高边坡安全监测的改进GM模型预测研究

242Vol.24No.220051ChineseJournalofRockMechanicsandEngineeringJan.20052003052720030713(1973)[e-mail]121(1.6100652.610041)GM(11)GM(11)GM(11)8a(67a)GM(11)GM(11)GM(11)GM(11)TU413.6+2A10006915(2005)02030706IMPROVEDGMMODELFORSAFETYMONITORINGOFHIGHROCKSLOPESTANGTian-guo1WANXing2LIUHao-wu1(1.SchoolofHydraulicEngineeringSichuanUniversityChengdu610065China2.ChengduUniversityofInformationTechnologyChengdu610041China)AbstractTheconventionalGM(11)modelishighlylimitedandpronetoaccumulatesystematicerrorinprediction.Thepapertracesitserrorsourcesandproposesanimprovedmethod.ThisimprovedmodelisappliedforanalyzingthemonitoringdatafromeightsuccessiveyearsofahighrockslopemonitoringoftheBikouhydroelectricpowerstationwherethesixthandtheseventhyears’dataisomitted.AgreysafetymonitoringmodelofthehighrockslopeisestablishedbyusingtheimprovedGM(11)predictionmodel.BycomparingthepredictionresultsoftheimprovedGM(11)modelwiththoseoftheconventionalGM(11)modelandthestatisticalmodelandwiththoseofthemeanerrorcorrelationcoefficientandmaximumerroritisprovedthatthemodifiedGM(11)modelisofhighaccuracyinsafetymonitoringanditspredictionagreeswellwiththeactualbehaviorofthehighrockslope.KeywordsslopeengineeringGM(11)modelsafetymonitoringstatisticalmodelhighrockslope11982()()•308•2005[14]2[5]22GM(11)GM(11)[6]/[7][8]()2.1GM(11))1({)0()0(XX=)2()0(X)}()0(nX)0(X)1({)1()1(XX=)2()1(X)}()1(nX∑==kiiXkX1)0()1()()((1=k2n)(1))1(X=)1(Z)2({)1(Z)3()1(Z)}()1(nZ)()1()1()()1()1()1(kXαkXαkZ−+−=2=k3n(2)α0.5)1(X()µaXtX=+)1()1(dd(3)(3)GM(11)µkaZkX=+)()()1()0((4)aX(0)µ()aµ(4)aµ)1(XaµaµXkXak+−=+−e)1()1(ˆ)0()1((5)0=k12nX(0)=−+=+)()1()1(ˆ)1()1()0(kXkXkXakaaµX−−−e])1()[e1()0((6)0=k12n)1()1(ˆ)0()0(XX=2.2GM(11)GM(11))1(ˆX)1(X∑==−NiiXiX1)1()1(0)](ˆ)([[6])1()1()(ˆ)0()1()1(XXkX==(3)ataCaµX−−=e)1(aµaCkXat+−=+−e)1(ˆ)1(CGM(11))1()1()1(ˆ)0()1()1(XXX==aµXaCXaµaCX−=−=+−=)1()1()1(ˆ)0()0()1(aµaµXkXat+−=+−e)1()1(ˆ)0()1((7)242.GM•309)1(ˆX(k)(ˆ)1(kX)(1)1()1(X)1=)1(ˆ)1(X)1()1(X)1()1(X=)1(ˆ)1(X)1()1(X=)(ˆ)1(mX=mmX()()1(23n)=+−=+−+−aµaµmXkXmaak)1()1()1(e))(()1(()aµaµmXmka+−+−−1)1(e))(((8)m12n(8)(4)=m1(8)(4)MATLAB[9]13[10]101.8m297.36m24(k1k4)8a(67a)k2k41GM(11)GM(11)12367a2aGM(11)1GM(11)(8)=)()1(mX=mX()2()1(23n)GM(11)→−=→−=−−)4k(194.4e754.20)()2k(816.27e606.54)()1(393.0)1()1(292.0)1(kkkXkX(9)GM(11)→−=→−=−−)4k(425.13e625.22)()2k(993.34e593.47)()1(306.0)1()1(266.0)1(kkkXkX(10)→=→=−−)4k(338.2)2k(483.3153.2140134.2038tXtX(11))()1(kX=k12NXt41Fig.1TheprogramflowchartX(0)(n)Z(0)(n)m=1X(0)(n)Z(0)(n)(23)(4)X(0)(n)E1X(1)(m+1)E1Ekk=12nE1E2EnaµX(k)E1=Ekm=k•310•20052Fig.2Thehighrockslopeandstationpointarrangementintherightabutmentofthedam1Table1Theannualmeanhorizontaldisplacementatstationpointsofthehighrockslope/mm1a2a3a4a5a8ak212.6014.1918.4724.4833.6960.51k49.208.339.0613.8922.8341.912k2Table2Computationresultsandrelativeerrorofmodelsatthek2stationpointGM(11)GM(11)/mm/%/mm/%/mm/%112.282.5412.600.0011.905.56214.623.0314.502.1815.197.05318.570.5418.932.4919.334.66424.831.4324.680.8224.530.20533.490.5932.214.3931.047.87856.691.3656.137.2461.912.313k4Table3Computationresultsandrelativeerrorofmodelsatthek4stationpointGM(11)GM(11)/mm/%/mm/%/mm/%18.745.009.200.007.1122.7228.633.607.0215.739.1910.3239.575.6310.1812.3611.8430.68413.24.9714.796.4815.219.50522.830.0021.117.5319.4814.67840.862.5140.164.1840.243.98R[11]∑−∑−−=22)()ˆ(1iiiiYYYYR(12)iYiYˆY4Table4Accuracycomparisonofcomputationresultsbetweenthemodelsk2k4GM(11)GM(11)1.582.854.613.037.247.871.0000.9930.9963.627.7115.315.6315.7330.680.9990.9940.9833424GM(11)1GM(11)66%(k2)76%(k4)45%(k2)53%(k4)61%(k2)82%(k4)58%(k2)64%(k4)56GM(11)3k2Fig.3Computationresultscomparisonofthemodelsatthek2stationpoint242.GM•3114k4Fig.4Computationresultscomparisonofthemodelsatthek4stationpoint5Fig.5Themeanerrorcomparisonofthemodels6Fig.6Themaximumerrorcomparisonofthemodels4GM(11)k2k46ak27GM(11)GM(11)GM(11)GM(11)7k2Fig.7Predictionbehaviorcomparisonofthethreemodelsatthek2stationpointGM(11)(References)[1].[J].200234(4)2629.(WangJunWangChangminLiXiaoxiongetal.Deformationmechanismandengineeringimprovementofthehighslopeinhydropowerproject[J].NorthChinaInstituteofWaterConservancyandHydroelectricPower200234(4)2629.(inChinese))•312•2005[2].[J].200219(6)6668.(HuangYuhui.Integratedtreatmentforhighslopeagainstslide[J].JournalofHighwayandTransportationResearchandDevelopment200219(6)6668.(inChinese))[3].[J].200233(11)2729.(PengShixiongDengLiangshenMengYulinetal.ComplexsamdwichbedrocksdeformationdestroymodeofhighslopeinZipingpuengineering[J].WaterConservancyandHydroelectricPowerTechnology200233(11)2729.(inChinese))[4].[J].200213(3)3235.(ZhaoYuguangGaoBo.Fieldmonitormeasuringandgeologicaldisasterforecastatthemouthoftunnelneartherockysteepsideslopeunderunsymmetricalloading[J].JournalofGeologicalHazardsandEnvironmentPreservation200213(3)3235.(inChinese))[5].[J].199615(1)18.(YinKunlongYanTongzhen.Landslidepredictionandrelevantmodels[J].ChineseJournalofRockMechanicsandEngineering199615(1)18.(inChinese))[6].GM(11)[J].199210(6)2731.(LiYunguiLiQingfuZhaoGuofan.Animprovemento