Sachpazis Propped Cantilever Retaining Wall Example

ProjectJob Ref.Retaining wall Analysis & Design (EN1997-1:2004incorporating Corrigendum dated February 2009)SectionGEODOMISI Ltd. - Dr. Costas SachpazisCivil & Geotechnical Engineering Consulting Company forStructural Engineering, Soil Mechanics, Rock Mechanics,Foundation Engineering & Retaining Structures.Sheet no./rev.Civil & Geotechnical EngineeringCalc. byDateDr.C.Sachpazis 23/05/2013Chk'd by1DateApp'd byDate-Tel.: ( 30) 210 5238127, 210 5711263 - Fax.: 30 210 5711461 Mobile: ( 30) 6936425722 & ( 44) 7585939944, costas@sachpazis.infoUsing Coulomb theoryActive pressure coefficient;22KA sin(α φ'r.d) / (sin(α) sin(α - δr.d) [1 [sin(φ'r.d δr.d) sin(φ'r.d - β) / (sin(α - δr.d) sin(α 2β))]] ) 0.425Passive pressure coefficient;2KP sin(90 - φ'b.d) / (sin(90 δb.d) [1 - [sin(φ'b.d 2δb.d) sin(φ'b.d) / (sin(90 δb.d))]] ) 1.965Bearing pressure checkVertical forces on wallWall stem;Fstem γG Astem γstem 68.8 kN/mWall base;Fbase γG Abase γbase 60.6 kN/mSurcharge load;Fsur v γQ SurchargeQ lheel 195 kN/mSaturated retained soil;Fsat v γG Asat (γsr - γw) 19.9 kN/mWater;Fwater v γG Awater γw 19.1 kN/mMoist retained soil;Fmoist v γG Amoist γmr 232.8 kN/mBase soil;Fpass v γG Apass γmb 9 kN/mTotal;Ftotal v Fstem Fbase Fsat v Fmoist v Fpass v Fwater v Fsur v 605.2 kN/mHorizontal forces on wallSurcharge load;Fsur h KA cos(δr.d) γQ SurchargeQ heff 176.5 kN/mSaturated retained soil;Fsat h γG KA cos(δr.d) (γsr - γw) (hsat hbase)2/ 2 5.8 kN/mWater;2Fwater h γG γw (hwater dcover hbase) / 2 13.4kN/mMoist retained soil;Fmoist h γG KA cos(δr.d) γmr ((heff - hsat 2hbase) / 2 (heff - hsat - hbase) (hsat hbase)) 132.1kN/mTotal;Ftotal h Fsat h Fmoist h Fwater h Fsur h 327.8kN/mMoments on wallWall stem;Mstem Fstem xstem 85.9 kNm/mWall base;Mbase Fbase xbase 145.5 kNm/mSurcharge load;Msur Fsur v xsur v - Fsur h xsur h 99.5 kNm/mSaturated retained soil;Msat Fsat v xsat v - Fsat h xsat h 59.3 kNm/mWater;Mwater Fwater v xwater v - Fwater h xwater h 56.7kNm/mMoist retained soil;Mmoist Fmoist v xmoist v - Fmoist h xmoist h 463.5kNm/mBase soil;Mpass Fpass v xpass v 4.5 kNm/m

ProjectJob Ref.Retaining wall Analysis & Design (EN1997-1:2004incorporating Corrigendum dated February 2009)SectionGEODOMISI Ltd. - Dr. Costas SachpazisCivil & Geotechnical Engineering Consulting Company forStructural Engineering, Soil Mechanics, Rock Mechanics,Foundation Engineering & Retaining Structures.Sheet no./rev.Civil & Geotechnical EngineeringCalc. byDateDr.C.Sachpazis 23/05/2013Chk'd by1DateApp'd byDate-Tel.: ( 30) 210 5238127, 210 5711263 - Fax.: 30 210 5711461 Mobile: ( 30) 6936425722 & ( 44) 7585939944, costas@sachpazis.infoTotal;Mtotal Mstem Mbase Msat Mmoist Mpass Mwater Msur 915 kNm/mCheck bearing pressureMaximum friction force;Ffriction max Ftotal v tan(δbb.d) 102.9 kN/mMaximum base soil resistance;Fpass h max γGf KP cos(δb.d) γmb (dcover 2hbase) / 2 39.5 kN/mBase soil resistance;Fpass h min(max((Mtotal Ftotal h (hprop tbase) Ffriction max (hprop tbase) - Ftotal v lbase / 2) / (xpass h- hprop - tbase), 0 kN/m), Fpass h max) 0 kN/mFprop stem min((Ftotal v lbase / 2 - Mtotal) / (hprop Propping force;tbase), Ftotal h) 89.3 kN/mFriction force;Ffriction Ftotal h - Fpass h - Fprop stem 238.5 kN/mMoment from propping force;Mprop Fprop stem (hprop tbase) 446.7 kNm/mDistance to reaction; x (Mtotal Mprop) / Ftotal v 2250 mmEccentricity of reaction;e x - lbase / 2 0 mmLoaded length of base;lload lbase 4500 mmBearing pressure at toe;qtoe Ftotal v / lbase 134.5 kN/mBearing pressure at heel;qheel Ftotal v / lbase 134.5 kN/mEffective overburden pressure;q (tbase dcover) γmb - (tbase dcover hwater) γw 6.7 kN/m2222Design effective overburden pressure;q' q / γγ 6.7 kN/mBearing resistance factors;Nq Exp(π tan(φ'b.d)) (tan(45 deg φ'b.d / 2)) 23.784Nc (Nq - 1) cot(φ'b.d) 10.711Nγ 2 (Nq - 1) tan(φ'b.d) 1.447Foundation shape factors;sq 1sγ 1Load inclination factors;sc 1H Ftotal h - Fprop stem - Ffriction 0 kN/mV Ftotal v 605.2 kN/mm 2miq [1 - H / (V lload c'b.d cot(φ'b.d))] 1iγ [1 - H / (V lload c'b.d cot(φ'b.d))](m 1) 1ic iq - (1 - iq) / (Nc tan(φ'b.d)) 1Net ultimate bearing capacity;nf c'b.d Nc sc ic q' Nq sq iq 0.5 (γmb2- γw) lload Nγ sγ iγ 266.3 kN/mFactor of safety;FoSbp nf / max(qtoe, qheel) 1.98PASS - Allowable bearing pressure exceeds maximum applied bearing pressure

ProjectJob Ref.Retaining wall Analysis & Design (EN1997-1:2004incorporating Corrigendum dated February 2009)SectionGEODOMISI Ltd. - Dr. Costas SachpazisCivil & Geotechnical Engineering Consulting Company forStructural Engineering, Soil Mechanics, Rock Mechanics,Foundation Engineering & Retaining Structures.Sheet no./rev.Civil & Geotechnical EngineeringCalc. byDateChk'd byDr.C.Sachpazis 23/05/20131DateApp'd byDate-Tel.: ( 30) 210 5238127, 210 5711263 - Fax.: 30 210 5711461 Mobile: ( 30) 6936425722 & ( 44) 7585939944, costas@sachpazis.infoRETAINING WALL DESIGNIn accordance with EN1992-1-1:2004 incorporating Corrigendum dated January 2008 and therecommended valuesConcrete details - Table 3.1 - Strength and deformation characteristics for concreteConcrete strength class;Characteristic compressive cylinder strength;C30/372fck 30 N/mmCharacteristic compressive cube strength;fck,cube 37 N/mmMean value of compressive cylinder strength;fcm fck 8 N/mm 38 N/mm22222 2/3Mean value of axial tensile strength;fctm 0.3 N/mm (fck / 1 N/mm )5% fractile of axial tensile strength;fctk,0.05 0.7 fctm 2.0 N/mmSecant modulus of elasticity of concrete;Ecm 22 kN/mm (fcm / 10 N/mm )N/mm 2.9 N/mm2222 0.3 328372Partial factor for concrete - Table 2.1N;γC 1.50Compressive strength coefficient - cl.3.1.6(1);αcc 1.00Design compressive concrete strength - exp.3.15;fcd αcc fck / γC 20.0 N/mmMaximum aggregate size;hagg 20 mm2Reinforcement details2Characteristic yield strength of reinforcement;fyk 500 N/mmModulus of elasticity of reinforcement;Es 210000 N/mm2Partial factor for reinforcing steel - Table 2.1N;γS 1.15Design yield strength of reinforcement;fyd fyk / γS 435 N/mm2Cover to reinforcementFront face of stem;csf 40 mmRear face of stem;csr 50 mmTop face of base;cbt 50 mmBottom face of base;cbb 75 mmCheck stem design for maximum momentDepth of section;h 500 mmRectangular section in flexure - Section 6.1Design bending moment;M 94.6 kNm/mDepth to tension reinforcement;d h - csr - φsr / 2 442 mm2K M / (d fck) 0.016K' 0.196K' K - No compression reinforcement is requiredLever arm;0.5z min(0.5 0.5 (1 – 3.53 K) , 0.95) d 420 mmDepth of neutral axis;x 2.5 (d – z) 55 mmArea of tension reinforcement required;Asr.req M / (fyd z) 518 mm /mTension reinforcement provided;16 dia.bars @ 200 c/cArea of tension reinforcement provided;Asr.prov π φsr / (4 ssr) 1005 mm /m222

ProjectJob Ref.Retaining wall Analysis & Design (EN1997-1:2004incorporating Corrigendum dated February 2009)SectionGEODOMISI Ltd. - Dr. Costas SachpazisCivil & Geotechnical Engineering Consulting Company forStructural Engineering, Soil Mechanics, Rock Mechanics,Foundation Engineering & Retaining Structures.Sheet no./rev.Civil & Geotechnical EngineeringCalc. byDateDr.C.Sachpazis 23/05/2013Chk'd by1DateApp'd byDate-Tel.: ( 30) 210 5238127, 210 5711263 - Fax.: 30 210 5711461 Mobile: ( 30) 6936425722 & ( 44) 7585939944, costas@sachpazis.infoMinimum area of reinforcement - exp.9.1N;Asr.min max(0.26 fctm / fyk, 0.0013) d 6662mm /mMaximum area of reinforcement - cl.9.2.1.1(3);2Asr.max 0.04 h 20000 mm /mmax(Asr.req, Asr.min) / Asr.prov 0.662PASS - Area of reinforcement provided is greater than area of reinforcement requiredCrack control - Section 7.3Limiting crack width;wmax 0.3 mmVariable load factor - EN1990 – Table A1.1;ψ2 0.3Serviceability bending moment;Msls 44.8 kNm/mTensile stress in reinforcement;σs Msls / (Asr.prov z) 106.2 N/mm2Load duration;Long termLoad duration factor;kt 0.4Effective area of concrete in tension;Ac.eff min(2.5 (h - d), (h – x) / 3, h / 2) 1450002mm /mMean value of concrete tensile strength;2fct.eff fctm 2.9 N/mmReinforcement ratio;ρp.eff Asr.prov / Ac.eff 0.007Modular ratio;αe Es / Ecm 6.395Bond property coefficient;k1 0.8Strain distribution coefficient;k2 0.5k3 3.4k4 0.425Maximum crack spacing - exp.7.11;sr.max k3 csr k1 k2 k4 φsr / ρp.eff 562 mmMaximum crack width - exp.7.8;wk sr.max max(σs – kt (fct.eff / ρp.eff) (1 αe ρp.eff), 0.6 σs) / Eswk 0.171 mmwk / wmax 0.569PASS - Maximum crack width is less than limiting crack widthRectangular section in shear - Section 6.2Design shear force;V 151.5 kN/mCRd,c 0.18 / γC 0.120k min(1 (200 mm / d), 2) 1.673ρl min(Asr.prov / d, 0.02) 0.002Longitudinal reinforcement ratio;1/2vmin 0.035 N /mm kDesign shear resistance - exp.6.2a & 6.2b;3/2 fck20.5 0.415 N/mm421/3VRd.c max(CRd.c k (100 N /mm ρl fck) ,vmin) dVRd.c 183.3 kN/mV / VRd.c 0.827PASS - Design shear resistance exceeds design shear forceRectangular section in flexure - Section 6.1Design bending moment;M 63.7 kNm/m

ProjectJob Ref.Retaining wall Analysis & Design (EN1997-1:2004incorporating Corrigendum dated February 2009)SectionGEODOMISI Ltd. - Dr. Costas SachpazisCivil & Geotechnical Engineering Consulting Company forStructural Engineering, Soil Mechanics, Rock Mechanics,Foundation Engineering & Retaining Structures.Sheet no./rev.Civil & Geotechnical EngineeringCalc. byDateChk'd byDr.C.Sachpazis 23/05/20131DateApp'd byDate-Tel.: ( 30) 210 5238127, 210 5711263 - Fax.: 30 210 5711461 Mobile: ( 30) 6936425722 & ( 44) 7585939944, costas@sachpazis.infod h - csf - φsx - φsf / 2 440 mmDepth to tension reinforcement;2K M / (d fck) 0.011K' 0.196K' K - No compression reinforcement is required0.5z min(0.5 0.5 (1 – 3.53 K) , 0.95) d Lever arm;418 mmDepth of neutral axis;x 2.5 (d – z) 55 mmArea of tension reinforcement required;Asf.req M / (fyd z) 351 mm /mTension reinforcement provided;16 dia.bars @ 200 c/cArea of tension reinforcement provided;Asf.prov π φsf / (4 ssf) 1005 mm /mMinimum area of reinforcement - exp.9.1N;Asf.min max(0.26 fctm / fyk, 0.0013) d 6632222mm /mMaximum area of reinforcement - cl.9.2.1.1(3);2Asf.max 0.04 h 20000 mm /mmax(Asf.req, Asf.min) / Asf.prov 0.659PASS - Area of reinforcement provided is greater than area of reinforcement requiredCrack control - Section 7.3Limiting crack width;wmax 0.3 mmVariable load factor - EN1990 – Table A1.1;ψ2 0.3Serviceability bending moment;Msls 29.6 kNm/mTensile stress in reinforcement;σs Msls / (Asf.prov z) 70.4 N/mm2Load duration;Long termLoad duration factor;kt 0.4Effective area of concrete in tension;Ac.eff min(2.5 (h - d), (h – x) / 3, h / 2) 1483332mm /mMean value of concrete tensile strength;fct.eff fctm 2.9 N/mmReinforcement ratio;ρp.eff Asf.prov / Ac.eff 0.0072Modular ratio;αe Es / Ecm 6.395Bond property coefficient;k1 0.8Strain distribution coefficient;k2 0.5k3 3.4k4 0.425Maximum crack spacing - exp.7.11;sr.max k3 csf k1 k2 k4 φsf / ρp.eff 537 mmMaximum crack width - exp.7.8;wk sr.max max(σs – kt (fct.eff / ρp.eff) (1 αe ρp.eff), 0.6 σs) / Eswk 0.108 mmwk / wmax 0.36PASS - Maximum crack width is less than limiting crack widthRectangular section in shear - Section 6.2Design shear force;V 151.5 kN/mCRd,c 0.18 / γC 0.120k min(1 (200 mm / d), 2) 1.674

ProjectJob Ref.Retaining wall Analysis & Design (EN1997-1:2004incorporating Corrigendum dated February 2009)SectionGEODOMISI Ltd. - Dr. Costas SachpazisCivil & Geotechnical Engineering Consulting Company forStructural Engineering, Soil Mechanics, Rock Mechanics,Foundation Engineering & Retaining Structures.Sheet no./rev.Civil & Geotechnical EngineeringCalc. byDateChk'd byDr.C.Sachpazis 23/05/20131DateApp'd byDate-Tel.: ( 30) 210 5238127, 210 5711263 - Fax.: 30 210 5711461 Mobile: ( 30) 6936425722 & ( 44) 7585939944, costas@sachpazis.infoρl min(Asf.prov / d, 0.02) 0.002Longitudinal reinforcement ratio;1/2vmin 0.035 N /mm kDesign shear resistance - exp.6.2a & 6.2b;3/2 fck0.5 0.415 N/mm2421/3VRd.c max(CRd.c k (100 N /mm ρl fck) ,vmin) dVRd.c 182.7 kN/mV / VRd.c 0.829PASS - Design shear resistance exceeds design shear forceHorizontal reinforcement parallel to face of stem - Section 9.6Minimum area of reinforcement – cl.9.6.3(1);Asx.req max(0.25 Asr.prov, 0.001 tstem) 5002mm /mMaximum spacing of reinforcement – cl.9.6.3(2);ssx max 400 mmTransverse reinforcement provided;12 dia.bars @ 200 c/cArea of transverse reinforcement provided;Asx.prov π φsx / (4 ssx) 565 mm /m22PASS - Area of reinforcement provided is greater than area of reinforcement requiredCheck base designDepth of section;h 500 mmRectangular section in flexure - Section 6.1Design bending moment at toe;M 72 kNm/mDepth to tension reinforcement;d h - cbb - φbb / 2 417 mm2K M / (d fck) 0.014K' 0.196K' K - No compression reinforcement is required0.5z min(0.5 0.5 (1 – 3.53 K) , 0.95) d Lever arm;396 mmDepth of neutral axis;x 2.5 (d – z) 52 mmArea of tension reinforcement required;Abb.req M / (fyd z) 418 mm /m2Tension reinforcement provided;16 dia.bars @ 200 c/cArea of tension reinforcement provided;Abb.prov π φbb / (4 sbb) 1005 mm /mMinimum area of reinforcement - exp.9.1N;Abb.min max(0.26 fctm / fyk, 0.0013) d 628222mm /mMaximum area of reinforcement - cl.9.2.1.1(3);2Abb.max 0.04 h 20000 mm /mmax(Abb.req, Abb.min) / Abb.prov 0.625PASS - Area of reinforcement provided is greater than area of reinforcement requiredCrack control - Section 7.3Limiting crack width;wmax 0.3 mmVariable load factor - EN1990 – Table A1.1;ψ2 0.3Serviceability bending moment;Msls 39.8 kNm/mTensile stress in reinforcement;σs Msls / (Abb.prov z) 100 N/mmLoad duration;Long termLoad duration factor;kt 0.42

ProjectJob Ref.Retaining wall Analysis & Design (EN1997-1:2004incorporating Corrigendum dated February 2009)SectionGEODOMISI Ltd. - Dr. Costas SachpazisCivil & Geotechnical Engineering Consulting Company forStructural Engineering, Soil Mechanics, Rock Mechanics,Foundation Engineering & Retaining Structures.Sheet no./rev.Civil & Geotechnical EngineeringCalc. byDateChk'd byDr.C.Sachpazis 23/05/20131DateApp'd byDate-Tel.: ( 30) 210 5238127, 210 5711263 - Fax.: 30 210 5711461 Mobile: ( 30) 6936425722 & ( 44) 7585939944, costas@sachpazis.infoAc.eff min(2.5 (h - d), (h – x) / 3, h / 2) 149292Effective area of concrete in tension;2mm /mMean value of concrete tensile strength;fct.eff fctm 2.9 N/mmReinforcement ratio;ρp.eff Abb.prov / Ac.eff 0.007Modular ratio;αe Es / Ecm 6.3952Bond property coefficient;k1 0.8Strain distribution coefficient;k2 0.5k3 3.4k4 0.425Maximum crack spacing - exp.7.11;sr.max k3 cbb k1 k2 k4 φbb / ρp.eff 659 mmMaximum crack width - exp.7.8;wk sr.max max(σs – kt (fct.eff / ρp.eff) (1 αe ρp.eff), 0.6 σs) / Eswk 0.188 mmwk / wmax 0.628PASS - Maximum crack width is less than limiting crack widthRectangular section in shear - Section 6.2V 144 kN/mDesign shear force;CRd,c 0.18 / γC 0.120k min(1 (200 mm / d), 2) 1.693ρl min(Abb.prov / d, 0.02) 0.002Longitudinal reinforcement ratio;1/2vmin 0.035 N /mm kDesign shear resistance - exp.6.2a & 6.2b;3/2 fck0.5 0.422 N/mm2421/3VRd.c max(CRd.c k (100 N /mm ρl fck) ,vmin) dVRd.c 176 kN/mV / VRd.c 0.818PASS - Design shear resistance exceeds design shear forceRectangular section in flexure - Section 6.1Design bending moment at heel;M 186.4 kNm/mDepth to tension reinforcement;d h - cbt - φbt / 2 442 mm2K M / (d fck) 0.032K' 0.196K' K - No compression reinforcement is requiredLever arm;0.5z min(0.5 0.5 (1 – 3.53 K) , 0.95) d 420 mmDepth of neutral axis;x 2.5 (d – z) 55 mmArea of tension reinforcement required;Abt.req M / (fyd z) 1021 mm /mTension reinforcement provided;16 dia.bars @ 175 c/cArea of tension reinforcement provided;Abt.prov π φbt / (4 sbt) 1149 mm /mMinimum area of reinforcement - exp.9.1N;Abt.min max(0.26 fctm / fyk, 0.0013) d 6662222mm /mMaximum area of reinforcement - cl.9.2.1.1(3);2Abt.max 0.04 h 20000 mm /m

ProjectJob Ref.Retaining wall Analysis & Design (EN1997-1:2004incorporating Corrigendum dated February 2009)SectionGEODOMISI Ltd. - Dr. Costas SachpazisCivil & Geotechnical Engineering Consulting Company forStructural Engineering, Soil Mechanics, Rock Mechanics,Foundation Engineering & Retaining Structures.Sheet no./rev.Civil & Geotechnical EngineeringCalc. byDateDr.C.Sachpazis 23/05/2013Chk'd by1DateApp'd byDate-Tel.: ( 30) 210 5238127, 210 5711263 - Fax.: 30 210 5711461 Mobile: ( 30) 6936425722 & ( 44) 7585939944, costas@sachpazis.infomax(Abt.req, Abt.min) / Abt.prov 0.888PASS - Area of reinforcement provided is greater than area of reinforcement requiredCrack control - Section 7.3Limiting crack width;wmax 0.3 mmVariable load factor - EN1990 – Table A1.1;ψ2 0.3Serviceability bending moment;Msls 81.2 kNm/mTensile stress in reinforcement;σs Msls / (Abt.prov z) 168.2 N/mmLoad duration;Long term2Load duration factor;kt 0.4Effective area of concrete in tension;Ac.eff min(2.5 (h - d), (h – x) / 3, h / 2) 1450002mm /mMean value of concrete tensile strength;2fct.eff fctm 2.9 N/mmReinforcement ratio;ρp.eff Abt.prov / Ac.eff 0.008Modular ratio;αe Es / Ecm 6.395Bond property coefficient;k1 0.8Strain distribution coefficient;k2 0.5k3 3.4k4 0.425Maximum crack spacing - exp.7.11;sr.max k3 cbt k1 k2 k4 φbt / ρp.eff 513 mmMaximum crack widt

RETAINING WALL ANALYSIS In accordance with EN1997-1:2004 incorporating Corrigendum dated February 2009 and the recommended values Retaining wall details Stem type; Propped cantilever Stem height; h stem 5500 mm Prop height; h prop 4500 mm Stem thickness; t stem 500 mm Angle to rear