydrol. Eng. 31 pp 5– (2012)
[10] DOI: 10.1016/S0167-4730(00)00027-8 · doi:10.1016/S0167-4730(00)00027-8
[11] DOI: 10.1007/s00158-007-0215-2 · doi:10.1007/s00158-007-0215-2
[12] DOI: 10.1016/S0167-4730(97)00026-X · doi:10.1016/S0167-4730(97)00026-X
[13] Hohenbichler, Nonnormal dependent vectors in structural reliability, J. Eng. Mech. Div. 107 pp 1127– (1981)
[14] DOI: 10.1080/00207540110095709 · Zbl 1020.62069 · doi:10.1080/00207540110095709
[15] DOI: 10.1007/s00158-008-0299-3 · Zbl 06227658 · doi:10.1007/s00158-008-0299-3
[16] DOI: 10.1016/S0045-7825(98)00135-2 · Zbl 0958.60056 · doi:10.1016/S0045-7825(98)00135-2
[17] Zhang, A method of maximum entropy density function for calculation of approximate failure probability (in Chinese), Chin. J. Rock Mech. Eng. 14 pp 119– (1995)
[18] Zheng, Reliability analysis for vertical bearing capacity of piles based on the maximum entropy principle (in Chinese), Chin. J. Geotech. Eng. 32 pp 1643– (2010)
[19] DOI: 10.1680/geot.1955.5.1.7 · doi:10.1680/geot.1955.5.1.7
[20] Li, Reliability analysis of structures based on maximum entropy theory (in Chinese), J. Dalian Univ. Technol. 32 pp 455– (1992) · Zbl 0766.60105
[21] DOI: 10.1103/PhysRev.106.620 · Zbl 0084.43701 · doi:10.1103/PhysRev.106.620
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.