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["Slope Stability Calculator for Mohr-Coulomb Dry Ground "]
["by C. Carranza-Torres and E. Hormazabal (2018)"]
[]
["Input Data"]
["H [m] =",300,"(slope height)"]
["a [deg] =",52,"(slope angle; allowable range 20 to 80 deg)"]
["g [kN/m3] =",25,"(ground unit weight)"]
["c [kPa] =",667,"(ground cohesion; must be larger than 0)"]
["f [deg] =",37,"(ground friction angle)"]
["Make Plot?","yes","(select 'yes' to plot results; otherwise select 'no') "]
[]
["Results"]
["Message:",{"$f":"IF(OR(B14<0.01,B14>100),\"X value out of range (allowable range is 0.01 to 100)\",IF(OR(B6<20,B6>80),\"slope angle value out of range (allowable range is 20 to 80)\",\"\"))","v":""}]
["X [-] =",{"$f":"IF(B8<>0,B7*B5*TAN(B9*PI()/180)/B8,1E+30)","v":8.4732464404362169},"(dimensionless ratio X=gH/c tan(f); allowable range 0.01 to 100)"]
["FS [-] =",{"$f":"IF(B13<>\"\",\"N/A\",TAN(B9*PI()/180)*(10^(LOG(INDEX(FS_tanPhi!B2:H82,IF(MATCH(Main_Page!B14,FS_tanPhi!A2:A82,1)<>ROWS(FS_tanPhi!A2:A82),MATCH(Main_Page!B14,FS_tanPhi!A2:A82,1),MATCH(Main_Page!B14,FS_tanPhi!A2:A82,1)-1),IF(MATCH(Main_Page!B6,FS_tanPhi!B1:H1,1)<>COLUMNS(FS_tanPhi!B1:H1),MATCH(Main_Page!B6,FS_tanPhi!B1:H1,1),MATCH(Main_Page!B6,FS_tanPhi!B1:H1,1)-1)))+(LOG(Main_Page!B14)-LOG(INDEX(FS_tanPhi!A2:A82,IF(MATCH(Main_Page!B14,FS_tanPhi!A2:A82,1)<>ROWS(FS_tanPhi!A2:A82),MATCH(Main_Page!B14,FS_tanPhi!A2:A82,1),MATCH(Main_Page!B14,FS_tanPhi!A2:A82,1)-1))))/(LOG(INDEX(FS_tanPhi!A2:A82,IF(MATCH(Main_Page!B14,FS_tanPhi!A2:A82,1)<>ROWS(FS_tanPhi!A2:A82),MATCH(Main_Page!B14,FS_tanPhi!A2:A82,1),MATCH(Main_Page!B14,FS_tanPhi!A2:A82,1)-1)+1))-LOG(INDEX(FS_tanPhi!A2:A82,IF(MATCH(Main_Page!B14,FS_tanPhi!A2:A82,1)<>ROWS(FS_tanPhi!A2:A82),MATCH(Main_Page!B14,FS_tanPhi!A2:A82,1),MATCH(Main_Page!B14,FS_tanPhi!A2:A82,1)-1))))*(LOG(INDEX(FS_tanPhi!B2:H82,IF(MATCH(Main_Page!B14,FS_tanPhi!A2:A82,1)<>ROWS(FS_tanPhi!A2:A82),MATCH(Main_Page!B14,FS_tanPhi!A2:A82,1),MATCH(Main_Page!B14,FS_tanPhi!A2:A82,1)-1)+1,IF(MATCH(Main_Page!B6,FS_tanPhi!B1:H1,1)<>COLUMNS(FS_tanPhi!B1:H1),MATCH(Main_Page!B6,FS_tanPhi!B1:H1,1),MATCH(Main_Page!B6,FS_tanPhi!B1:H1,1)-1)))-LOG(INDEX(FS_tanPhi!B2:H82,IF(MATCH(Main_Page!B14,FS_tanPhi!A2:A82,1)<>ROWS(FS_tanPhi!A2:A82),MATCH(Main_Page!B14,FS_tanPhi!A2:A82,1),MATCH(Main_Page!B14,FS_tanPhi!A2:A82,1)-1),IF(MATCH(Main_Page!B6,FS_tanPhi!B1:H1,1)<>COLUMNS(FS_tanPhi!B1:H1),MATCH(Main_Page!B6,FS_tanPhi!B1:H1,1),MATCH(Main_Page!B6,FS_tanPhi!B1:H1,1)-1)))))+(LOG(Main_Page!B6)-LOG(INDEX(FS_tanPhi!B1:H1,IF(MATCH(Main_Page!B6,FS_tanPhi!B1:H1,1)<>COLUMNS(FS_tanPhi!B1:H1),MATCH(Main_Page!B6,FS_tanPhi!B1:H1,1),MATCH(Main_Page!B6,FS_tanPhi!B1:H1,1)-1))))/(LOG(INDEX(FS_tanPhi!B1:H1,IF(MATCH(Main_Page!B6,FS_tanPhi!B1:H1,1)<>COLUMNS(FS_tanPhi!B1:H1),MATCH(Main_Page!B6,FS_tanPhi!B1:H1,1),MATCH(Main_Page!B6,FS_tanPhi!B1:H1,1)-1)+1))-LOG(INDEX(FS_tanPhi!B1:H1,IF(MATCH(Main_Page!B6,FS_tanPhi!B1:H1,1)<>COLUMNS(FS_tanPhi!B1:H1),MATCH(Main_Page!B6,FS_tanPhi!B1:H1,1),MATCH(Main_Page!B6,FS_tanPhi!B1:H1,1)-1))))*(10^(LOG(INDEX(FS_tanPhi!B2:H82,IF(MATCH(Main_Page!B14,FS_tanPhi!A2:A82,1)<>ROWS(FS_tanPhi!A2:A82),MATCH(Main_Page!B14,FS_tanPhi!A2:A82,1),MATCH(Main_Page!B14,FS_tanPhi!A2:A82,1)-1),IF(MATCH(Main_Page!B6,FS_tanPhi!B1:H1,1)<>COLUMNS(FS_tanPhi!B1:H1),MATCH(Main_Page!B6,FS_tanPhi!B1:H1,1),MATCH(Main_Page!B6,FS_tanPhi!B1:H1,1)-1)+1))+(LOG(Main_Page!B14)-LOG(INDEX(FS_tanPhi!A2:A82,IF(MATCH(Main_Page!B14,FS_tanPhi!A2:A82,1)<>ROWS(FS_tanPhi!A2:A82),MATCH(Main_Page!B14,FS_tanPhi!A2:A82,1),MATCH(Main_Page!B14,FS_tanPhi!A2:A82,1)-1))))/(LOG(INDEX(FS_tanPhi!A2:A82,IF(MATCH(Main_Page!B14,FS_tanPhi!A2:A82,1)<>ROWS(FS_tanPhi!A2:A82),MATCH(Main_Page!B14,FS_tanPhi!A2:A82,1),MATCH(Main_Page!B14,FS_tanPhi!A2:A82,1)-1)+1))-LOG(INDEX(FS_tanPhi!A2:A82,IF(MATCH(Main_Page!B14,FS_tanPhi!A2:A82,1)<>ROWS(FS_tanPhi!A2:A82),MATCH(Main_Page!B14,FS_tanPhi!A2:A82,1),MATCH(Main_Page!B14,FS_tanPhi!A2:A82,1)-1))))*(LOG(INDEX(FS_tanPhi!B2:H82,IF(MATCH(Main_Page!B14,FS_tanPhi!A2:A82,1)<>ROWS(FS_tanPhi!A2:A82),MATCH(Main_Page!B14,FS_tanPhi!A2:A82,1),MATCH(Main_Page!B14,FS_tanPhi!A2:A82,1)-1)+1,IF(MATCH(Main_Page!B6,FS_tanPhi!B1:H1,1)<>COLUMNS(FS_tanPhi!B1:H1),MATCH(Main_Page!B6,FS_tanPhi!B1:H1,1),MATCH(Main_Page!B6,FS_tanPhi!B1:H1,1)-1)+1))-LOG(INDEX(FS_tanPhi!B2:H82,IF(MATCH(Main_Page!B14,FS_tanPhi!A2:A82,1)<>ROWS(FS_tanPhi!A2:A82),MATCH(Main_Page!B14,FS_tanPhi!A2:A82,1),MATCH(Main_Page!B14,FS_tanPhi!A2:A82,1)-1),IF(MATCH(Main_Page!B6,FS_tanPhi!B1:H1,1)<>COLUMNS(FS_tanPhi!B1:H1),MATCH(Main_Page!B6,FS_tanPhi!B1:H1,1),MATCH(Main_Page!B6,FS_tanPhi!B1:H1,1)-1)+1))))-10^(LOG(INDEX(FS_tanPhi!B2:H82,IF(MATCH(Main_Page!B14,FS_tanPhi!A2:A82,1)<>ROWS(FS_tanPhi!A2:A82),MATCH(Main_Page!B14,FS_tanPhi!A2:A82,1),MATCH(Main_Page!B14,FS_tanPhi!A2:A82,1)-1),IF(MATCH(Main_Page!B6,FS_tanPhi!B1:H1,1)<>COLUMNS(FS_tanPhi!B1:H1),MATCH(Main_Page!B6,FS_tanPhi!B1:H1,1),MATCH(Main_Page!B6,FS_tanPhi!B1:H1,1)-1)))+(LOG(Main_Page!B14)-LOG(INDEX(FS_tanPhi!A2:A82,IF(MATCH(Main_Page!B14,FS_tanPhi!A2:A82,1)<>ROWS(FS_tanPhi!A2:A82),MATCH(Main_Page!B14,FS_tanPhi!A2:A82,1),MATCH(Main_Page!B14,FS_tanPhi!A2:A82,1)-1))))/(LOG(INDEX(FS_tanPhi!A2:A82,IF(MATCH(Main_Page!B14,FS_tanPhi!A2:A82,1)<>ROWS(FS_tanPhi!A2:A82),MATCH(Main_Page!B14,FS_tanPhi!A2:A82,1),MATCH(Main_Page!B14,FS_tanPhi!A2:A82,1)-1)+1))-LOG(INDEX(FS_tanPhi!A2:A82,IF(MATCH(Main_Page!B14,FS_tanPhi!A2:A82,1)<>ROWS(FS_tanPhi!A2:A82),MATCH(Main_Page!B14,FS_tanPhi!A2:A82,1),MATCH(Main_Page!B14,FS_tanPhi!A2:A82,1)-1))))*(LOG(INDEX(FS_tanPhi!B2:H82,IF(MATCH(Main_Page!B14,FS_tanPhi!A2:A82,1)<>ROWS(FS_tanPhi!A2:A82),MATCH(Main_Page!B14,FS_tanPhi!A2:A82,1),MATCH(Main_Page!B14,FS_tanPhi!A2:A82,1)-1)+1,IF(MATCH(Main_Page!B6,FS_tanPhi!B1:H1,1)<>COLUMNS(FS_tanPhi!B1:H1),MATCH(Main_Page!B6,FS_tanPhi!B1:H1,1),MATCH(Main_Page!B6,FS_tanPhi!B1:H1,1)-1)))-LOG(INDEX(FS_tanPhi!B2:H82,IF(MATCH(Main_Page!B14,FS_tanPhi!A2:A82,1)<>ROWS(FS_tanPhi!A2:A82),MATCH(Main_Page!B14,FS_tanPhi!A2:A82,1),MATCH(Main_Page!B14,FS_tanPhi!A2:A82,1)-1),IF(MATCH(Main_Page!B6,FS_tanPhi!B1:H1,1)<>COLUMNS(FS_tanPhi!B1:H1),MATCH(Main_Page!B6,FS_tanPhi!B1:H1,1),MATCH(Main_Page!B6,FS_tanPhi!B1:H1,1)-1))))))))","v":1.5564489259655077},"(factor of safety)"]
["xc [m] =",{"$f":"IF(B13<>\"\",\"N/A\",B5*((INDEX(Xc_H!B2:H82,IF(MATCH(Main_Page!B14,Xc_H!A2:A82,1)<>ROWS(Xc_H!A2:A82),MATCH(Main_Page!B14,Xc_H!A2:A82,1),MATCH(Main_Page!B14,Xc_H!A2:A82,1)-1),IF(MATCH(Main_Page!B6,Xc_H!B1:H1,1)<>COLUMNS(Xc_H!B1:H1),MATCH(Main_Page!B6,Xc_H!B1:H1,1),MATCH(Main_Page!B6,Xc_H!B1:H1,1)-1))+(LOG(Main_Page!B14)-LOG(INDEX(Xc_H!A2:A82,IF(MATCH(Main_Page!B14,Xc_H!A2:A82,1)<>ROWS(Xc_H!A2:A82),MATCH(Main_Page!B14,Xc_H!A2:A82,1),MATCH(Main_Page!B14,Xc_H!A2:A82,1)-1))))/(LOG(INDEX(Xc_H!A2:A82,IF(MATCH(Main_Page!B14,Xc_H!A2:A82,1)<>ROWS(Xc_H!A2:A82),MATCH(Main_Page!B14,Xc_H!A2:A82,1),MATCH(Main_Page!B14,Xc_H!A2:A82,1)-1)+1))-LOG(INDEX(Xc_H!A2:A82,IF(MATCH(Main_Page!B14,Xc_H!A2:A82,1)<>ROWS(Xc_H!A2:A82),MATCH(Main_Page!B14,Xc_H!A2:A82,1),MATCH(Main_Page!B14,Xc_H!A2:A82,1)-1))))*(INDEX(Xc_H!B2:H82,IF(MATCH(Main_Page!B14,Xc_H!A2:A82,1)<>ROWS(Xc_H!A2:A82),MATCH(Main_Page!B14,Xc_H!A2:A82,1),MATCH(Main_Page!B14,Xc_H!A2:A82,1)-1)+1,IF(MATCH(Main_Page!B6,Xc_H!B1:H1,1)<>COLUMNS(Xc_H!B1:H1),MATCH(Main_Page!B6,Xc_H!B1:H1,1),MATCH(Main_Page!B6,Xc_H!B1:H1,1)-1))-INDEX(Xc_H!B2:H82,IF(MATCH(Main_Page!B14,Xc_H!A2:A82,1)<>ROWS(Xc_H!A2:A82),MATCH(Main_Page!B14,Xc_H!A2:A82,1),MATCH(Main_Page!B14,Xc_H!A2:A82,1)-1),IF(MATCH(Main_Page!B6,Xc_H!B1:H1,1)<>COLUMNS(Xc_H!B1:H1),MATCH(Main_Page!B6,Xc_H!B1:H1,1),MATCH(Main_Page!B6,Xc_H!B1:H1,1)-1))))+((Main_Page!B6)-(INDEX(Xc_H!B1:H1,IF(MATCH(Main_Page!B6,Xc_H!B1:H1,1)<>COLUMNS(Xc_H!B1:H1),MATCH(Main_Page!B6,Xc_H!B1:H1,1),MATCH(Main_Page!B6,Xc_H!B1:H1,1)-1))))/((INDEX(Xc_H!B1:H1,IF(MATCH(Main_Page!B6,Xc_H!B1:H1,1)<>COLUMNS(Xc_H!B1:H1),MATCH(Main_Page!B6,Xc_H!B1:H1,1),MATCH(Main_Page!B6,Xc_H!B1:H1,1)-1)+1))-(INDEX(Xc_H!B1:H1,IF(MATCH(Main_Page!B6,Xc_H!B1:H1,1)<>COLUMNS(Xc_H!B1:H1),MATCH(Main_Page!B6,Xc_H!B1:H1,1),MATCH(Main_Page!B6,Xc_H!B1:H1,1)-1))))*((INDEX(Xc_H!B2:H82,IF(MATCH(Main_Page!B14,Xc_H!A2:A82,1)<>ROWS(Xc_H!A2:A82),MATCH(Main_Page!B14,Xc_H!A2:A82,1),MATCH(Main_Page!B14,Xc_H!A2:A82,1)-1),IF(MATCH(Main_Page!B6,Xc_H!B1:H1,1)<>COLUMNS(Xc_H!B1:H1),MATCH(Main_Page!B6,Xc_H!B1:H1,1),MATCH(Main_Page!B6,Xc_H!B1:H1,1)-1)+1)+(LOG(Main_Page!B14)-LOG(INDEX(Xc_H!A2:A82,IF(MATCH(Main_Page!B14,Xc_H!A2:A82,1)<>ROWS(Xc_H!A2:A82),MATCH(Main_Page!B14,Xc_H!A2:A82,1),MATCH(Main_Page!B14,Xc_H!A2:A82,1)-1))))/(LOG(INDEX(Xc_H!A2:A82,IF(MATCH(Main_Page!B14,Xc_H!A2:A82,1)<>ROWS(Xc_H!A2:A82),MATCH(Main_Page!B14,Xc_H!A2:A82,1),MATCH(Main_Page!B14,Xc_H!A2:A82,1)-1)+1))-LOG(INDEX(Xc_H!A2:A82,IF(MATCH(Main_Page!B14,Xc_H!A2:A82,1)<>ROWS(Xc_H!A2:A82),MATCH(Main_Page!B14,Xc_H!A2:A82,1),MATCH(Main_Page!B14,Xc_H!A2:A82,1)-1))))*(INDEX(Xc_H!B2:H82,IF(MATCH(Main_Page!B14,Xc_H!A2:A82,1)<>ROWS(Xc_H!A2:A82),MATCH(Main_Page!B14,Xc_H!A2:A82,1),MATCH(Main_Page!B14,Xc_H!A2:A82,1)-1)+1,IF(MATCH(Main_Page!B6,Xc_H!B1:H1,1)<>COLUMNS(Xc_H!B1:H1),MATCH(Main_Page!B6,Xc_H!B1:H1,1),MATCH(Main_Page!B6,Xc_H!B1:H1,1)-1)+1)-INDEX(Xc_H!B2:H82,IF(MATCH(Main_Page!B14,Xc_H!A2:A82,1)<>ROWS(Xc_H!A2:A82),MATCH(Main_Page!B14,Xc_H!A2:A82,1),MATCH(Main_Page!B14,Xc_H!A2:A82,1)-1),IF(MATCH(Main_Page!B6,Xc_H!B1:H1,1)<>COLUMNS(Xc_H!B1:H1),MATCH(Main_Page!B6,Xc_H!B1:H1,1),MATCH(Main_Page!B6,Xc_H!B1:H1,1)-1)+1)))-(INDEX(Xc_H!B2:H82,IF(MATCH(Main_Page!B14,Xc_H!A2:A82,1)<>ROWS(Xc_H!A2:A82),MATCH(Main_Page!B14,Xc_H!A2:A82,1),MATCH(Main_Page!B14,Xc_H!A2:A82,1)-1),IF(MATCH(Main_Page!B6,Xc_H!B1:H1,1)<>COLUMNS(Xc_H!B1:H1),MATCH(Main_Page!B6,Xc_H!B1:H1,1),MATCH(Main_Page!B6,Xc_H!B1:H1,1)-1))+(LOG(Main_Page!B14)-LOG(INDEX(Xc_H!A2:A82,IF(MATCH(Main_Page!B14,Xc_H!A2:A82,1)<>ROWS(Xc_H!A2:A82),MATCH(Main_Page!B14,Xc_H!A2:A82,1),MATCH(Main_Page!B14,Xc_H!A2:A82,1)-1))))/(LOG(INDEX(Xc_H!A2:A82,IF(MATCH(Main_Page!B14,Xc_H!A2:A82,1)<>ROWS(Xc_H!A2:A82),MATCH(Main_Page!B14,Xc_H!A2:A82,1),MATCH(Main_Page!B14,Xc_H!A2:A82,1)-1)+1))-LOG(INDEX(Xc_H!A2:A82,IF(MATCH(Main_Page!B14,Xc_H!A2:A82,1)<>ROWS(Xc_H!A2:A82),MATCH(Main_Page!B14,Xc_H!A2:A82,1),MATCH(Main_Page!B14,Xc_H!A2:A82,1)-1))))*(INDEX(Xc_H!B2:H82,IF(MATCH(Main_Page!B14,Xc_H!A2:A82,1)<>ROWS(Xc_H!A2:A82),MATCH(Main_Page!B14,Xc_H!A2:A82,1),MATCH(Main_Page!B14,Xc_H!A2:A82,1)-1)+1,IF(MATCH(Main_Page!B6,Xc_H!B1:H1,1)<>COLUMNS(Xc_H!B1:H1),MATCH(Main_Page!B6,Xc_H!B1:H1,1),MATCH(Main_Page!B6,Xc_H!B1:H1,1)-1))-INDEX(Xc_H!B2:H82,IF(MATCH(Main_Page!B14,Xc_H!A2:A82,1)<>ROWS(Xc_H!A2:A82),MATCH(Main_Page!B14,Xc_H!A2:A82,1),MATCH(Main_Page!B14,Xc_H!A2:A82,1)-1),IF(MATCH(Main_Page!B6,Xc_H!B1:H1,1)<>COLUMNS(Xc_H!B1:H1),MATCH(Main_Page!B6,Xc_H!B1:H1,1),MATCH(Main_Page!B6,Xc_H!B1:H1,1)-1)))))))","v":-124.98830327647674},"(abscissa of critical circular-failure-surface center)"]
["yc [m] =",{"$f":"IF(B13<>\"\",\"N/A\",B5*((INDEX(Yc_H!B2:H82,IF(MATCH(Main_Page!B14,Yc_H!A2:A82,1)<>ROWS(Yc_H!A2:A82),MATCH(Main_Page!B14,Yc_H!A2:A82,1),MATCH(Main_Page!B14,Yc_H!A2:A82,1)-1),IF(MATCH(Main_Page!B6,Yc_H!B1:H1,1)<>COLUMNS(Yc_H!B1:H1),MATCH(Main_Page!B6,Yc_H!B1:H1,1),MATCH(Main_Page!B6,Yc_H!B1:H1,1)-1))+(LOG(Main_Page!B14)-LOG(INDEX(Yc_H!A2:A82,IF(MATCH(Main_Page!B14,Yc_H!A2:A82,1)<>ROWS(Yc_H!A2:A82),MATCH(Main_Page!B14,Yc_H!A2:A82,1),MATCH(Main_Page!B14,Yc_H!A2:A82,1)-1))))/(LOG(INDEX(Yc_H!A2:A82,IF(MATCH(Main_Page!B14,Yc_H!A2:A82,1)<>ROWS(Yc_H!A2:A82),MATCH(Main_Page!B14,Yc_H!A2:A82,1),MATCH(Main_Page!B14,Yc_H!A2:A82,1)-1)+1))-LOG(INDEX(Yc_H!A2:A82,IF(MATCH(Main_Page!B14,Yc_H!A2:A82,1)<>ROWS(Yc_H!A2:A82),MATCH(Main_Page!B14,Yc_H!A2:A82,1),MATCH(Main_Page!B14,Yc_H!A2:A82,1)-1))))*(INDEX(Yc_H!B2:H82,IF(MATCH(Main_Page!B14,Yc_H!A2:A82,1)<>ROWS(Yc_H!A2:A82),MATCH(Main_Page!B14,Yc_H!A2:A82,1),MATCH(Main_Page!B14,Yc_H!A2:A82,1)-1)+1,IF(MATCH(Main_Page!B6,Yc_H!B1:H1,1)<>COLUMNS(Yc_H!B1:H1),MATCH(Main_Page!B6,Yc_H!B1:H1,1),MATCH(Main_Page!B6,Yc_H!B1:H1,1)-1))-INDEX(Yc_H!B2:H82,IF(MATCH(Main_Page!B14,Yc_H!A2:A82,1)<>ROWS(Yc_H!A2:A82),MATCH(Main_Page!B14,Yc_H!A2:A82,1),MATCH(Main_Page!B14,Yc_H!A2:A82,1)-1),IF(MATCH(Main_Page!B6,Yc_H!B1:H1,1)<>COLUMNS(Yc_H!B1:H1),MATCH(Main_Page!B6,Yc_H!B1:H1,1),MATCH(Main_Page!B6,Yc_H!B1:H1,1)-1))))+((Main_Page!B6)-(INDEX(Yc_H!B1:H1,IF(MATCH(Main_Page!B6,Yc_H!B1:H1,1)<>COLUMNS(Yc_H!B1:H1),MATCH(Main_Page!B6,Yc_H!B1:H1,1),MATCH(Main_Page!B6,Yc_H!B1:H1,1)-1))))/((INDEX(Yc_H!B1:H1,IF(MATCH(Main_Page!B6,Yc_H!B1:H1,1)<>COLUMNS(Yc_H!B1:H1),MATCH(Main_Page!B6,Yc_H!B1:H1,1),MATCH(Main_Page!B6,Yc_H!B1:H1,1)-1)+1))-(INDEX(Yc_H!B1:H1,IF(MATCH(Main_Page!B6,Yc_H!B1:H1,1)<>COLUMNS(Yc_H!B1:H1),MATCH(Main_Page!B6,Yc_H!B1:H1,1),MATCH(Main_Page!B6,Yc_H!B1:H1,1)-1))))*((INDEX(Yc_H!B2:H82,IF(MATCH(Main_Page!B14,Yc_H!A2:A82,1)<>ROWS(Yc_H!A2:A82),MATCH(Main_Page!B14,Yc_H!A2:A82,1),MATCH(Main_Page!B14,Yc_H!A2:A82,1)-1),IF(MATCH(Main_Page!B6,Yc_H!B1:H1,1)<>COLUMNS(Yc_H!B1:H1),MATCH(Main_Page!B6,Yc_H!B1:H1,1),MATCH(Main_Page!B6,Yc_H!B1:H1,1)-1)+1)+(LOG(Main_Page!B14)-LOG(INDEX(Yc_H!A2:A82,IF(MATCH(Main_Page!B14,Yc_H!A2:A82,1)<>ROWS(Yc_H!A2:A82),MATCH(Main_Page!B14,Yc_H!A2:A82,1),MATCH(Main_Page!B14,Yc_H!A2:A82,1)-1))))/(LOG(INDEX(Yc_H!A2:A82,IF(MATCH(Main_Page!B14,Yc_H!A2:A82,1)<>ROWS(Yc_H!A2:A82),MATCH(Main_Page!B14,Yc_H!A2:A82,1),MATCH(Main_Page!B14,Yc_H!A2:A82,1)-1)+1))-LOG(INDEX(Yc_H!A2:A82,IF(MATCH(Main_Page!B14,Yc_H!A2:A82,1)<>ROWS(Yc_H!A2:A82),MATCH(Main_Page!B14,Yc_H!A2:A82,1),MATCH(Main_Page!B14,Yc_H!A2:A82,1)-1))))*(INDEX(Yc_H!B2:H82,IF(MATCH(Main_Page!B14,Yc_H!A2:A82,1)<>ROWS(Yc_H!A2:A82),MATCH(Main_Page!B14,Yc_H!A2:A82,1),MATCH(Main_Page!B14,Yc_H!A2:A82,1)-1)+1,IF(MATCH(Main_Page!B6,Yc_H!B1:H1,1)<>COLUMNS(Yc_H!B1:H1),MATCH(Main_Page!B6,Yc_H!B1:H1,1),MATCH(Main_Page!B6,Yc_H!B1:H1,1)-1)+1)-INDEX(Yc_H!B2:H82,IF(MATCH(Main_Page!B14,Yc_H!A2:A82,1)<>ROWS(Yc_H!A2:A82),MATCH(Main_Page!B14,Yc_H!A2:A82,1),MATCH(Main_Page!B14,Yc_H!A2:A82,1)-1),IF(MATCH(Main_Page!B6,Yc_H!B1:H1,1)<>COLUMNS(Yc_H!B1:H1),MATCH(Main_Page!B6,Yc_H!B1:H1,1),MATCH(Main_Page!B6,Yc_H!B1:H1,1)-1)+1)))-(INDEX(Yc_H!B2:H82,IF(MATCH(Main_Page!B14,Yc_H!A2:A82,1)<>ROWS(Yc_H!A2:A82),MATCH(Main_Page!B14,Yc_H!A2:A82,1),MATCH(Main_Page!B14,Yc_H!A2:A82,1)-1),IF(MATCH(Main_Page!B6,Yc_H!B1:H1,1)<>COLUMNS(Yc_H!B1:H1),MATCH(Main_Page!B6,Yc_H!B1:H1,1),MATCH(Main_Page!B6,Yc_H!B1:H1,1)-1))+(LOG(Main_Page!B14)-LOG(INDEX(Yc_H!A2:A82,IF(MATCH(Main_Page!B14,Yc_H!A2:A82,1)<>ROWS(Yc_H!A2:A82),MATCH(Main_Page!B14,Yc_H!A2:A82,1),MATCH(Main_Page!B14,Yc_H!A2:A82,1)-1))))/(LOG(INDEX(Yc_H!A2:A82,IF(MATCH(Main_Page!B14,Yc_H!A2:A82,1)<>ROWS(Yc_H!A2:A82),MATCH(Main_Page!B14,Yc_H!A2:A82,1),MATCH(Main_Page!B14,Yc_H!A2:A82,1)-1)+1))-LOG(INDEX(Yc_H!A2:A82,IF(MATCH(Main_Page!B14,Yc_H!A2:A82,1)<>ROWS(Yc_H!A2:A82),MATCH(Main_Page!B14,Yc_H!A2:A82,1),MATCH(Main_Page!B14,Yc_H!A2:A82,1)-1))))*(INDEX(Yc_H!B2:H82,IF(MATCH(Main_Page!B14,Yc_H!A2:A82,1)<>ROWS(Yc_H!A2:A82),MATCH(Main_Page!B14,Yc_H!A2:A82,1),MATCH(Main_Page!B14,Yc_H!A2:A82,1)-1)+1,IF(MATCH(Main_Page!B6,Yc_H!B1:H1,1)<>COLUMNS(Yc_H!B1:H1),MATCH(Main_Page!B6,Yc_H!B1:H1,1),MATCH(Main_Page!B6,Yc_H!B1:H1,1)-1))-INDEX(Yc_H!B2:H82,IF(MATCH(Main_Page!B14,Yc_H!A2:A82,1)<>ROWS(Yc_H!A2:A82),MATCH(Main_Page!B14,Yc_H!A2:A82,1),MATCH(Main_Page!B14,Yc_H!A2:A82,1)-1),IF(MATCH(Main_Page!B6,Yc_H!B1:H1,1)<>COLUMNS(Yc_H!B1:H1),MATCH(Main_Page!B6,Yc_H!B1:H1,1),MATCH(Main_Page!B6,Yc_H!B1:H1,1)-1)))))))","v":437.8817606733441},"(ordinate of critical circular-failure-surface center)"]
["xA [m] =",{"$f":"IF(B13<>\"\",\"N/A\",B5*((INDEX(XA_H!B2:H82,IF(MATCH(Main_Page!B14,XA_H!A2:A82,1)<>ROWS(XA_H!A2:A82),MATCH(Main_Page!B14,XA_H!A2:A82,1),MATCH(Main_Page!B14,XA_H!A2:A82,1)-1),IF(MATCH(Main_Page!B6,XA_H!B1:H1,1)<>COLUMNS(XA_H!B1:H1),MATCH(Main_Page!B6,XA_H!B1:H1,1),MATCH(Main_Page!B6,XA_H!B1:H1,1)-1))+(LOG(Main_Page!B14)-LOG(INDEX(XA_H!A2:A82,IF(MATCH(Main_Page!B14,XA_H!A2:A82,1)<>ROWS(XA_H!A2:A82),MATCH(Main_Page!B14,XA_H!A2:A82,1),MATCH(Main_Page!B14,XA_H!A2:A82,1)-1))))/(LOG(INDEX(XA_H!A2:A82,IF(MATCH(Main_Page!B14,XA_H!A2:A82,1)<>ROWS(XA_H!A2:A82),MATCH(Main_Page!B14,XA_H!A2:A82,1),MATCH(Main_Page!B14,XA_H!A2:A82,1)-1)+1))-LOG(INDEX(XA_H!A2:A82,IF(MATCH(Main_Page!B14,XA_H!A2:A82,1)<>ROWS(XA_H!A2:A82),MATCH(Main_Page!B14,XA_H!A2:A82,1),MATCH(Main_Page!B14,XA_H!A2:A82,1)-1))))*(INDEX(XA_H!B2:H82,IF(MATCH(Main_Page!B14,XA_H!A2:A82,1)<>ROWS(XA_H!A2:A82),MATCH(Main_Page!B14,XA_H!A2:A82,1),MATCH(Main_Page!B14,XA_H!A2:A82,1)-1)+1,IF(MATCH(Main_Page!B6,XA_H!B1:H1,1)<>COLUMNS(XA_H!B1:H1),MATCH(Main_Page!B6,XA_H!B1:H1,1),MATCH(Main_Page!B6,XA_H!B1:H1,1)-1))-INDEX(XA_H!B2:H82,IF(MATCH(Main_Page!B14,XA_H!A2:A82,1)<>ROWS(XA_H!A2:A82),MATCH(Main_Page!B14,XA_H!A2:A82,1),MATCH(Main_Page!B14,XA_H!A2:A82,1)-1),IF(MATCH(Main_Page!B6,XA_H!B1:H1,1)<>COLUMNS(XA_H!B1:H1),MATCH(Main_Page!B6,XA_H!B1:H1,1),MATCH(Main_Page!B6,XA_H!B1:H1,1)-1))))+((Main_Page!B6)-(INDEX(XA_H!B1:H1,IF(MATCH(Main_Page!B6,XA_H!B1:H1,1)<>COLUMNS(XA_H!B1:H1),MATCH(Main_Page!B6,XA_H!B1:H1,1),MATCH(Main_Page!B6,XA_H!B1:H1,1)-1))))/((INDEX(XA_H!B1:H1,IF(MATCH(Main_Page!B6,XA_H!B1:H1,1)<>COLUMNS(XA_H!B1:H1),MATCH(Main_Page!B6,XA_H!B1:H1,1),MATCH(Main_Page!B6,XA_H!B1:H1,1)-1)+1))-(INDEX(XA_H!B1:H1,IF(MATCH(Main_Page!B6,XA_H!B1:H1,1)<>COLUMNS(XA_H!B1:H1),MATCH(Main_Page!B6,XA_H!B1:H1,1),MATCH(Main_Page!B6,XA_H!B1:H1,1)-1))))*((INDEX(XA_H!B2:H82,IF(MATCH(Main_Page!B14,XA_H!A2:A82,1)<>ROWS(XA_H!A2:A82),MATCH(Main_Page!B14,XA_H!A2:A82,1),MATCH(Main_Page!B14,XA_H!A2:A82,1)-1),IF(MATCH(Main_Page!B6,XA_H!B1:H1,1)<>COLUMNS(XA_H!B1:H1),MATCH(Main_Page!B6,XA_H!B1:H1,1),MATCH(Main_Page!B6,XA_H!B1:H1,1)-1)+1)+(LOG(Main_Page!B14)-LOG(INDEX(XA_H!A2:A82,IF(MATCH(Main_Page!B14,XA_H!A2:A82,1)<>ROWS(XA_H!A2:A82),MATCH(Main_Page!B14,XA_H!A2:A82,1),MATCH(Main_Page!B14,XA_H!A2:A82,1)-1))))/(LOG(INDEX(XA_H!A2:A82,IF(MATCH(Main_Page!B14,XA_H!A2:A82,1)<>ROWS(XA_H!A2:A82),MATCH(Main_Page!B14,XA_H!A2:A82,1),MATCH(Main_Page!B14,XA_H!A2:A82,1)-1)+1))-LOG(INDEX(XA_H!A2:A82,IF(MATCH(Main_Page!B14,XA_H!A2:A82,1)<>ROWS(XA_H!A2:A82),MATCH(Main_Page!B14,XA_H!A2:A82,1),MATCH(Main_Page!B14,XA_H!A2:A82,1)-1))))*(INDEX(XA_H!B2:H82,IF(MATCH(Main_Page!B14,XA_H!A2:A82,1)<>ROWS(XA_H!A2:A82),MATCH(Main_Page!B14,XA_H!A2:A82,1),MATCH(Main_Page!B14,XA_H!A2:A82,1)-1)+1,IF(MATCH(Main_Page!B6,XA_H!B1:H1,1)<>COLUMNS(XA_H!B1:H1),MATCH(Main_Page!B6,XA_H!B1:H1,1),MATCH(Main_Page!B6,XA_H!B1:H1,1)-1)+1)-INDEX(XA_H!B2:H82,IF(MATCH(Main_Page!B14,XA_H!A2:A82,1)<>ROWS(XA_H!A2:A82),MATCH(Main_Page!B14,XA_H!A2:A82,1),MATCH(Main_Page!B14,XA_H!A2:A82,1)-1),IF(MATCH(Main_Page!B6,XA_H!B1:H1,1)<>COLUMNS(XA_H!B1:H1),MATCH(Main_Page!B6,XA_H!B1:H1,1),MATCH(Main_Page!B6,XA_H!B1:H1,1)-1)+1)))-(INDEX(XA_H!B2:H82,IF(MATCH(Main_Page!B14,XA_H!A2:A82,1)<>ROWS(XA_H!A2:A82),MATCH(Main_Page!B14,XA_H!A2:A82,1),MATCH(Main_Page!B14,XA_H!A2:A82,1)-1),IF(MATCH(Main_Page!B6,XA_H!B1:H1,1)<>COLUMNS(XA_H!B1:H1),MATCH(Main_Page!B6,XA_H!B1:H1,1),MATCH(Main_Page!B6,XA_H!B1:H1,1)-1))+(LOG(Main_Page!B14)-LOG(INDEX(XA_H!A2:A82,IF(MATCH(Main_Page!B14,XA_H!A2:A82,1)<>ROWS(XA_H!A2:A82),MATCH(Main_Page!B14,XA_H!A2:A82,1),MATCH(Main_Page!B14,XA_H!A2:A82,1)-1))))/(LOG(INDEX(XA_H!A2:A82,IF(MATCH(Main_Page!B14,XA_H!A2:A82,1)<>ROWS(XA_H!A2:A82),MATCH(Main_Page!B14,XA_H!A2:A82,1),MATCH(Main_Page!B14,XA_H!A2:A82,1)-1)+1))-LOG(INDEX(XA_H!A2:A82,IF(MATCH(Main_Page!B14,XA_H!A2:A82,1)<>ROWS(XA_H!A2:A82),MATCH(Main_Page!B14,XA_H!A2:A82,1),MATCH(Main_Page!B14,XA_H!A2:A82,1)-1))))*(INDEX(XA_H!B2:H82,IF(MATCH(Main_Page!B14,XA_H!A2:A82,1)<>ROWS(XA_H!A2:A82),MATCH(Main_Page!B14,XA_H!A2:A82,1),MATCH(Main_Page!B14,XA_H!A2:A82,1)-1)+1,IF(MATCH(Main_Page!B6,XA_H!B1:H1,1)<>COLUMNS(XA_H!B1:H1),MATCH(Main_Page!B6,XA_H!B1:H1,1),MATCH(Main_Page!B6,XA_H!B1:H1,1)-1))-INDEX(XA_H!B2:H82,IF(MATCH(Main_Page!B14,XA_H!A2:A82,1)<>ROWS(XA_H!A2:A82),MATCH(Main_Page!B14,XA_H!A2:A82,1),MATCH(Main_Page!B14,XA_H!A2:A82,1)-1),IF(MATCH(Main_Page!B6,XA_H!B1:H1,1)<>COLUMNS(XA_H!B1:H1),MATCH(Main_Page!B6,XA_H!B1:H1,1),MATCH(Main_Page!B6,XA_H!B1:H1,1)-1)))))))","v":0},"(abscissa of critical circular-failure-surface starting point)"]
["yA [m] =",{"$f":"IF(B13<>\"\",\"N/A\",0)","v":0},"(ordinate of critical circular-failure-surface starting point)"]
["xB [m] =",{"$f":"IF(B13<>\"\",\"N/A\",B16+SQRT((B22)^2-(B5-B17)^2))","v":309.00608880703743},"(abscissa of circular-failure-surface ending point)"]
["yB [m] =",{"$f":"IF(B13<>\"\",\"N/A\",B5)","v":300},"(ordinate of critical circular-failure-surface ending point)"]
["R [m] =",{"$f":"IF(B13<>\"\",\"N/A\",SQRT((B16-B18)^2+(B17-B19)^2))","v":455.37074157912292},"(radius of critical circular-failure-surface)"]
[]
["Note:"]
["-If you find this worksheet (or modified versions of this worksheet) useful, please credit the original development by citing"]
["the following bibliographical source: Carranza-Torres C. and Hormazabal E. (2018) \"Computational tools for determination"]
["of factor of safety and location of the critical circular failure surface for slopes in Mohr-Coulomb dry ground\". Proceedings "]
["of Slope Stability 2018 (congress), April 11-13 2018, Sevilla, Spain. Available for downloading at www.d.umn.edu/~carranza"]
["-If you find errors or problems in this worksheet, please contact the first author of the publication at carranza@d.umn.edu."]

{"sheet":"Plot_Data","index":2,"n_rows":103,"n_cols":11,"rows_kept":103,"cut":false,"hidden":false,"merged":[]}
["Slope Geometry",null,null,"Circular Surface",null,null,"Circular Center",null,null,"Radial Lines"]
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