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Home My WebLink About2013-12-03 Planning Board Supplemental Materials (85) DESIGN CALCULATIONS FOR UNIVERSIRL uja11TM Precast Concrete Retaining Wall Produced by Concrete Systems, Inc. The Arbors at North Andover North Andover, MA Revision 1 Pro Con, Inc. � ,OkA OF Aq�SgC C] CHRISTOPHER M. Uwall Scope of Engineering: C) S CTURAL Cn • Overturning 48517 • Sliding • Applied bearing pressureAL • Pullout _g ^ Analysis not in Uwall Scope of Engineering: ' 17 l Y P • Slip circle/ global stability • Bearing capacity of foundation soils • Settlement • Scour • Slope stability for temporary cut • Site drainage (runoff must be diverted away from wall) Design 1: pp. 1 —3 Design 2: pp. 1—8 Design 3: pp. 1 - 8 • 12' high • 6:1 Batter • Seismic analysis • No geogrid Pro Con, Inc. Uwall Calculations Page 1 of 3 The Arbors Design 1 HNorth Andover, MA WALL PARAMETERS H:= 12ft wall height from top of leveling pad L:= 3.83ft stem length (fromface)* P:= 0 radians backslope angle w:= 0.16515 radians wall batter WU := 5in depth of UWall face L := L—Wu L =3.413-ft L •tan((3)•tan(w) L := P - L =O-ft L := L + L L =3.413-ft PP 1 —tan((3)•tan(w) PP p p pP R h:= Lp•tan(p) h =O-ft height of backslope soil wedge H Hs:= Oft height of broken back slope I:= atan s I=0 (2-H) 5:= if(I>0,I,(3) =0 RETAINED FILL PROPERTIES .5236 angle of internal friction lbf 125 ft3 soil unit weight 6:= .6667•(0 friction angle between soil & wall cos( + w) 2 Ka '= 2 2 Ka= 0.235 cos(W)2•cos(w—S)•11 + (4 sin( + S)•sin(�— (3) Cos(W—6)•cos(W+ R) HORIZONTAL FORCES Ps:= .5•Ka•-yr(H+ h)2 cos( — W) Ps= 1.98 x 103•lbf Horizontal force due to retained soil ft ql •= 0 lbf live load surcharge qd:= 0 lbf dead load surcharge ft2 ft2 Pq:= (ql + gd)Ia•(H+ h)•cos((�— w) P —0 lbf Horizontal force due to surcharges behind wall q ft Pa:= Ps+ Pq Pa= 1.98 x 103•lbf ft Total Horizontal active force PH (603)889-4163 Concrete Systems, Inc. Arbor-NOGRID-seismicD1.xmcd FAX(603)598-1344 9 Commercial Street csigroup.biz Hudson, NH 03051 Pro Con, Inc. Uwall Calculations Page 2 of 3 The Arbors North Andover, MA Resisting Moment: Wri:= L•ryr H•1 ft Wri=5.745 x 103•lbf Weight of reinforced soil mass L•�yr h•lft Wrp:= Wro=0•1bf Weight of soil due to backslope 2 L+ H•tan(w) Xri:= Xri=2.915-ft Moment arm for soil mass 2 2•L Xrp• 3 H•tan(w) + Wu+ P Xrp=4.692-ft Moment arm for backslope L Moment arm for dead load Xqp := L+ [(H+ h)•tan(w)] — P Xqp =4.123-ft surcharge Mr:= Wri'Xn + WrO'Xr(3+ qd*l ft•LO•Xgp Mr= 1.675 x 104•ft•1bf Overturning Moment: Ys.— H+ h Ys=4-ft 3 Yq .— H+ h Yq = 6•ft 2 Mo := (Ps'Ys+ Pq•Yq)•l ft Mo =7.921 x 103 ft.IV M FSot:= r FSot=2.114 Mo Base Sliding: Cds := 1 Coefficient of direct sliding Rs:= Cds'(gd•lft•Lp+ Wri+ Wrp)•tan(�)) Rs=3.317 x 103 IV R FSSl := s FSSI = 1.675 Pa•1 ft PH(603)889-4163 Concrete Systems, Inc. Arbor-NOGRID-seismicD1.xmcd FAX(603)598-1344 8 Commercial Street csigroup.biz Hudson, NH 03051 Pro Con, Inc. Uwall Calculations Page 3 of 3 The Arbors North Andover, MA Seismic: Seismic Load A:= .17 Am:= (1.45 —A)•A Am=0.218 PAE:= .375•Am•'yr H2 MSeis:= .5•PAE•.6•H•lft MSeis =5.288 x 103•lbf-ft Seis:= .5•PAE Overturning M i'Sot'R r FSot= 1.268 M + M if(FSot>_ 1.125,"OK" ,"NG") _ "OK" Sets o Slidin R FSsI ;= s FSsj = 1.222 if(FS,l >_ 1.125,"OK" ,"NG") ="OK" (Pa+ Seis)•1 ft Soil Bearing Stress: ( 1 MD —[Wri. I X — 2 I + WrP•I XrO— 2 I + lftgd•Lp (XqP 2lJ Wri+ WrR+ qd•1 ft-Lo e =4.546.in eccentricity Check a<U6 6 =7.66-in Be := L—2•e Be =3.072-ft effective base width Wri + Wr(3+ (ql + gd)•LR•lft Qa Be•lft Qa= 1.87 x 103.lbf applied bearing pressure ft2 PH(603)889-4163 Concrete Systems, Inc. Arbor-NOGRID-seismicD1.xmcd FAX(603)598-1344 8 Commercial Street csigroup.biz Hudson, NH 03051 Design 2 • 10.5' high • 6:1 Batter • Seismic analysis • 3:1 Backslope • Geogrid Pro Con, Inc. Uwall Calculations Page 1 of 8 The Arbors Design 2 North Andover, MA WALL PARAMETERS H:= 10.5ft wall height from top of leveling pad L := 7ft reinforcement length P:= 0.321 F radians backslope angle W:= 0 radians wall batter Wu := 5in depth of UWall face L := L-Wu L =6.583-ft L •tan((3)•tan(w) L := P L =0•ft L := L + L L =6.583-ft PP 1 -tan(p)•tan(w) PP R P PP h:= Lp•tan((3) h =2.195-ft height of backslope soil wedge H Hs:= 6.5ft height of broken back slope I.= atan s I=0.3 (2-H) (3:= if(I> 0,I,(d) (3=0.3 RETAINED FILL PROPERTIES .5236 angle of internal friction - 125 lbf 3 soil unit weight ft 8:= .6667• friction angle between soil & wall cos( + W)2 Ka: 2 ' Ka=0.388 S)•sin(�- (d) COS(W) cos(W— b) 1 + HORIZONTAL FORCES Ps:= .5-Ka'-If(H+ h)2•cos(q)- W) Ps=3.382 x 103•Ibf Horizontal force due to retained soil ft ql 0 IV live load surcharge qd:= 0 lbf dead load surcharge ft2 ft2 Pq := (qt + gd)Ka•(H+ h)•cos((� - w) Pq =0 lbf Horizontal force due to surcharges behind wall ft Pa:= Ps+ P Pa=3.382 x 103.lbf ft Total Horizontal active force 2/17/2012 Concrete Systems, Inc. Arbor-GEOGIDD2.xmcd 11:30 AM 9 Connercial Street Hudson, NH 03051 Pro Con, Inc. Uwall Calculations Page 2 of 8 The Arbors North Andover, MA Resisting Moment: Wri := L•-Yr•H•1ft Wri =9.188 x 103•IV Weight of reinforced soil mass L•ryr h•lft Wrp:= 2 Wr(3=960.228•1bf Weight of soil due to backslope L+ H•tan(w) Xri:= Xri=3.5.ft Moment arm for soil mass 2 2•L Xrp• 3 = H•tan(w) + Wu+ P Xro=4.806•ft Moment arm for backslope L Moment arm for dead load XqP := L+ [(H+ h)-tan(w)] - XqP =3.708-ft surcharge Mr:= Wri'Xn + Wr(3•XrR+ qd.1 ft•L P'Xq(3 Mr=3.677 x 104•ft.IV Overturning Moment: Ys H+ h Ys=4.232-ft 3 Yq .- H+ h Yq =6.347-ft 2 Mo := (Ps'Ys+ Pq•Yq)•lft Mo = 1.431 x 104 ft.IV M FSot:= r FSot=2.57 Mo Base Sliding: Cds := 1 Coefficient of direct sliding Rs Cds'(gd'lft•Lp+ Wri + Wro)•tan((�) Rs=5.859 x 103 IV R FSsI := s FSsI= 1.733 Pa•1 ft PH (603) 889-4163 Concrete Systems, Inc. Arbor-GEOGIDD2.xmcd FAX(603) 589-1344 9 Commercial Street csigroup.biz Hudson, NH 03051 Pro Con, Inc. Uwall Calculations Page 3 of 8 The Arbors North Andover, MA Seismic: Seismic Load A:_ .17 Am:_ (1.45 -A)•A Am=0.218 Pte:_ .375•Atn" H2 MSeis` .5•PA•.6•H•lft 3 MSeis =3.542 x 10 •lbf-ft Seis :_ .5•PAE Overturning Mr FS r5ot.-- MSeis+ Mo of=2.06 if(FSot>_ 1.125,"OK" "NG") _ "OK" Sliding FS Rs FSsl = 1.486 if(FSsl > 1.125,"OK" ,"NG") _"OK" sl (Pa+ Seis)•1 ft — Soil Bearing Stress: Mo — Wri' ' — + WrO' Xr.O—2) 2 J + lftgd•L�- XqO 2/J e:= Wri+ Wro+ qd•lft•Lo e = 15.439•in eccentricity Check a<U6 L = 14-in 6 Be:= L —2•e Be =4.427-ft effective base width Wri+ WrO+ (ql+ gd)•LO•lft Qa Be•lft Qa= 2.292 x 103•IV applied bearing pressure ft2 Note: The eccentricity is slightly outside the kem, therefore, Qa is underestimated. Recalculate for Qmax. a:= L-�L + e) a=26.561-in 2 2•(Wri+ WrO+ ql + gd)•lft 3 2 lbf Qmax�= 3-a Qmax= 3.056 x 10 ft Z ft PH (603) 889-4163 Concrete Systems, Inc. Arbor-GEOGIDD2.xmcd FAX(603) 589-1344 9 Commercial Street csigroup.biz Hudson, NH 03051 Pro Con, Inc. Uwall Calculations Page 4 of 8 The Arbors North Andover, MA INFILL PROPERTIES � := .5934 angle of internal friction Si:= .6667•(�friction angle between soil & wall -yl .- 125 lbf infill unit weight ft3 cos(0)i + w)2 Kai:= 2 rcos(w Kai=0.32] 2 ni + S sin �i - p cos(w) •cos(w- S) 1 + HORIZONTAL FORCES DUE TO REINFORCED SOIL Ps:= .5•Kal ryi•H2•cos((�i -w) Ps= 1.832 x 103.IV Horizontal force due to reinforced soil ft q1 =0 1bf live load surcharge qd=0.IV dead load surcharge ft ft2 Pq:= (ql + gd)Kai•H•cos(Oi -w) Pq =0 lbf Horizontal force due to surcharges above zone ft Pa:= Ps+ Pq Pa= 1.832 x 103.lbf ft Total Horizontal active force GEOGRID MATERIAL PROPERTIES Tult:= 5475 llbt ultimate tensile strength ft RFD:= 1.2 durability reduction factor RFID:= 1.1 installation damage reduction factor RFCR:= 1.42 creep reduction factor FSunc 1.1 factor of safety against uncertainties PH (603)889-4163 Concrete Systems, Inc. Arbor-GEOGIDD2.xmcd FAX(603) 589-1344 9 Commercial Street csigroup.biz Hudson, NH 03051 Pro Con, Inc. Uwall Calculations Page 5 of 8 The Arbors North Andover, MA ALLOWABLE WORKING STRESS OF GEOGRID T Tult 3lbf T =2.655 x 10 . a RFD'RFID'RFCR'FSunc a ft P Nmin` a Nmin=0.69 minimum number of geogrid layers Ta CHECK TENSION AT FIRST GEOGRID LAYER E1 := 2ft E2 := 4-ft Act •- E2 + El Acl D1 =9 ft 2 2 Fgl := (ryi'D1 + ql + gd)'Kafcos(-�i —w)•Acl Fg1 = 897.107•IVft if(Fg1 <Ta,"OK" ,"NG") ="OK" CHECK TENSION AT SECOND GEOGRID LAYER E3 := 6ft Ac2:= E3 -El D2 := H-Ac1 - Ac2 2 2 D2 =6.5 ft Fg2 := (,Yi•D2 + ql + gd)•Kai-cos((i — w)•Ac2 Fg2 =431.941.IV ft if N2 <Ta,"OK" ,"NG")_ "OK" CHECK TENSION AT TOP GEOGRID LAYER Ac3 := (H_ E3 2 E2/ Ac3 = 5.5 ft D3 := A2 3 D3 =2.75 ft IV Fg3 := (7i'D3 + ql + gd)'Kai•cos(N - w)•Ac3 Fg3 = 502.546• ft if(Fg3 <Ta,"OK" ,"NG") _ "OK" PH (603) 889-4163 Concrete Systems, Inc. Arbor-GEOGIDD2.xmcd FAX(603) 589-1344 9 Commercial Street csigroup.biz Hudson, NH 03051 Pro Con, Inc. Uwall Calculations Page 6 of 8 The Arbors North Andover, MA FAILURE PLANE ANGLE + tan (pi- tan(4)i- R + cot '4)i + w 1 + tan 6i -w •cot (�i + w I + tan(6i —w)•(tan(Oj — 0) + cot(-�i + w)11 res=0.362 atan(res) =0.347 o,:= atan(res) + a,=0.871 radians adeg:= a• 180 o.deg=49.909 degrees 7T EMBEDMENT LENGTH La3 := L—Wu—E3•tan(1.5708 —o) + E3-tan(w) La3= 1.533-ft La2:= L—Wu—E2•tan(1.5708 —cx) + E2-tan(w) La2=3.216-ft Lal := L— Wu—E1•tan(1.5708 —(i) + E1-tan(w) Lal =4.9-ft PH (603) 889-4163 Concrete Systems, Inc. Arbor-GEOGIDD2.xmcd FAX(603) 589-1344 9 Commercial Street csigroup.biz Hudson, NH 03051 Pro Con, Inc. Uwall Calculations Page 7 of 8 The Arbors North Andover, MA SHEAR STRENGTH TRANSFERED TO GEOGRID(ANCHORAGE CAPACITY/PULLOUT) Ci := .7 coefficient of interaction between soil &geogrid(from manufacturer) E1 Lal depth of d = H-E + -H•tan(w) + tan(p) d =9.79.779-ft1 1) (tan(a) 2 1 overburr den AC := 2•La1'Ci'(dli+ qd)"N AC=4.976 x 103.lbf ft anchorage capacity FS:= AC FS= 5.547 Fgl of d = H-E + E2 -H•tan(w) + La2 tan(p) d =8.04-ft depth 2 2) tan(o) 2 2 overburr den 3lbf AC := 2•La2•Ci•(d2•1i + gd)4i AC =2.685 x 10 •—ft anchorage capacity FS:= AC FS=6.217 Fg2 of d �H-E3) + E3 -H•tan(w) + La3J tan(p) d 6.301-ft depth 3 3 tan(a) 2 3 overburden AC:= 2•La3' i �C• d3'1i + qd)4i x AC= 1.003 103. ft IVanchorage capacity FS:= AC FS= 1.995 Fg3 PH (603) 889-4163 Concrete Systems, Inc. Arbor-GEOGIDD2.xmcd FAX(603) 589-1344 9 Commercial Street csigroup.biz Hudson, NH 03051 Pro Con, Inc. Uwall Calculations Page 8 of 8 The Arbors North Andover, MA FAILURE PLANE ANGLE(RETAINED SOIL) -tan( - (3) + tan(O - (3)•(tan(O- p) + cot(4)+ w))•(1 + tan(6- w)•cot(O + w)) res.- 1 + tan(8- w)•(tan(4- (3) + cot(O + w)) res=0.365 atan(res) = 0.35 ae:= atan(res) + 4) oe =0.873 radians E2 -El a,deg:= ae• 180 a.deg=50.036 degrees DL:= � tan(ae) RESISTING FORCE OF LOWEST GEOGRID(INTERNAL SLIDING) Lps•tan((3)-tan(w) Lps := L-Wu-DL Lpps;= I - tan(p)-tan(w) LO1 := Lps+ Lpps Lel =4.907.ft Wpri := Lps•�H-El) ryi Wpri = 5.214 x 103•lbf ft 'ii•LRl•Lps•tan((3) IV from geogrid WprO:= 2 WprO=465.858•ft Cds 1 manufacturer Rps := cds'Od•L�1 + Wpri + WprO)•tan(0) Rps=3.831 x 103.lbf ft SLIDING FORCE AT LOWEST GEOGRID hl := LRl•tan((3) hl = 1.519ft PShl :_ .5•Ka•-yr(H-El + hl)2•cos(O - w) PShl =2.106 x 103.lbf ft Pqhl (ql + gd)•Ka•(H-El + hl)•cos(O -w) Pqhl =0.Ibfbf Pahl := PShl + Pqhl Pahl =2.106 x 103.lbf ft R FSsll := ps FSs11 = 1.819 Factor of Safety against internal sliding Pahl PH (603) 889-4163 Concrete Systems, Inc. Arbor-GEOGIDD2.xmcd FAX(603) 589-1344 9 Commercial Street csigroup.biz Hudson, NH 03051 Design 3 • 11' high • 6:1 Batter • Seismic analysis • Lower tiers with groundwater present (saturated backfill 165 pst) • Geogrid Pro Con, Inc. Uwall Calculations Page 1 of 8 The Arbors Design 3 North Andover, MA WALL PARAMETERS H:= l lft wall height from top of leveling pad L:= 6ft reinforcement length 0:= 0 radians backslope angle W:= 0 radians wall batter WU:= 5in depth of UWall face L := L-WU L = 5.583-ft L tan(�)•tan(w) L := P L =O•ft L := L + L L = 5.583-ft PP 1 - tan(R)•tan(w) PP P PP h := LP•tan(p) h=0•ft height of backslope soil wedge H Hs:= Oft height of broken back slope I:= atan s I= 0 (2-H) 0:= if(I>0,I, 0 71 = 125 Ibf infill unit weight 3 ft RETAINED FILL PROPERTIES �):= .5236 angle of internal friction = 165 lbf ryr'• 3 unit weight saturated soil 8:= .6667• friction angle between soil & wall ft cos( + w)2 Ka:= n(�('�' (3) 2 1a=0.297 S)•si - cos(w) cos(w-S) 1 + HORIZONTAL FORCES Ps:= .5•Ia•^lr(H+ h)2•cos((� - w) Ps=2.57 x 103.lbf Horizontal force due to retained soil ft ql 0 lbf live load surcharge qd := 0 1bf dead load surcharge ft2 ft2 P (ql + gd)Ka'(H+ h)•cos(�)- w) P _0 IV0.— force due to surcharges behind wall q ft Pa:= Ps+ P Pa=2.57 x 103.lbf ft Total Horizontal active force 2/17/2012 Concrete Systems, Inc. Arbor-GEOGID-IowertierD3.xmcd 11:11 AM 9 Connercial Street Hudson, NH 03051 Pro Con, Inc. Uwall Calculations Page 2 of 8 The Arbors North Andover, MA Resisting Moment: Wri := L•-yi•H•l ft Wri= 8.25 x 103 lbf Weight of reinforced soil mass L•ryr•h•1ft WrP:= WrP=0•1bf Weight of soil due to backslope 2Xn L+ H•tan(w) ;= Xri=3-ft Moment arm for soil mass 2 2•L Xrp:= H•tan(w) + Wu+ P 3 Xro=4.139•ft Moment arm for backslope L Moment arm for dead load Xq� := L+ [(H+ h)•tan(w)] - 2 XqP =3.208-ft surcharge Mr:= Wri'Xn+ Wrp•Xrp+ gd•1ft•LR'XgP Mr=2.475 x 104•ft•lbf Overturning Moment: YS = H+ h Ys=3.667 ft 3 Yq.- H+ h Yq = 5.5•ft 2 Mo := (Ps•Ys+ Pq•Yq)•lft Mo =9.424 x 103 ft•lbf M FSot:= r FSot=2.626 Mo Base Sliding: Cds 1 Coefficient of direct sliding Rs:= Cds'(gd'lft•Lp+ Wri+ Wrp)•tan((�) Rs=4.763 x 103 IV R FSSI := s FSsI = 1.853 Pa 1 ft PH (603) 889-4163 Concrete Systems, Inc. Arbor-GEOGID-IowertierD3.xmcd FAX(603) 589-1344 9 Commercial Street csigroup.biz Hudson, NH 03051 Pro Con, Inc. Uwall Calculations Page 3 of 8 The Arbors North Andover, MA Seismic: Seismic Load A:= .17 Am:= (1.45 —A)•A Am=0.218 PAE:= .375•Am•^yr H2 MSeis := .5•PA•.6•H•lft MSeis =5.376 x 103•lbf-ft Seis:= .5•PAE Overturning Mr FSot:= MSeis + Mo FSot 1.67 if(FSot>_ 1.125,"OK" ,"NG") _ "OK" Slidin R FSSI:= s FSsI= 1.407 if(FSs, >— 1.125,"OK" ,"NG") _ "OK" �Pa+ Seis)•1ft Soil Bearing Stress: Mo —[Wri.(Xri — 2) + Wrp•(Xro— 2/ + lftgd•L�- NO L C:= .— J Wri+ Wro+ qd•lft•Lo e = 13.708•in eccentricity Check a<L/6 L = 12.in 6 Be := L —2•e Be=3.715-ft effective base width Wn+ Wro+ (ql+ gd)•Lo.1ft Qa Be•lft Qa=2.221 x 103.lbf applied bearing pressure 2 ft Note: The eccentricity is slightly outside the kem, therefore, Qa is underestimated. Recalculate for Qmax. a:= L— L + e V a=22.292-in 2 / 2'(Wri + Wr{3+ ql + qd)'I f•t 3 2 lbf 3-a Qmax�= Qmax=2.961 x 10 ft 2 ft PH (603) 889-4163 Concrete Systems, Inc. Arbor-GEOGID-IowertierD3.xmcd FAX(603) 589-1344 9 Commercial Street csigroup.biz Hudson, NH 03051 Pro Con, Inc. Uwall Calculations Page 4 of 8 The Arbors North Andover, MA INFILL PROPERTIES 4)i := .5934 angle of internal friction 6i:= .6667•,Ofriction angle between soil & wall cos(�i + W)2 Kai:= ? Fn Kai=0.255 cos(w) cos(w— 6) 1 + —S) cos(w+ �i) HORIZONTAL FORCES DUE TO REINFORCED SOIL Ps:= .5-Kai ryi•H2•cos(�i —w) Ps= 1.598 x 103.IV Horizontal force due to reinforced soil ft ql —0 lbf live load surcharge qd =0.IV dead load surcharge ft ft2 P :_ (ql + gd)Kai•H•cos(�i —w) P _0 Ibf Horizontal force due to surcharges above zone q ft Pa:= Ps+ Pq Pa= 1.598 x 103.IV ft Total Horizontal active force GEOGRID MATERIAL PROPERTIES Tult:= 5475 lbf ultimate tensile strength ft RFD:= 1.2 durability reduction factor RFID:= 1.1 installation damage reduction factor RFCR:= 1.42 creep reduction factor FSunc := 1.1 factor of safety against uncertainties PH (603) 889-4163 Concrete Systems, Inc. Arbor-GEOGID-IowertierM.xmcd FAX(603) 589-1344 9 Commercial Street csigroup.biz Hudson, NH 03051 Pro Con, Inc. Uwall Calculations Page 5 of 8 The Arbors North Andover, MA ALLOWABLE WORKING STRESS OF GEOGRID T Tult 3lbf T =2.655 x 10 . a RFD'RFID'RFCR°FSunc a ft P Nmin a Nmin=0.602 minimum number of geogrid layers Ta CHECK TENSION AT FIRST GEOGRID LAYER E1 := 2ft E2 := 4-ft - E2 + E1 Ael Acl :- D1 := H- — D1 =9.5 ft 2 2 Fgl := (ryi-Dl + ql + qd)-Kafcos(�i - w)•Acl Fg1 =752.931.lbf ft if(Fgl <Ta,"OK" "NG") = "OK" CHECK TENSION AT SECOND GEOGRID LAYER E3 -El Act E3 := 6ft Ac2:= 2 D2 := H-Acl - 2 D2 =7 ft Fg2 := (ryi•D2 + ql + gd)•Kai•cos(�)i - w)•Ac2 Fg2 =369.861.lbf ft if(Fg2 <Ta,"OK" ,"NG") = "OK" CHECK TENSION AT TOP GEOGRID LAYER Ac3 := CH- E3 2 E2 Ac3 = 6-ft D3 := Ac3 D3 -3 ft Fg3 := (�i•D3 + ql + gd)•Kai•cos((�i - w)•Ac3 Fg3 =475.536•lbf — ft if(Fg3 <Ta,"OK" ,"NG") _ "OK" PH (603) 889-4163 Concrete Systems, Inc. Arbor-GEOGID-IowertierD3.xmcd FAX(603) 589-1344 9 Commercial Street csigroup.biz Hudson, NH 03051 Pro Con, Inc. Uwall Calculations Page 6 of 8 The Arbors North Andover, MA FAILURE PLANE ANGLE —tan(cpi — 13)+ tan(4)i — (3 • tan (�i -- + cot Oi + w I + tan $i — w•cot(4)i + w I + tan(Si -w)•(tan(4)i - p)+ cot((�i + w)) res=0.453 atan(res) =0.425 oc:= atan(res) + a=0.949 radians a.deg:= a• 180 a.deg=54.353 degrees 7 EMBEDMENT LENGTH La3 := L-Wu-E3•tan(1.5708 -a) + E3•tan(w) Lai = 1.28-ft La2:= L-Wu-E2•tan(1.5708 -o) + E2-tan(w) La2=2.715-ft Lal := L-Wu-El•tan(1.5708-oc) + El•tan(w) Lal =4.149-ft PH (603) 889-4163 Concrete Systems, Inc. Arbor-GEOGID-IowertierD3.xmcd FAX(603) 589-1344 9 Commercial Street csigroup.biz Hudson, NH 03051 Pro Con, Inc. Uwall Calculations Page 7 of 8 The Arbors North Andover, MA SHEAR STRENGTH TRANSFERED TO GEOGRID(ANCHORAGE CAPACITY/PULLOUT) Ci := .7 coefficient of interaction between soil &geogrid(from manufacturer) d = H—E + —H•tan(w) + tan(p) d =9 tan(E1 Lal ft depth of 1 1) ( cx) 2 1 overburden AC:= 2•La1'Ci'(dl'-ji + gd)4i AC =3.878 x 103.IV anchorage capacity ft FS:= AC FS=5.15 Fgl of d = (H—E2) + E2 —Man(w) + I a21 tan(p) d 7-ft depth 2 2 tan((.) 2 2 overburden AC := 2•La2' i•C• (d2'ryi + qd)4i AC = 1.973 x 103.IVanchorage capacity ft FS:= AC FS=5.335 Fg2 of d = H—E + E3 —H•tan(w) + La3 tan(p) d =5-ft depth 3 ( 3) tan(a) 2 3 overburden ). AC:= 2•La3'Ci'(d3'^fi + gd)•gi AC =664.709•IV anchorage capacity ft FS:= AC FS= 1.398 Fg3 PH (603) 889-4163 Concrete Systems, Inc. Arbor-GEOGID-IowertierD3.xmcd FAX(603) 589-1344 9 Commercial Street csigroup.biz Hudson, NH 03051 Pro Con, Inc. Uwall Calculations Page 8 of 8 The Arbors North Andover, MA FAILURE PLANE ANGLE(RETAINED SOIL) —tan( — 0) + tan( — 0)•(tan((�— 0) + cot( + w))•(1 + tan(6— w)-cot( + w)) res:= 1 + tan(6 — w)•(tan(�)— 0) + cot( + w)) res=0.487 atan(res) =0.454 ae:= atan(res) + ae=0.977 radians E2 —El adeg:= ote• 180 odeg= 55.984 degrees DL:= � tan(o e) RESISTING FORCE OF LOWEST GEOGRID(INTERNAL SLIDING) Lps•tan(0)•tan(w) Lps := L—Wu —DL Lpps' 1 —tan(0)-tan(w) LO1 := Lps + Lpps LOl =4.233-ft Wpri := Lps•(H—El)--Ii Wpri =4.763 x 103.lbf ft ryi•L0l•Lps•tan(0) lbf from geogrid WprO 2 WprO 0 ft Cds .— 1 manufacturer Rps := Cds•(gd•L01 + Wpri + WprO)•ta+' ) =3.212 x 103.lbf Rs ft SLIDING FORCE AT LOWEST GEOGRID hl := LOl•tan(0) hl =0 ft PShl .5'Ka'1r(H—El + hl)2•cos(4— w) PShl = 1.721 x 103.lbf ft Pqhl (ql + gd)•Ka•(H—El + hl)•cos((� — w) Pghl =0.lbf ft P P + P P = 1.721 x 103.lbf Pahl '= PShl qhl Pahl ft FSsll :=: Rps FSsll = 1.867 Factor of Safety against internal sliding Pahl PH (603) 889-4163 Concrete Systems, Inc. Arbor-GEOGID-IowertierD3.xmcd FAX(603) 589-1344 9 Commercial Street csigroup.biz Hudson, NH 03051