{"text_format":"1","workbook":"xlsx","n_sheets":4,"sheets":["step 1 CA model 3D","step 2 inverse triangle","step 2 uniform","Sheet1"],"not_rendered":{"charts":0,"images":2,"macros":1,"external_links":3,"defined_names":219,"comments":0,"pivot_tables":0},"unopened":[],"bounds":{"document_bytes":16777216,"sheet_cells":100000,"rows_first":2000,"rows_last":500,"rows_between":2000,"halvings":0,"cell_chars":16384,"cell_head_chars":4096},"cells_cut":0,"cells_raw":0,"read":"whole","date_system":"1900"}

{"sheet":"step 1 CA model 3D","index":0,"n_rows":60,"n_cols":13,"rows_kept":60,"cut":false,"hidden":false,"merged":[[54,7,55,12],[56,7,57,12],[24,1,24,4],[34,1,34,4],[38,1,38,4],[44,7,45,12],[46,7,47,12],[22,5,22,6],[48,7,49,12],[50,7,51,12],[52,7,53,12],[42,7,43,7]]}
[null,"NO SAFETY FACTORS (SLS = Servicability Limit State); NO REDUCTION FACTORS; NO OPTIMIZATION; THEREFORE, NOT SUITABLE FOR DESIGN PURPOSES!!"]
[]
[null,"1. Input parameters",null,null,null,null,null,"2. Calculated parameters",null,null,null,null,"eq.no. in Van Eekelen et al 2013"]
[null,null,null,null,null,"Input:",null,"internal friction angle fill","j",null,"rad",{"$f":"+F11*PI()/180","v":0.75049157835756164}]
[null,"equivalent) width square pile cap","ax",null,"m",0.75,null,null,"tan j",null,"-",{"$f":"TAN(L4)","v":0.93251508613766154}]
[null,"height embankment","H",null,"m",2,null,"3D arch height for full arching","Hg,full 3Darch",null,"m",{"$f":"0.5*SQRT(F8^2+F7^2)","v":1.5909902576697319},4]
[null,"ctc distance piles longitudinal","sx",null,"m",2.25,null,"3D arch height  ","Hg,3D",null,"m",{"$f":"+MIN(F6,L6)","v":1.5909902576697319},4]
[null,"ctc distance piles transversal","sy",null,"m",2.25]
[null,"unit weight fill","g",null,"kN/m3",18.3,null,"width square loaded by 3D arches","Lx3D",null,"m",{"$f":"+MIN(SQRT(2)*L7,(SQRT((F7-F5)^2+(F8-F5)^2))/SQRT(2))","v":1.4999999999999998},8]
[null,"surcharge load","p",null,"kPa",6,null,"2D arch height for full arching, x dir","Hg,x,full 2Darch",null,"m",{"$f":"+F7/2","v":1.125},2]
[null,"internal friction angle fill","j",null,"deg",43,null,"2D arch height for full arching, y dir","Hg,y,full 2Darch",null,"m",{"$f":"F8/2","v":1.125},2]
[null,"GR stifness to be determined from isochronous curves)","J",null,"kN/m ",5000,null,"2D arch height , x dir","Hxg 2D",null,"m",{"$f":"+MIN(L10,F6)","v":1.125},13]
[null,"subgrade reaction","k",null,"kN/m3",200,null,"2D arch height, y dir","Hyg2D",null,"m",{"$f":"+MIN(L11,F6)","v":1.125},13]
[null,null,null,null,null,null,null,"length GR strip loaded by 2D arches x dir","Lx2D",null,"m",{"$f":"IF(F6<0.5*(F7-F5),2*L12,F7-F5)","v":1.5},12]
[null,"GR = geosynthetic reinforcement",null,null,null,null,null,"length GR strip loaded by 2D arches x dir","Ly2D",null,"m",{"$f":"IF(F6<0.5*(F8-F5),2*L12,F8-F5)","v":1.5},12]
[null,null,null,null,null,null,null,"passive earth pressure coefficient ","Kp",null,"-",{"$f":"+(1+SIN(L4))/(1-SIN(L4))","v":5.2892757420781553},2]
[]
["eq.no. in Van Eekelen et al 2013","3. Calculation parameters",null,"SLS",null,null,null,"total load per unit excluding p",null,null,"kN/pile",{"$f":"+(F9*F6)*F7*F8","v":185.28750000000002}]
[14,"P2Dx",null,{"$f":"+L16*((L12)^(1-L16))*(F9*F6+D37-L12*F9*(L16-1)/(L16-2))","v":105.78885855582476},"kPa/mKp-1",null,null,"total load pre unit including p",null,null,"kN/pile",{"$f":"+L18+F10*F7*F8","v":215.66250000000002}]
[14,"P2Dy",null,{"$f":"+L16*((L13)^(1-L16))*(F9*F6+D37-L13*F9*(L16-1)/(L16-2))","v":105.78885855582476},"kPa/mKp-1",null,null,"factor to get the loads with p","(p+gH)/(gH)",null,"-",{"$f":"+(F10+F9*F6)/(F9*F6)","v":1.1639344262295082},5]
[14,"Q2D",null,{"$f":"+L16*F9/(L16-2)","v":29.427069564826517},"kN/m3"]
[7,"P3D",null,{"$f":"+F9*L16*L7^(2-2*L16)*(F6-L7*(2*L16-2)/(2*L16-3))","v":0.35879962645477897},"kPa/m2Kp-2"]
[7,"Q3D",null,{"$f":"+L16*F9/(2*L16-3)","v":12.772064197543141},"kN/m3"]
[null,null,null,null,null,null,null,"Calculations with Concentric Arches (CA) model of Van Eekelen et al., 2013 "]
[null,"4. 3D hemispheres transfer load in the direction of GR strips and pile caps and exert first FGRsquare load part on GR",null,null,null,null,null,"and inverse triangular load distribution of Van Eekelen et al., 2012b and 2015 for cases with no or limited subsoil support"]
[7,"FGRsq1;p=0 (inside circle)",null,{"$f":"+(PI()*D22/L16)*(L9/2)^(2*L16)+(2/3)*PI()*D23*(L9/2)^3","v":11.295211195093534},"kN/pile"," ",null,"uniform load distribution of Van Eekelen et al., 2015 with considerable subsoil support,"]
[7,"1FGRsq2",null,{"$f":"2*PI()*D22/(2*L16)*(2^L16-1)*(L9/2)^(2*L16)","v":0.38718192565391379},"kN/pile",null,null,"the load distribution that gives the lowest GR strain is normative."]
[7,"2FGRsq2",null,{"$f":"+(2*PI()*D23/3)*((SQRT(2))^3-1)*(L9/2)^3","v":20.63389195194658},"kN/pile"]
[7,"3FGRsq2",null,{"$f":"(D22/L16)*2^(2-2*L16)*L9^(2*L16)*(-PI()/(2^(2-L16))+1+(1/3)*(L16-1)+(1/10)*(L16-1)*(L16-2)+(1/42)*(L16-1)*(L16-2)*(L16-3)+(1/216)*(L16-1)*(L16-2)*(L16-3)*(L16-4)+(1/1320)*(L16-1)*(L16-2)*(L16-3)*(L16-4)*(L16-5)+(1/9360)*(L16-1)*(L16-2)*(L16-3)*(L16-4)*(L16-5)*(L16-6)+(1/75600)*(L16-1)*(L16-2)*(L16-3)*(L16-4)*(L16-5)*(L16-6)*(L16-7))","v":-0.3351036610614137},"kN/pile"]
[7,"4FGRsq2",null,{"$f":"+(1/6)*D23*L9^3*(SQRT(2)*(1-PI())+LN(1+SQRT(2)))","v":-15.426787311691818},"kN/pile",null,null,"Results step 1 en Results step 2  "]
[7,"FGRsq2;p=0 (outside circle, inside hemispheres-square)",null,{"$f":"+SUM(D27:D30)","v":5.2591829048472611},"kN/pile",null,null,"(Without safety factors!! Therefore, not usable for design!)"]
[9,"FGRsq3;p=0 (outside hemispheres-square, inside GR square)",null,{"$f":"IF(L9^2<(F7-F5)*(F8-F5),F9*F6*((F7-F5)*(F8-F5)-L9^2),0)","v":0},"kN/pile",null,null,"Result step 1"]
[6,"total  FGRsquare",null,{"$f":"+D26+D31+D32","v":16.554394099940794},"kN/pile",null,null,"B+C",null,"kN/pile",{"$f":"D50","v":63.417248072181216}]
[null,null,null,null,null,null,null,"A",null,"kN/pile",{"$f":"D54","v":152.2452519278188}]
[null,"5. Determine load transferred from 3D hemispheres 2D arches; to be applied as surcharge load on the 2D arches"]
[10,"Ftransferred",null,{"$f":"+($F$7-$F$5)*($F$8-$F$5)*($F$9*$F$6)-D33","v":65.795605900059215},"kN/pile",null,null,"Result step 2 (Be sure to press the yellow calculation button first!)"]
[11,"ptransferred;x",null,{"$f":"D36/((F5*(L14+L15)+F5^2))","v":23.393993208909944},"kPa",null,null,null,null,null,"along  (x)","across  (y)"]
[null,null,null,null,null,null,null,"max GR strain",null,"%",{"$f":"MIN('step 2 inverse triangle'!C31,'step 2 uniform'!C31)","v":5.9591383218836674E-3},{"$f":"MIN('step 2 inverse triangle'!D31,'step 2 uniform'!D31)","v":5.9591383218816933E-3}]
[null,"6. 2D arches transfer load in the direction of the pile caps and exert second FGRstrips load part on GR",null,null,null,null,null,"max GR tensile force",null,"kN/m",{"$f":"IF(K38='step 2 inverse triangle'!C31,'step 2 inverse triangle'!C35,'step 2 uniform'!C35)","v":29.795691609418338},{"$f":"IF(L38='step 2 inverse triangle'!D31,'step 2 inverse triangle'!D35,'step 2 uniform'!D35)","v":29.795691609408468}]
[14,"FxGRstr2p=0 (outside arches on strip)",null,{"$f":"IF(F6<0.5*(F7-F5),F9*F6*F5*(F7-F5-L14),0)","v":0},null,null,null,"max deflection",null,"m",{"$f":"IF(K38='step 2 inverse triangle'!C31,'step 2 inverse triangle'!C34,'step 2 uniform'!C34)","v":6.1869792596570723E-2},{"$f":"IF(L38='step 2 inverse triangle'!D31,'step 2 inverse triangle'!D34,'step 2 uniform'!D34)","v":6.1869792596574803E-2}]
[14,"FyGRstr2p=0 (outside arches on strip)",null,{"$f":"IF(F6<0.5*(F8-F5),F9*F6*F5*(F8-F5-L15),0)","v":0}]
[14,"FGRstrips (total load on GR strips)",null,{"$f":"(2*F5*(D19/L16)*(0.5*L14)^L16+2*F5*(D20/L16)*(0.5*L15)^L16+0.25*F5*D21*(L14)^2+0.25*F5*D21*(L15)^2+D40+D41)","v":37.930847201510673},"kN/pile"]
[null,null,null,null,null,null,null,"Sources"]
[null,"7. Load distribution for p=0"]
[16,"(B+C)p=0 total load on GR with p=0",null,{"$f":"+D42+D33","v":54.485241301451467},"kN/pile",null,null,"Van Eekelen, S.J.M., Bezuijen, A., Lodder, H.J., van Tol, A.F., 2012a. Model experiments on piled embankments Part I. Geotextiles and Geomembranes 32: 69-81. "]
[15,"Ap=0 total load on pile cap with p=0",null,{"$f":"+$L$18-D45","v":130.80225869854854},"kN/pile"]
[null,"total load on pile cap with p=0",null,{"$f":"+D46/($F$5^2)","v":232.53734879741964},"kPa",null,null,"Van Eekelen, S.J.M., Bezuijen, A., Lodder, H.J., van Tol, A.F., 2012b. Model experiments on piled embankments. Part II. Geotextiles and Geomembranes 32: 82-94 "]
[]
[null,"8. Load distribution for p>0",null,null,null,null,null,"Van Eekelen, S.J.M., Bezuijen, A. van Tol, A.F., 2013. An analytical model for arching in piled embankments. Geotextiles and Geomembranes 39: 78-102. "]
[16,"B+C total load on GR with p>0",null,{"$f":"+D45*$L$20","v":63.417248072181216},"kN/pile"]
[null,"total load on GR with p>0",null,{"$f":"+D50/(F8*F7-F5^2)","v":14.092721793818049},"kPa op total GR",null,null,"Van Eekelen, S.J.M., Bezuijen, A. van Tol, A.F., 2015. Validation of analytical models for the design of basal reinforced piled embankments. Geotextiles and Geomembranes. Volume 43, Issue 1, 56 - 81."]
[null,"total load on GR with p>0",null,{"$f":"+D50/(($F7-$F5+$F8-$F5)*$F5)","v":28.185443587636097},"kPa op GR strip"]
[null,null,null,null,null,null,null,"Van Eekelen, S.J.M., 2015. Basal Reinforced Piled Embankments. PhD thesis Delft University of Technology. ISBN 978-94-6203-825-7 (print); ISBN 978-94-6203-826-4 (electronic version) \n"]
[15,"A total load on pile cap with p>0",null,{"$f":"+D46*$L$20","v":152.2452519278188},"kN/pile"]
[null,"total load on pile cap with p>0",null,{"$f":"+D47*$L$20","v":270.65822564945563},"kPa",null,null,"Van Eekelen, S. J. M. & Brugman, M. H. A. (Eds.) (2016). Design Guideline Basal Reinforced Piled Embankments (CUR 226, 2016). CRC press, Delft, the Netherlands. ISBN9789053676240."]
[null,"total load on pile cap with p>0",null,{"$f":"+D54/($L$18*$L$20)","v":0.70594216392659259}]
[null,null,null,null,null,null,null,"Van Eekelen, S. J. M., Venmans, A. A. M., Bezuijen, A. and van Tol, A. F., 2017. Long term measurements in the Woerden geosynthetic-reinforced pile-supported embankment. Geosynthetics International. [http://dx.doi.org/10.1680/jgein.17.00022]"]
[]
[]
[null,null,null,null,null,null,null,"© 2018, Suzanne J.M. van Eekelen, Deltares, Delft, Netherlands"]

{"sheet":"step 2 inverse triangle","index":1,"n_rows":154,"n_cols":12,"rows_kept":154,"cut":false,"hidden":false,"merged":[[41,0,41,4],[42,2,42,3],[1,4,1,6]]}
["Inverse triangular load distribution"]
["author: Suzanne van Eekelen",null,"along  (x)","across  (y)","eq.no. in Van Eekelen et al 2015"]
[null,null,"SLS","SLS"]
["Geometry & properties"]
["centre-to-centre distance","m",{"$f":"'step 1 CA model 3D'!F7","v":2.25},{"$f":"'step 1 CA model 3D'!F8","v":2.25}]
["size (square) pile cap","m",{"$f":"'step 1 CA model 3D'!F5","v":0.75},{"$f":"C6","v":0.75}]
["equivalent diameter pile cap","m",{"$f":"SQRT(4*C6^2/PI())","v":0.84628437532163447},{"$f":"C7","v":0.84628437532163447}]
["length between pile caps","m",{"$f":"+C5-C6","v":1.5},{"$f":"+D5-D6","v":1.5}]
["area GR strip","m2",{"$f":"+C6*C8","v":1.125},{"$f":"+D6*D8","v":1.125}]
["AL (area belonging to GR strip)","m",{"$f":"0.5*C5*D5-0.5*C7^2*ATAN((D5)/(C5))","v":2.25},{"$f":"0.5*C5*D5-0.5*C7^2*ATAN((C5)/(D5))","v":2.25},8]
["GR stiffness J'  ","kN/m",{"$f":"'step 1 CA model 3D'!F12","v":5000},{"$f":"C11","v":5000}]
["subgrade reaction","kN/m3",{"$f":"'step 1 CA model 3D'!F13","v":200},{"$f":"C12","v":200}]
[]
["qav (average load strip=(B+C)/area_two_GRstrips)","kPa on strip",{"$f":"'step 1 CA model 3D'!D50/SUM('step 2 inverse triangle'!C9:D9)","v":28.185443587636097},{"$f":"'step 1 CA model 3D'!D50/SUM('step 2 inverse triangle'!C9:D9)","v":28.185443587636097},9]
[]
["Calculation step 2 inverse triangle"]
["mod. K=(ks)*AL/(L*Bers)","kN/m2",{"$f":"C10*C12/(C8*C6)","v":400},{"$f":"D10*D12/(D8*D6)","v":400},7]
["a = sqrt((K/Th)",null,{"$f":"+SQRT(C17/C21)","v":3.6018896754757339},{"$f":"+SQRT(D17/D21)","v":3.6018896783529954},6]
["term 2qav/(L*K*a)",null,{"$f":"2*C14/(C8*C17*C18)","v":2.6083941233720504E-2},{"$f":"2*D14/(D8*D17*D18)","v":2.608394121288413E-2},5]
["M=(2*exp(-0.5*a*L)+a*L)/(exp(0.5*a*L)+exp(-0.5*a*L))","-(?)",{"$f":"+(2*EXP(-0.5*C8*C18)+C8*C18)/(EXP(0.5*C8*C18)+EXP(-0.5*C8*C18))","v":0.36992753703256048},{"$f":"+(2*EXP(-0.5*D8*D18)+D8*D18)/(EXP(0.5*D8*D18)+EXP(-0.5*D8*D18))","v":0.36992753651042665},5]
["Horizontal force Th","kN/m",30.831821182228069,30.831821132969921,"to be determined with yellow button"]
["delta L geometric","cm",{"$f":"100*(B48*SUM(J48:J97)/C21-0.5*C8)","v":0.46546840539449796},{"$f":"100*(B105*SUM(J105:J154)/D21-0.5*D8)","v":0.46546840621367602},11]
["delta L constitutive","cm",{"$f":"100*(B48*SUM(J48:J97)/C11)","v":0.46534756546164102},{"$f":"100*(B105*SUM(J105:J154)/D11)","v":0.46534756472323446},11]
["difference","cm",{"$f":"+C23-C22","v":-1.2083993285694206E-4},{"$f":"+D23-D22","v":-1.208414904415589E-4},11]
["average strain geometric","%",{"$f":"0.01*C22/(0.5*C8)","v":6.2062454052599731E-3},{"$f":"0.01*D22/(0.5*D8)","v":6.2062454161823473E-3},11]
["average strain force","%",{"$f":"AVERAGE(L47:L97)","v":6.2074061688100236E-3},{"$f":"AVERAGE(L104:L154)","v":6.2074061589663197E-3},11]
["difference","%",{"$f":"+C25-C26","v":-1.1607635500504934E-6},{"$f":"+D25-D26","v":-1.1607427839724002E-6},11]
[]
["Results inverse triangle (step 2)"]
["average strain","%",{"$f":"+C25","v":6.2062454052599731E-3},{"$f":"+D25","v":6.2062454161823473E-3},11]
["max strain","%",{"$f":"C35/C11","v":6.5135453807281633E-3},{"$f":"D35/D11","v":6.513545371052254E-3}]
["min strain","%",{"$f":"C21/C11","v":6.1663642364456137E-3},{"$f":"D21/D11","v":6.1663642265939846E-3}]
["deflection in the centre","m",{"$f":"D47","v":3.2869546194056458E-2},{"$f":"D104","v":3.2869546195038228E-2}]
["max deflection","m",{"$f":"MAX(D47:D97)","v":4.4489625316074186E-2},{"$f":"MAX(D104:D154)","v":4.4489625343186769E-2}]
["max tensile force","kN/m",{"$f":"MAX(G47:G97)","v":32.567726903640818},{"$f":"MAX(G104:G154)","v":32.56772685526127}]
["min strain","%",{"$f":"MIN(L47:L97)","v":6.1663642364456137E-3},{"$f":"MIN(L104:L154)","v":6.1663642265939846E-3}]
["spreading force","kN/m",null,"no spreading force in this calculation!"]
[]
[]
[]
[]
[]
[]
[null,"along SLS"]
[null,"L(x)",null,"z(x)",null,"dz/dx in nodes between increments","T_GR in nodes between increments",null,"dz/dx (average in increment)","T_GR average in increment",null,"strain"]
[null,null,null,null,null,null,"kN/m",null,null,"kN/m",null,"-"]
[null,0,null,{"$f":"-C$19*((C$20)*EXP(C$18*B47)+(C$20-2)*EXP(-C$18*B47)-2*C$18*B47)","v":3.2869546194056458E-2},null,{"$f":"-C$19*(C$20*C$18*EXP(C$18*B47)-(C$20-2)*C$18*EXP(-C$18*B47)-2*C$18)","v":0},{"$f":"C$21*SQRT(1+F47^2)","v":30.831821182228069},null,0,{"$f":"C$21*SQRT(1+I47^2)","v":30.831821182228069},null,{"$f":"G47/C$11","v":6.1663642364456137E-3}]
[null,{"$f":"C$8*0.01","v":1.4999999999999999E-2},null,3.2916160536904771E-2,null,6.1253452446395169E-3,30.832399579523074,null,{"$f":"-(D47-D48)/(B48-B47)","v":3.1076228565541748E-3},30.831970058247503,null,6.1664799159046151E-3]
[null,{"$f":"B48+B$48","v":0.03},null,3.3050653063471526E-2,null,1.171994126684096E-2,30.833938593110478,null,8.9661684377836948E-3,30.833060475925638,null,6.1667877186220958E-3]
[null,4.4999999999999998E-2,null,3.326518695376994E-2,null,1.6800123012673161E-2,30.836171925579688,null,1.4302259353227617E-2,30.834974416757252,null,6.1672343851159371E-3]
[null,0.06,null,3.3552159090363777E-2,null,2.138072345568932E-2,30.838867534495861,null,1.9131475772922457E-2,30.837463095335245,null,6.1677735068991725E-3]
[null,7.4999999999999997E-2,null,3.3904177858996319E-2,null,2.547511690583109E-2,30.841824201581083,null,2.3467917908836143E-2,30.84031022105135,null,6.1683648403162167E-3]
[null,0.09,null,3.4314041566760281E-2,null,2.909525805936734E-2,30.844868514656163,null,2.7324247184264128E-2,30.843328776828891,null,6.1689737029312327E-3]
[null,0.105,null,3.4774717414794959E-2,null,3.2251716903884259E-2,30.847852232261424,null,3.0711723202311858E-2,30.846358195307548,null,6.169570446452285E-3]
[null,0.12,null,3.5279320964115457E-2,null,3.4953709580241563E-2,30.850650003779137,null,3.3640236621366545E-2,30.849261903831909,null,6.1701300007558271E-3]
[null,0.13500000000000001,null,3.5821096034618902E-2,null,3.7209125291604486E-2,30.853157420867795,null,3.6118338033562944E-2,30.851925212549553,null,6.1706314841735591E-3]
[null,0.15000000000000002,null,3.6393394978577534E-2,null,3.9024549338120072E-2,30.855289379038531,null,3.8153262930575457E-2,30.854253522933391,null,6.1710578758077065E-3]
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[]
[]
[null,"across SLS"]
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[null,0.66000000000000048,null,2.3990215672756499E-2,null,-0.20080467248740783,31.447286476160492,null,-0.19125873149338993,31.390668888394988,null,6.2894572952320984E-3]
[null,0.67500000000000049,null,2.0829282333925062E-2,null,-0.22084703510678641,31.574756672801968,null,-0.2107288892554289,31.508954646909924,null,6.3149513345603933E-3]
[null,0.6900000000000005,null,1.7358837915741224E-2,null,-0.24208285460222168,31.722394769367536,null,-0.23136296121225566,31.646259722607187,null,6.3444789538735068E-3]
[null,0.70500000000000052,null,1.3560520003429001E-2,null,-0.26457413472972474,31.892675911474512,null,-0.25322119415414795,31.804947226088562,null,6.3785351822949025E-3]
[null,0.72000000000000053,null,9.4150088662900734E-3,null,-0.28838654490439325,32.088310225145889,null,-0.27636740914259494,31.987608703400603,null,6.4176620450291776E-3]
[null,0.73500000000000054,null,4.9019710484901865E-3,null,-0.31358961194014773,32.312255219594917,null,-0.3008691878533255,32.197077051240051,null,6.4624510439189832E-3]
[null,0.75000000000000056,null,-1.6217035580207276E-16,null,-0.34025692305218985,32.56772685526127,null,-0.32679806989935628,32.436438301448597,null,6.513545371052254E-3]

{"sheet":"step 2 uniform","index":2,"n_rows":154,"n_cols":12,"rows_kept":154,"cut":false,"hidden":false,"merged":[[41,0,41,4],[42,2,42,3],[1,4,1,6]]}
["Uniform load distribution"]
["author: Suzanne van Eekelen",null,"along  (x)","across  (y)","eq.no. in Van Eekelen et al 2015"]
[null,null,"SLS","SLS"]
["Geometry & properties"]
["centre-to-centre distance","m",{"$f":"'step 1 CA model 3D'!F7","v":2.25},{"$f":"'step 1 CA model 3D'!F8","v":2.25}]
["size (square) pile cap","m",{"$f":"'step 1 CA model 3D'!F5","v":0.75},{"$f":"C6","v":0.75}]
["equivalent diameter pile cap","m",{"$f":"SQRT(4*C6^2/PI())","v":0.84628437532163447},{"$f":"C7","v":0.84628437532163447}]
["length between pile caps","m",{"$f":"+C5-C6","v":1.5},{"$f":"+D5-D6","v":1.5}]
["area GR strip","m2",{"$f":"+C6*C8","v":1.125},{"$f":"+D6*D8","v":1.125}]
["AL (area belonging to GR strip)","m",{"$f":"0.5*C5*D5-0.5*C7^2*ATAN((D5)/(C5))","v":2.25},{"$f":"0.5*C5*D5-0.5*C7^2*ATAN((C5)/(D5))","v":2.25},8]
["GR stiffness J'  ","kN/m",{"$f":"'step 1 CA model 3D'!F12","v":5000},{"$f":"C11","v":5000}]
["subgrade reaction","kN/m3",{"$f":"'step 1 CA model 3D'!F13","v":200},{"$f":"C12","v":200}]
[]
["qav (average load strip=(B+C)/area_two_GRstrips)","kPa on strip",{"$f":"'step 1 CA model 3D'!D50/SUM('step 2 uniform'!C9:D9)","v":28.185443587636097},{"$f":"'step 1 CA model 3D'!D50/SUM('step 2 uniform'!C9:D9)","v":28.185443587636097},9]
[]
["Calculation step 2 inverse triangle"]
["mod. K=(ks)*AL/(L*Bers)","kN/m2",{"$f":"C10*C12/(C8*C6)","v":400},{"$f":"D10*D12/(D8*D6)","v":400},7]
["a = sqrt((K/Th)",null,{"$f":"+SQRT(C17/C21)","v":3.724614818338885},{"$f":"+SQRT(D17/D21)","v":3.7246148183395227},6]
["term qa/K",null,{"$f":"C14/C17","v":7.046360896909025E-2},{"$f":"D14/D17","v":7.046360896909025E-2},4]
["exp(0.5*a*L)+exp(-0.5*a*L)","-(?)",{"$f":"EXP(0.5*C8*C18)+EXP(-0.5*C8*C18)","v":16.398676889213494},{"$f":"EXP(0.5*D8*D18)+EXP(-0.5*D8*D18)","v":16.398676889221278},4]
["Horizontal force Th","kN/m",28.833493007412446,28.833493007402573,"to be determined with yellow button"]
["delta L geometric","cm",{"$f":"100*(B48*SUM(J48:J97)/C21-0.5*C8)","v":0.43582480054986661},{"$f":"100*(B105*SUM(J105:J154)/D21-0.5*D8)","v":0.43582480054994432},11]
["delta L constitutive","cm",{"$f":"100*(B48*SUM(J48:J97)/C11)","v":0.43501566537900899},{"$f":"100*(B105*SUM(J105:J154)/D11)","v":0.43501566537886049},11]
["difference","cm",{"$f":"+C23-C22","v":-8.0913517085762221E-4},{"$f":"+D23-D22","v":-8.0913517108383015E-4},11]
["average strain geometric","%",{"$f":"0.01*C22/(0.5*C8)","v":5.8109973406648878E-3},{"$f":"0.01*D22/(0.5*D8)","v":5.8109973406659243E-3},11]
["average strain force","%",{"$f":"AVERAGE(L47:L97)","v":5.801482228478076E-3},{"$f":"AVERAGE(L104:L154)","v":5.8014822284760985E-3},11]
["difference","%",{"$f":"+C25-C26","v":9.5151121868117944E-6},{"$f":"+D25-D26","v":9.5151121898258764E-6},11]
[]
["Results inverse triangle (step 2)"]
["average strain","%",{"$f":"+C25","v":5.8109973406648878E-3},{"$f":"+D25","v":5.8109973406659243E-3},11]
["max strain","%",{"$f":"C35/C11","v":5.9591383218836674E-3},{"$f":"D35/D11","v":5.9591383218816933E-3}]
["min strain","%",{"$f":"C21/C11","v":5.7666986014824895E-3},{"$f":"D21/D11","v":5.7666986014805145E-3}]
["deflection in the centre","m",{"$f":"-D47","v":6.1869792596570723E-2},{"$f":"-D104","v":6.1869792596574803E-2}]
["max deflection","m",{"$f":"-MIN(D47:D97)","v":6.1869792596570723E-2},{"$f":"-MIN(D104:D154)","v":6.1869792596574803E-2}]
["max tensile force","kN/m",{"$f":"MAX(G47:G97)","v":29.795691609418338},{"$f":"MAX(G104:G154)","v":29.795691609408468}]
["min strain","%",{"$f":"MIN(L47:L97)","v":5.7666986014824895E-3},{"$f":"MIN(L104:L154)","v":5.7666986014805145E-3}]
["spreading force","kN/m",null,"no spreading force in this calculation!"]
[]
[]
[]
[]
[]
[]
[null,"along SLS"]
[null,"L(x)",null,"z(x)",null,"dz/dx in nodes between increments","T_GR in nodes between increments",null,"dz/dx (average in increment)","T_GR average in increment",null,"strain"]
[null,null,null,null,null,null,"kN/m",null,null,"kN/m",null,"-"]
[null,0,null,{"$f":"C$19*((EXP(C$18*B47)+EXP(-C$18*B47))/(C$20)-1)","v":-6.1869792596570723E-2},null,{"$f":"C$19*C$18*((EXP(C$18*B47)-EXP(-C$18*B47))/C$20)","v":0},{"$f":"C$21*SQRT(1+F47^2)","v":28.833493007412446},null,0,{"$f":"C$21*SQRT(1+I47^2)","v":28.833493007412446},null,{"$f":"G47/C$11","v":5.7666986014824895E-3}]
[null,{"$f":"C$8*0.01","v":1.4999999999999999E-2},null,{"$f":"C$19*((EXP(C$18*B48)+EXP(-C$18*B48))/(C$20)-1)","v":-6.185637686719888E-2},null,{"$f":"C$19*C$18*((EXP(C$18*B48)-EXP(-C$18*B48))/C$20)","v":1.7892291748770246E-3},28.833539160297761,null,{"$f":"-(D47-D48)/(B48-B47)","v":8.9438195812289556E-4},28.833504539640842,null,5.7667078320595526E-3]
[null,{"$f":"B48+B$48","v":0.03},null,-6.1816087792734668E-2,null,3.5840446488681669E-3,28.833678195347932,null,2.6859382976140989E-3,28.833597013447928,null,5.7667356390695866E-3]
[null,4.4999999999999998E-2,null,-6.1748799583355211E-2,null,5.3900501625300584E-3,28.833911848927379,null,4.4858806252971268E-3,28.833783115944744,null,5.7667823697854755E-3]
[null,0.06,null,-6.1654302153024726E-2,null,7.2128843937597064E-3,28.834243039004342,null,6.2998286886990313E-3,28.8340651712858,null,5.7668486078008684E-3]
[null,7.4999999999999997E-2,null,-6.1532300463567696E-2,null,9.0582385627731056E-3,28.834675901503577,null,8.1334459638019822E-3,28.83444670185354,null,5.7669351803007153E-3]
[null,0.09,null,-6.1382413603505999E-2,null,1.0931874201130518E-2,28.835215841826443,null,9.9924573374464889E-3,28.83493247213848,null,5.7670431683652882E-3]
[null,0.105,null,-6.1204173598783884E-2,null,1.2839641140286566E-2,28.835869602173734,null,1.1882666981474315E-2,28.835528548084721,null,5.7671739204347471E-3]
[null,0.12,null,-6.0997023951667902E-2,null,1.4787495775828698E-2,28.836645345500898,null,1.3809976474398838E-2,28.836242372632302,null,5.7673290691001794E-3]
[null,0.13500000000000001,null,-6.0760317903259621E-2,null,1.6781519664428212E-2,28.837552757139225,null,1.578040322721869E-2,28.837082858386982,null,5.7675105514278452E-3]
[null,0.15000000000000002,null,-6.0493316414196661E-2,null,1.8827938511567013E-2,28.838603165333101,null,1.780009927086396E-2,28.838060498557866,null,5.7677206330666204E-3]
[null,0.16500000000000004,null,-6.0195185857237342E-2,null,2.0933141609323167E-2,28.83980968217406,null,1.9875370463954621E-2,28.839187497526645,null,5.7679619364348119E-3]
[null,0.18000000000000005,null,-5.9864995414524662E-2,null,2.3103701784903584E-2,28.841187366660556,null,2.2012696180845316E-2,28.840477922651385,null,5.7682374733321112E-3]
[null,0.19500000000000006,null,-5.9501714171403569E-2,null,2.5346395922206798E-2,28.842753411880373,null,2.4218749541406161E-2,28.841947879165552,null,5.7685506823760748E-3]
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[null,0.2400000000000001,null,-5.8201445179256898E-2,null,3.2578561116174992E-2,28.848790345675866,null,3.1319355151999011E-2,28.847630956858346,null,5.7697580691351731E-3]
[null,0.25500000000000012,null,-5.769337014497674E-2,null,3.518239687309245E-2,28.851332552623813,null,3.3871668952010554E-2,28.850028454518778,null,5.7702665105247627E-3]
[null,0.27000000000000013,null,-5.7145424100972446E-2,null,3.7896078476056014E-2,28.854189653066459,null,3.652973626695289E-2,28.852724612177756,null,5.7708379306132922E-3]
[null,0.28500000000000014,null,-5.6555896259971372E-2,null,4.0728078532905686E-2,28.857397257159619,null,3.9301856066738215E-2,28.855753038889237,null,5.7714794514319235E-3]
[null,0.30000000000000016,null,-5.5922946008763012E-2,null,4.3687239063227842E-2,28.860995331003245,null,4.2196683413890622E-2,28.859151474350053,null,5.7721990662006487E-3]
[null,0.31500000000000017,null,-5.5244597161469525E-2,null,4.6782799104749535E-2,28.865028689966977,null,4.5223256486232467E-2,28.862962255047957,null,5.773005737993395E-3]
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[null,0.3450000000000002,null,-5.374308360916099E-2,null,5.3422233368372096E-2,28.874608151019128,null,5.1709878691519745E-2,28.872016377634495,null,5.7749216302038255E-3]
[null,0.36000000000000021,null,-5.291523090556819E-2,null,5.6986837112585551E-2,28.880273436903948,null,5.5190180239519888E-2,28.877372394586803,null,5.7760546873807895E-3]
[null,0.37500000000000022,null,-5.2032588971949997E-2,null,6.0729364133564466E-2,28.886613838000887,null,5.8842795574546157E-2,28.883367490890048,null,5.7773227676001775E-3]
[null,0.39000000000000024,null,-5.1092402039553557E-2,null,6.4661499281788257E-2,28.893708127176897,null,6.2679128826429301E-2,28.89007617317959,null,5.7787416254353793E-3]
[null,0.40500000000000025,null,-5.0091734673666906E-2,null,6.8795519398817256E-2,28.901644381983822,null,6.6711157725776682E-2,28.897581761384281,null,5.7803288763967646E-3]
[null,0.42000000000000026,null,-4.9027462608657632E-2,null,7.3144331647826452E-2,28.910521056223029,null,7.0951471000618188E-2,28.90597740388063,null,5.7821042112446057E-3]
[null,0.43500000000000028,null,-4.7896262993446945E-2,null,7.772151381211781E-2,28.920448173954231,null,7.541330768071243E-2,28.91536720899547,null,5.7840896347908458E-3]
[null,0.45000000000000029,null,-4.6694604016963896E-2,null,8.2541356687430956E-2,28.931548659092019,null,8.0110598432203167E-2,28.925867505402628,null,5.7863097318184035E-3]
[null,0.4650000000000003,null,-4.5418733881188354E-2,null,8.761890870040831E-2,28.943959814996315,null,8.5058009051702729E-2,28.937608245181405,null,5.7887919629992634E-3]
[null,0.48000000000000032,null,-4.4064669087354895E-2,null,9.2970022892521709E-2,{"$f":"C$21*SQRT(1+F79^2)","v":28.957834969802231},null,9.0270986255563873E-2,{"$f":"C$21*SQRT(1+I79^2)","v":28.950734564606439},null,{"$f":"G79/C$11","v":5.7915669939604467E-3}]
[null,0.49500000000000033,null,-4.2628181998744616E-2,null,9.8611406416153097E-2,28.973345304644194,null,{"$f":"-(D79-D80)/(B80-B79)","v":9.5765805907351856E-2},28.965408519114384,null,5.7946690609288389E-3]
[null,{"$f":"B80+B$48","v":0.51000000000000034},null,-4.1104787641233882E-2,null,0.10456067269736498,28.9906818833974,null,0.10155962383404882,28.981811010333281,null,5.7981363766794799E-3]
[null,0.52500000000000036,null,-3.9489729700388915E-2,null,0.11083639642822196,29.010057904069381,null,0.1076705293896644,29.000143924552056,null,5.8020115808138763E-3]
[null,0.54000000000000037,null,-3.7777965671386485E-2,null,0.11745817156035994,29.031711193502538,null,0.11411760193349522,29.020632503530226,null,5.8063422387005072E-3]
[null,0.55500000000000038,null,-3.5964151115396123E-2,null,0.12444667248086927,29.055906968562411,null,0.12092097039935734,29.043527970073072,null,5.8111813937124822E-3]
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[null,0.60000000000000042,null,-2.9852073455822303E-2,null,0.14783686114517222,29.146878571762446,null,0.14368722857444649,29.129620782901938,null,5.829375714352489E-3]
[null,0.61500000000000044,null,-2.7569968422250651E-2,null,0.1565229535936794,29.184557939111993,null,0.15214033557144332,29.165283869077928,null,5.8369115878223986E-3]
[null,0.63000000000000045,null,-2.5153941636478303E-2,null,0.16569773918964756,29.226635231808682,null,0.16106845238482306,29.205112527288478,null,5.8453270463617365E-3]
[null,0.64500000000000046,null,-2.2596449823176094E-2,null,0.17538986328346934,29.273616169816531,null,0.17049945422014712,29.24958644661158,null,5.8547232339633062E-3]
[null,0.66000000000000048,null,-1.9889508027453068E-2,null,0.18562958645048025,29.326062860960597,null,0.18046278638153496,29.29923897083642,null,5.8652125721921191E-3]
[null,0.67500000000000049,null,-1.7024664684374035E-2,null,0.19644887896998281,29.384599658359207,null,0.1909895562052687,29.354662711917605,null,5.8769199316718417E-3]
[null,0.6900000000000005,null,-1.3992975231635663E-2,null,0.20788152064227639,29.449919525666207,null,0.20211263018255793,29.416515659703926,null,5.8899839051332415E-3]
[null,0.70500000000000052,null,-1.0784974183015271E-2,null,0.21996320625534144,29.522790930296939,null,0.21386673657469266,29.48552781017316,null,5.9045581860593874E-3]
[null,0.72000000000000053,null,-7.3906455754000101E-3,null,0.23273165703046425,29.604065279506123,null,0.22628857384101717,29.562508329888054,null,5.9208130559012251E-3]
[null,0.73500000000000054,null,-3.7993916971271868E-3,null,0.24622673839475473,29.694684907098019,null,0.23941692521818803,29.648353268220173,null,5.9389369814196041E-3]
[null,0.75000000000000056,null,1.5646064215133538E-16,null,0.26049058444826473,29.795691609418338,null,0.25329277980848935,29.744053820806656,null,5.9591383218836674E-3]
[]
[]
[]
[null,"across SLS"]
[null,"L(x)",null,"z(x)",null,"dz/dx in nodes between increments","T_GR in nodes between increments",null,"dz/dx (average in increment)","T_GR average in increment",null,"strain"]
[null,null,null,null,null,null,"kN/m",null,null,"kN/m",null,"-"]
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