GEODOMISI Ltd. - Dr. Costas Sachpazis
Civil & Geotechnical Engineering Consulting Company for
Structural Engineering, Soil...
GEODOMISI Ltd. - Dr. Costas Sachpazis
Civil & Geotechnical Engineering Consulting Company for
Structural Engineering, Soil...
GEODOMISI Ltd. - Dr. Costas Sachpazis
Civil & Geotechnical Engineering Consulting Company for
Structural Engineering, Soil...
GEODOMISI Ltd. - Dr. Costas Sachpazis
Civil & Geotechnical Engineering Consulting Company for
Structural Engineering, Soil...
GEODOMISI Ltd. - Dr. Costas Sachpazis
Civil & Geotechnical Engineering Consulting Company for
Structural Engineering, Soil...
GEODOMISI Ltd. - Dr. Costas Sachpazis
Civil & Geotechnical Engineering Consulting Company for
Structural Engineering, Soil...
GEODOMISI Ltd. - Dr. Costas Sachpazis
Civil & Geotechnical Engineering Consulting Company for
Structural Engineering, Soil...
GEODOMISI Ltd. - Dr. Costas Sachpazis
Civil & Geotechnical Engineering Consulting Company for
Structural Engineering, Soil...
GEODOMISI Ltd. - Dr. Costas Sachpazis
Civil & Geotechnical Engineering Consulting Company for
Structural Engineering, Soil...
GEODOMISI Ltd. - Dr. Costas Sachpazis
Civil & Geotechnical Engineering Consulting Company for
Structural Engineering, Soil...
GEODOMISI Ltd. - Dr. Costas Sachpazis
Civil & Geotechnical Engineering Consulting Company for
Structural Engineering, Soil...
GEODOMISI Ltd. - Dr. Costas Sachpazis
Civil & Geotechnical Engineering Consulting Company for
Structural Engineering, Soil...
GEODOMISI Ltd. - Dr. Costas Sachpazis
Civil & Geotechnical Engineering Consulting Company for
Structural Engineering, Soil...
GEODOMISI Ltd. - Dr. Costas Sachpazis
Civil & Geotechnical Engineering Consulting Company for
Structural Engineering, Soil...
GEODOMISI Ltd. - Dr. Costas Sachpazis
Civil & Geotechnical Engineering Consulting Company for
Structural Engineering, Soil...
GEODOMISI Ltd. - Dr. Costas Sachpazis
Civil & Geotechnical Engineering Consulting Company for
Structural Engineering, Soil...
GEODOMISI Ltd. - Dr. Costas Sachpazis
Civil & Geotechnical Engineering Consulting Company for
Structural Engineering, Soil...
GEODOMISI Ltd. - Dr. Costas Sachpazis
Civil & Geotechnical Engineering Consulting Company for
Structural Engineering, Soil...
Upcoming SlideShare
Loading in...5
×

Sachpazis cantilever retaining wall analysis & design (en1997-1-2004)

257

Published on

RETAINING WALL ANALYSIS (EN1997-1:2004)
In accordance with EN1997-1:2004 incorporating Corrigendum dated February 2009 and the recommended values

Published in: Design, Technology, Business
0 Comments
0 Likes
Statistics
Notes
  • Be the first to comment

  • Be the first to like this

No Downloads
Views
Total Views
257
On Slideshare
0
From Embeds
0
Number of Embeds
1
Actions
Shares
0
Downloads
38
Comments
0
Likes
0
Embeds 0
No embeds

No notes for slide

Sachpazis cantilever retaining wall analysis & design (en1997-1-2004)

  1. 1. GEODOMISI Ltd. - Dr. Costas Sachpazis Civil & Geotechnical Engineering Consulting Company for Structural Engineering, Soil Mechanics, Rock Mechanics, Foundation Engineering & Retaining Structures. Tel.: (+30) 210 5238127, 210 5711263 - Fax.:+30 210 5711461 - Mobile: (+30) 6936425722 & (+44) 7585939944, costas@sachpazis.info Project: Retaining wall Analysis & Design, In accordance with EN1997-1:2004 incorporating Corrigendum dated February 2009 and the recommended values. Job Ref. Section Civil & Geotechnical Engineering Sheet no./rev. 1 Calc. by Dr. C. Sachpazis Date 04/04/2014 Chk'd by Date App'd by Date RETAINING WALL ANALYSIS (EN1997-1:2004) In accordance with EN1997-1:2004 incorporating Corrigendum dated February 2009 and the recommended values Retaining wall details Stem type; Cantilever with inclined front face Stem height; hstem = 4000 mm Stem thickness; tstem = 450 mm Slope length to front of stem; lslf = 100 mm Angle to rear face of stem; α = 90 deg Angle to front face of stem; αf = 88.6 deg Stem density; γstem = 25 kN/m 3 Toe length; ltoe = 1000 mm Heel length; lheel = 4000 mm Base thickness; tbase = 450 mm Base density; γbase = 25 kN/m 3 Height of retained soil; hret = 3000 mm Angle of soil surface; β = 15 deg Depth of cover; dcover = 500 mm Height of water; hwater = 300 mm Water density; γw = 9.8 kN/m 3 Retained soil properties Soil type; Medium dense well graded sand and gravel Moist density; γmr = 20 kN/m 3 Saturated density; γsr = 22.3 kN/m 3 Characteristic effective shear resistance angle; φ'r.k = 25 deg Characteristic wall friction angle; δr.k = 16 deg Base soil properties Moist density; γmb = 20 kN/m3 Characteristic cohesion; c'b.k = 5 kN/m 2 Characteristic adhesion; ab.k = 5 kN/m 2 Characteristic effective shear resistance angle; φ'b.k = 25 deg Characteristic wall friction angle; δb.k = 20 deg Characteristic base friction angle; δbb.k = 25 deg Loading details Variable surcharge load; SurchargeQ = 10 kN/m 2
  2. 2. GEODOMISI Ltd. - Dr. Costas Sachpazis Civil & Geotechnical Engineering Consulting Company for Structural Engineering, Soil Mechanics, Rock Mechanics, Foundation Engineering & Retaining Structures. Tel.: (+30) 210 5238127, 210 5711263 - Fax.:+30 210 5711461 - Mobile: (+30) 6936425722 & (+44) 7585939944, costas@sachpazis.info Project: Retaining wall Analysis & Design, In accordance with EN1997-1:2004 incorporating Corrigendum dated February 2009 and the recommended values. Job Ref. Section Civil & Geotechnical Engineering Sheet no./rev. 1 Calc. by Dr. C. Sachpazis Date 04/04/2014 Chk'd by Date App'd by Date Calculate retaining wall geometry Base length; lbase = ltoe + lslf + tstem + lheel = 5550 mm Saturated soil height; hsat = hwater + dcover = 800 mm Moist soil height; hmoist = hret - hwater = 2700 mm Length of surcharge load; lsur = lheel = 4000 mm
  3. 3. GEODOMISI Ltd. - Dr. Costas Sachpazis Civil & Geotechnical Engineering Consulting Company for Structural Engineering, Soil Mechanics, Rock Mechanics, Foundation Engineering & Retaining Structures. Tel.: (+30) 210 5238127, 210 5711263 - Fax.:+30 210 5711461 - Mobile: (+30) 6936425722 & (+44) 7585939944, costas@sachpazis.info Project: Retaining wall Analysis & Design, In accordance with EN1997-1:2004 incorporating Corrigendum dated February 2009 and the recommended values. Job Ref. Section Civil & Geotechnical Engineering Sheet no./rev. 1 Calc. by Dr. C. Sachpazis Date 04/04/2014 Chk'd by Date App'd by Date - Distance to vertical component; xsur_v = lbase - lheel / 2 = 3550 mm Effective height of wall; heff = hbase + dcover + hret + lsur × tan(β) = 5022 mm - Distance to horizontal component; xsur_h = heff / 2 = 2511 mm Area of wall stem; Astem = hstem × (tstem + lslf / 2) = 2 m 2 - Distance to vertical component; xstem = (hstem × tstem × (ltoe + lslf + tstem / 2) + hstem × lslf / 2 × (ltoe + 2 × lslf / 3)) / Astem = 1299 mm Area of wall base; Abase = lbase × tbase = 2.498 m 2 - Distance to vertical component; xbase = lbase / 2 = 2775 mm Area of saturated soil; Asat = hsat × lheel = 3.2 m 2 - Distance to vertical component; xsat_v = lbase - (hsat × lheel 2 / 2) / Asat = 3550 mm - Distance to horizontal component; xsat_h = (hsat + hbase) / 3 = 417 mm Area of water; Awater = hsat × lheel = 3.2 m 2 - Distance to vertical component; xwater_v = lbase - (hsat × lheel 2 / 2) / Asat = 3550 mm - Distance to horizontal component; xwater_h = (hsat + hbase) / 3 = 417 mm Area of moist soil; Amoist = hmoist × lheel + tan(β) × lheel 2 / 2 = 12.944 m 2 - Distance to vertical component; xmoist_v = lbase - (hmoist × lheel 2 / 2 + tan(β) × lheel 3 / 6) / Amoist = 3660 mm - Distance to horizontal component; xmoist_h = ((heff - hsat - hbase) × (tbase + hsat + (heff - hsat - hbase) / 3) / 2 + (hsat + tbase) 2 /2) / (hsat + tbase + (heff - hsat - hbase) / 2) = 1757 mm Area of base soil; Apass = dcover × (ltoe + lslf × dcover / (2 × hstem)) = 0.503 m 2 - Distance to vertical component; xpass_v = lbase - (dcover × ltoe × (lbase - ltoe / 2) + lslf × dcover 2 / (2 × hstem) × (lbase - ltoe - lslf × dcover / (3 × hstem))) / Apass = 503 mm - Distance to horizontal component; xpass_h = (dcover + hbase) / 3 = 317 mm Area of excavated base soil; Aexc = hpass × (ltoe + lslf × hpass / (2 × hstem)) = 0.503 m 2 - Distance to vertical component; xexc_v = lbase - (hpass × ltoe × (lbase - ltoe / 2) + lslf × hpass 2 / (2 × hstem) × (lbase - ltoe - lslf × hpass / (3 × hstem))) / Aexc = 503 mm - Distance to horizontal component; xexc_h = (hpass + hbase) / 3 = 317 mm Partial factors on actions - Table A.3 - Combination 1 Permanent unfavourable action; γG = 1.35 Permanent favourable action; γGf = 1.00 Variable unfavourable action; γQ = 1.50 Variable favourable action; γQf = 0.00 Partial factors for soil parameters – Table A.4 - Combination 1 Angle of shearing resistance; γφ' = 1.00
  4. 4. GEODOMISI Ltd. - Dr. Costas Sachpazis Civil & Geotechnical Engineering Consulting Company for Structural Engineering, Soil Mechanics, Rock Mechanics, Foundation Engineering & Retaining Structures. Tel.: (+30) 210 5238127, 210 5711263 - Fax.:+30 210 5711461 - Mobile: (+30) 6936425722 & (+44) 7585939944, costas@sachpazis.info Project: Retaining wall Analysis & Design, In accordance with EN1997-1:2004 incorporating Corrigendum dated February 2009 and the recommended values. Job Ref. Section Civil & Geotechnical Engineering Sheet no./rev. 1 Calc. by Dr. C. Sachpazis Date 04/04/2014 Chk'd by Date App'd by Date Effective cohesion; γc' = 1.00 Weight density; γγ = 1.00 Retained soil properties Design effective shear resistance angle; φ'r.d = atan(tan(φ'r.k) / γφ') = 25 deg Design wall friction angle; δr.d = atan(tan(δr.k) / γφ') = 16 deg Base soil properties Design effective shear resistance angle; φ'b.d = atan(tan(φ'b.k) / γφ') = 25 deg Design wall friction angle; δb.d = atan(tan(δb.k) / γφ') = 20 deg Design base friction angle; δbb.d = atan(tan(δbb.k) / γφ') = 25 deg Design effective cohesion; c'b.d = c'b.k / γc' = 5 kN/m 2 Design adhesion; ab.d = ab.k / γc' = 5 kN/m 2 Using Coulomb theory Active pressure coefficient; KA = sin(α + φ'r.d) 2 / (sin(α) 2 × sin(α - δr.d) × [1 + √[sin(φ'r.d + δr.d) × sin(φ'r.d - β) / (sin(α - δr.d) × sin(α + β))]] 2 ) = 0.469 Passive pressure coefficient; KP = sin(αf - φ'b.d) 2 / (sin(αf) 2 × sin(αf + δb.d) × [1 - √[sin(φ'b.d + δb.d) × sin(φ'b.d) / (sin(αf + δb.d) × sin(αf))]] 2 ) = 4.403 Sliding check Vertical forces on wall Wall stem; Fstem = γGf × Astem × γstem = 50 kN/m Wall base; Fbase = γGf × Abase × γbase = 62.4 kN/m Saturated retained soil; Fsat_v = γGf × Asat × (γsr - γw) = 39.8 kN/m Water; Fwater_v = γGf × Awater × γw = 31.4 kN/m Moist retained soil; Fmoist_v = γGf × Amoist × γmr = 258.9 kN/m Base soil; Fexc_v = γGf × Aexc × γmb = 10.1 kN/m Total; Ftotal_v = Fstem + Fbase + Fsat_v + Fmoist_v + Fexc_v + Fwater_v = 452.6 kN/m Horizontal forces on wall Surcharge load; Fsur_h = KA × cos(δr.d) × γQ × SurchargeQ × heff = 33.9 kN/m Saturated retained soil; Fsat_h = γG × KA × cos(δr.d) × (γsr - γw) × (hsat + hbase) 2 / 2 = 5.9 kN/m Water; Fwater_h = γG × γw × (hwater + dcover + hbase) 2 / 2 = 10.3 kN/m
  5. 5. GEODOMISI Ltd. - Dr. Costas Sachpazis Civil & Geotechnical Engineering Consulting Company for Structural Engineering, Soil Mechanics, Rock Mechanics, Foundation Engineering & Retaining Structures. Tel.: (+30) 210 5238127, 210 5711263 - Fax.:+30 210 5711461 - Mobile: (+30) 6936425722 & (+44) 7585939944, costas@sachpazis.info Project: Retaining wall Analysis & Design, In accordance with EN1997-1:2004 incorporating Corrigendum dated February 2009 and the recommended values. Job Ref. Section Civil & Geotechnical Engineering Sheet no./rev. 1 Calc. by Dr. C. Sachpazis Date 04/04/2014 Chk'd by Date App'd by Date Moist retained soil; Fmoist_h = γG × KA × cos(δr.d) × γmr × ((heff - hsat - hbase) 2 / 2 + (heff - hsat - hbase) × (hsat + hbase)) = 143.9 kN/m Total; Ftotal_h = Fsat_h + Fmoist_h + Fwater_h + Fsur_h = 194.1 kN/m Check stability against sliding Base soil resistance; Fexc_h = γGf × KP × cos(δb.d) × γmb × (hpass + hbase) 2 / 2 = 37.3 kN/m Base friction; Ffriction = ab.d × b + Ftotal_v × tan(δbb.d) = 216 kN/m Resistance to sliding; Frest = Fexc_h + Ffriction = 253.4 kN/m Factor of safety; FoSsl = Frest / Ftotal_h = 1.306 PASS - Resistance to sliding is greater than sliding force Overturning check Vertical forces on wall Wall stem; Fstem = γGf × Astem × γstem = 50 kN/m Wall base; Fbase = γGf × Abase × γbase = 62.4 kN/m Saturated retained soil; Fsat_v = γGf × Asat × (γsr - γw) = 39.8 kN/m Water; Fwater_v = γGf × Awater × γw = 31.4 kN/m Moist retained soil; Fmoist_v = γGf × Amoist × γmr = 258.9 kN/m Base soil; Fexc_v = γGf × Aexc × γmb = 10.1 kN/m Total; Ftotal_v = Fstem + Fbase + Fsat_v + Fmoist_v + Fexc_v + Fwater_v = 452.6 kN/m Horizontal forces on wall Surcharge load; Fsur_h = KA × cos(δr.d) × γQ × SurchargeQ × heff = 33.9 kN/m Saturated retained soil; Fsat_h = γG × KA × cos(δr.d) × (γsr - γw) × (hsat + hbase) 2 / 2 = 5.9 kN/m Water; Fwater_h = γG × γw × (hwater + dcover + hbase)2 / 2 = 10.3 kN/m Moist retained soil; Fmoist_h = γG × KA × cos(δr.d) × γmr × ((heff - hsat - hbase) 2 / 2 + (heff - hsat - hbase) × (hsat + hbase)) = 143.9 kN/m Base soil; Fexc_h = -γGf × KP × cos(δb.d) × γmb × (hpass + hbase) 2 / 2 = -37.3 kN/m Total; Ftotal_h = Fsat_h + Fmoist_h + Fexc_h + Fwater_h + Fsur_h = 156.7 kN/m Overturning moments on wall Surcharge load; Msur_OT = Fsur_h × xsur_h = 85.2 kNm/m
  6. 6. GEODOMISI Ltd. - Dr. Costas Sachpazis Civil & Geotechnical Engineering Consulting Company for Structural Engineering, Soil Mechanics, Rock Mechanics, Foundation Engineering & Retaining Structures. Tel.: (+30) 210 5238127, 210 5711263 - Fax.:+30 210 5711461 - Mobile: (+30) 6936425722 & (+44) 7585939944, costas@sachpazis.info Project: Retaining wall Analysis & Design, In accordance with EN1997-1:2004 incorporating Corrigendum dated February 2009 and the recommended values. Job Ref. Section Civil & Geotechnical Engineering Sheet no./rev. 1 Calc. by Dr. C. Sachpazis Date 04/04/2014 Chk'd by Date App'd by Date Saturated retained soil; Msat_OT = Fsat_h × xsat_h = 2.5 kNm/m Water; Mwater_OT = Fwater_h × xwater_h = 4.3 kNm/m Moist retained soil; Mmoist_OT = Fmoist_h × xmoist_h = 252.8 kNm/m Total; Mtotal_OT = Msat_OT + Mmoist_OT + Mwater_OT + Msur_OT = 344.8 kNm/m Restoring moments on wall Wall stem; Mstem_R = Fstem × xstem = 65 kNm/m Wall base; Mbase_R = Fbase × xbase = 173.3 kNm/m Saturated retained soil; Msat_R = Fsat_v × xsat_v = 141.3 kNm/m Water; Mwater_R = Fwater_v × xwater_v = 111.4 kNm/m Moist retained soil; Mmoist_R = Fmoist_v × xmoist_v = 947.6 kNm/m Base soil; Mexc_R = Fexc_v × xexc_v - Fexc_h × xexc_h = 16.9 kNm/m Total; Mtotal_R = Mstem_R + Mbase_R + Msat_R + Mmoist_R + Mexc_R + Mwater_R = 1455.4 kNm/m Check stability against overturning Factor of safety; FoSot = Mtotal_R / Mtotal_OT = 4.222 PASS - Maximum restoring moment is greater than overturning moment Bearing pressure check Vertical forces on wall Wall stem; Fstem = γG × Astem × γstem = 67.5 kN/m Wall base; Fbase = γG × Abase × γbase = 84.3 kN/m Surcharge load; Fsur_v = γQ × SurchargeQ × lheel = 60 kN/m Saturated retained soil; Fsat_v = γG × Asat × (γsr - γw) = 53.7 kN/m Water; Fwater_v = γG × Awater × γw = 42.4 kN/m Moist retained soil; Fmoist_v = γG × Amoist × γmr = 349.5 kN/m Base soil; Fpass_v = γG × Apass × γmb = 13.6 kN/m Total; Ftotal_v = Fstem + Fbase + Fsat_v + Fmoist_v + Fpass_v + Fwater_v + Fsur_v = 671 kN/m Horizontal forces on wall Surcharge load; Fsur_h = KA × cos(δr.d) × γQ × SurchargeQ × heff = 33.9 kN/m Saturated retained soil; Fsat_h = γG × KA × cos(δr.d) × (γsr - γw) × (hsat + hbase) 2 / 2 = 5.9 kN/m Water; Fwater_h = γG × γw × (hwater + dcover + hbase) 2 / 2 = 10.3 kN/m Moist retained soil; Fmoist_h = γG × KA × cos(δr.d) × γmr × ((heff - hsat - hbase) 2 / 2 + (heff - hsat - hbase) × (hsat + hbase)) = 143.9 kN/m
  7. 7. GEODOMISI Ltd. - Dr. Costas Sachpazis Civil & Geotechnical Engineering Consulting Company for Structural Engineering, Soil Mechanics, Rock Mechanics, Foundation Engineering & Retaining Structures. Tel.: (+30) 210 5238127, 210 5711263 - Fax.:+30 210 5711461 - Mobile: (+30) 6936425722 & (+44) 7585939944, costas@sachpazis.info Project: Retaining wall Analysis & Design, In accordance with EN1997-1:2004 incorporating Corrigendum dated February 2009 and the recommended values. Job Ref. Section Civil & Geotechnical Engineering Sheet no./rev. 1 Calc. by Dr. C. Sachpazis Date 04/04/2014 Chk'd by Date App'd by Date Base soil; Fpass_h = -γGf × KP × cos(δb.d) × γmb × (dcover + hbase) 2 / 2 = -37.3 kN/m Total; Ftotal_h = max(Fsat_h + Fmoist_h + Fpass_h + Fwater_h + Fsur_h - (ab.d × b + Ftotal_v × tan(δbb.d)), 0 kN/m) = 0 kN/m Moments on wall Wall stem; Mstem = Fstem × xstem = 87.7 kNm/m Wall base; Mbase = Fbase × xbase = 233.9 kNm/m Surcharge load; Msur = Fsur_v × xsur_v - Fsur_h × xsur_h = 127.8 kNm/m Saturated retained soil; Msat = Fsat_v × xsat_v - Fsat_h × xsat_h = 188.3 kNm/m Water; Mwater = Fwater_v × xwater_v - Fwater_h × xwater_h = 146.1 kNm/m Moist retained soil; Mmoist = Fmoist_v × xmoist_v - Fmoist_h × xmoist_h = 1026.4 kNm/m Base soil; Mpass = Fpass_v × xpass_v - Fpass_h × xpass_h = 18.7 kNm/m Total; Mtotal = Mstem + Mbase + Msat + Mmoist + Mpass + Mwater + Msur = 1829 kNm/m Check bearing pressure Distance to reaction; x = Mtotal / Ftotal_v = 2726 mm Eccentricity of reaction; e = x - lbase / 2 = -49 mm Loaded length of base; lload = 2 × x = 5452 mm Bearing pressure at toe; qtoe = Ftotal_v / lload = 123.1 kN/m 2 Bearing pressure at heel; qheel = 0 kN/m 2 Effective overburden pressure; q = (tbase + dcover) × γmb - (tbase + dcover + hwater) × γw = 6.7 kN/m 2 Design effective overburden pressure; q' = q / γγ = 6.7 kN/m2 Bearing resistance factors; Nq = Exp(π × tan(φ'b.d)) × (tan(45 deg + φ'b.d / 2)) 2 = 10.662 Nc = (Nq - 1) × cot(φ'b.d) = 20.721 Nγ = 2 × (Nq - 1) × tan(φ'b.d) = 9.011 Foundation shape factors; sq = 1 sγ = 1 sc = 1 Load inclination factors; H = Ftotal_h = 0 kN/m V = Ftotal_v = 671 kN/m m = 2 iq = [1 - H / (V + lload × c'b.d × cot(φ'b.d))] m = 1 iγ = [1 - H / (V + lload × c'b.d × cot(φ'b.d))] (m + 1) = 1
  8. 8. GEODOMISI Ltd. - Dr. Costas Sachpazis Civil & Geotechnical Engineering Consulting Company for Structural Engineering, Soil Mechanics, Rock Mechanics, Foundation Engineering & Retaining Structures. Tel.: (+30) 210 5238127, 210 5711263 - Fax.:+30 210 5711461 - Mobile: (+30) 6936425722 & (+44) 7585939944, costas@sachpazis.info Project: Retaining wall Analysis & Design, In accordance with EN1997-1:2004 incorporating Corrigendum dated February 2009 and the recommended values. Job Ref. Section Civil & Geotechnical Engineering Sheet no./rev. 1 Calc. by Dr. C. Sachpazis Date 04/04/2014 Chk'd by Date App'd by Date ic = iq - (1 - iq) / (Nc × tan(φ'b.d)) = 1 Net ultimate bearing capacity; nf = c'b.d × Nc × sc × ic + q' × Nq × sq × iq + 0.5 × (γmb - γw) × lload × Nγ × sγ × iγ = 425.7 kN/m 2 Factor of safety; FoSbp = nf / max(qtoe, qheel) = 3.459 PASS - Allowable bearing pressure exceeds maximum applied bearing pressure Partial factors on actions - Table A.3 - Combination 2 Permanent unfavourable action; γG = 1.00 Permanent favourable action; γGf = 1.00 Variable unfavourable action; γQ = 1.30 Variable favourable action; γQf = 0.00 Partial factors for soil parameters – Table A.4 - Combination 2 Angle of shearing resistance; γφ' = 1.25 Effective cohesion; γc' = 1.25 Weight density; γγ = 1.00 Retained soil properties Design effective shear resistance angle; φ'r.d = atan(tan(φ'r.k) / γφ') = 20.5 deg Design wall friction angle; δr.d = atan(tan(δr.k) / γφ') = 12.9 deg Base soil properties Design effective shear resistance angle; φ'b.d = atan(tan(φ'b.k) / γφ') = 20.5 deg Design wall friction angle; δb.d = atan(tan(δb.k) / γφ') = 16.2 deg Design base friction angle; δbb.d = atan(tan(δbb.k) / γφ') = 20.5 deg Design effective cohesion; c'b.d = c'b.k / γc' = 4 kN/m 2 Design adhesion; ab.d = ab.k / γc' = 4 kN/m 2 Using Coulomb theory Active pressure coefficient; KA = sin(α + φ'r.d) 2 / (sin(α) 2 × sin(α - δr.d) × [1 + √[sin(φ'r.d + δr.d) × sin(φ'r.d - β) / (sin(α - δr.d) × sin(α + β))]] 2 ) = 0.590 Passive pressure coefficient; KP = sin(αf - φ'b.d) 2 / (sin(αf) 2 × sin(αf + δb.d) × [1 - √[sin(φ'b.d + δb.d) × sin(φ'b.d) / (sin(αf + δb.d) × sin(αf))]] 2 ) = 3.111 Sliding check Vertical forces on wall Wall stem; Fstem = γGf × Astem × γstem = 50 kN/m Wall base; Fbase = γGf × Abase × γbase = 62.4 kN/m Saturated retained soil; Fsat_v = γGf × Asat × (γsr - γw) = 39.8 kN/m Water; Fwater_v = γGf × Awater × γw = 31.4 kN/m
  9. 9. GEODOMISI Ltd. - Dr. Costas Sachpazis Civil & Geotechnical Engineering Consulting Company for Structural Engineering, Soil Mechanics, Rock Mechanics, Foundation Engineering & Retaining Structures. Tel.: (+30) 210 5238127, 210 5711263 - Fax.:+30 210 5711461 - Mobile: (+30) 6936425722 & (+44) 7585939944, costas@sachpazis.info Project: Retaining wall Analysis & Design, In accordance with EN1997-1:2004 incorporating Corrigendum dated February 2009 and the recommended values. Job Ref. Section Civil & Geotechnical Engineering Sheet no./rev. 1 Calc. by Dr. C. Sachpazis Date 04/04/2014 Chk'd by Date App'd by Date Moist retained soil; Fmoist_v = γGf × Amoist × γmr = 258.9 kN/m Base soil; Fexc_v = γGf × Aexc × γmb = 10.1 kN/m Total; Ftotal_v = Fstem + Fbase + Fsat_v + Fmoist_v + Fexc_v + Fwater_v = 452.6 kN/m Horizontal forces on wall Surcharge load; Fsur_h = KA × cos(δr.d) × γQ × SurchargeQ × heff = 37.5 kN/m Saturated retained soil; Fsat_h = γG × KA × cos(δr.d) × (γsr - γw) × (hsat + hbase) 2 / 2 = 5.6 kN/m Water; Fwater_h = γG × γw × (hwater + dcover + hbase) 2 / 2 = 7.7 kN/m Moist retained soil; Fmoist_h = γG × KA × cos(δr.d) × γmr × ((heff - hsat - hbase) 2 / 2 + (heff - hsat - hbase) × (hsat + hbase)) = 136 kN/m Total; Ftotal_h = Fsat_h + Fmoist_h + Fwater_h + Fsur_h = 186.8 kN/m Check stability against sliding Base soil resistance; Fexc_h = γGf × KP × cos(δb.d) × γmb × (hpass + hbase) 2 / 2 = 27 kN/m Base friction; Ffriction = ab.d × b + Ftotal_v × tan(δbb.d) = 172.8 kN/m Resistance to sliding; Frest = Fexc_h + Ffriction = 199.8 kN/m Factor of safety; FoSsl = Frest / Ftotal_h = 1.07 PASS - Resistance to sliding is greater than sliding force Overturning check Vertical forces on wall Wall stem; Fstem = γGf × Astem × γstem = 50 kN/m Wall base; Fbase = γGf × Abase × γbase = 62.4 kN/m Saturated retained soil; Fsat_v = γGf × Asat × (γsr - γw) = 39.8 kN/m Water; Fwater_v = γGf × Awater × γw = 31.4 kN/m Moist retained soil; Fmoist_v = γGf × Amoist × γmr = 258.9 kN/m Base soil; Fexc_v = γGf × Aexc × γmb = 10.1 kN/m Total; Ftotal_v = Fstem + Fbase + Fsat_v + Fmoist_v + Fexc_v + Fwater_v = 452.6 kN/m Horizontal forces on wall Surcharge load; Fsur_h = KA × cos(δr.d) × γQ × SurchargeQ × heff = 37.5 kN/m Saturated retained soil; Fsat_h = γG × KA × cos(δr.d) × (γsr - γw) × (hsat + hbase) 2 / 2 = 5.6 kN/m
  10. 10. GEODOMISI Ltd. - Dr. Costas Sachpazis Civil & Geotechnical Engineering Consulting Company for Structural Engineering, Soil Mechanics, Rock Mechanics, Foundation Engineering & Retaining Structures. Tel.: (+30) 210 5238127, 210 5711263 - Fax.:+30 210 5711461 - Mobile: (+30) 6936425722 & (+44) 7585939944, costas@sachpazis.info Project: Retaining wall Analysis & Design, In accordance with EN1997-1:2004 incorporating Corrigendum dated February 2009 and the recommended values. Job Ref. Section Civil & Geotechnical Engineering Sheet no./rev. 1 Calc. by Dr. C. Sachpazis Date 04/04/2014 Chk'd by Date App'd by Date Water; Fwater_h = γG × γw × (hwater + dcover + hbase) 2 / 2 = 7.7 kN/m Moist retained soil; Fmoist_h = γG × KA × cos(δr.d) × γmr × ((heff - hsat - hbase) 2 / 2 + (heff - hsat - hbase) × (hsat + hbase)) = 136 kN/m Base soil; Fexc_h = -γGf × KP × cos(δb.d) × γmb × (hpass + hbase) 2 / 2 = -27 kN/m Total; Ftotal_h = Fsat_h + Fmoist_h + Fexc_h + Fwater_h + Fsur_h = 159.8 kN/m Overturning moments on wall Surcharge load; Msur_OT = Fsur_h × xsur_h = 94.2 kNm/m Saturated retained soil; Msat_OT = Fsat_h × xsat_h = 2.3 kNm/m Water; Mwater_OT = Fwater_h × xwater_h = 3.2 kNm/m Moist retained soil; Mmoist_OT = Fmoist_h × xmoist_h = 238.9 kNm/m Total; Mtotal_OT = Msat_OT + Mmoist_OT + Mwater_OT + Msur_OT = 338.7 kNm/m Restoring moments on wall Wall stem; Mstem_R = Fstem × xstem = 65 kNm/m Wall base; Mbase_R = Fbase × xbase = 173.3 kNm/m Saturated retained soil; Msat_R = Fsat_v × xsat_v = 141.3 kNm/m Water; Mwater_R = Fwater_v × xwater_v = 111.4 kNm/m Moist retained soil; Mmoist_R = Fmoist_v × xmoist_v = 947.6 kNm/m Base soil; Mexc_R = Fexc_v × xexc_v - Fexc_h × xexc_h = 13.6 kNm/m Total; Mtotal_R = Mstem_R + Mbase_R + Msat_R + Mmoist_R + Mexc_R + Mwater_R = 1452.2 kNm/m Check stability against overturning Factor of safety; FoSot = Mtotal_R / Mtotal_OT = 4.288 PASS - Maximum restoring moment is greater than overturning moment Bearing pressure check Vertical forces on wall Wall stem; Fstem = γG × Astem × γstem = 50 kN/m Wall base; Fbase = γG × Abase × γbase = 62.4 kN/m Surcharge load; Fsur_v = γQ × SurchargeQ × lheel = 52 kN/m Saturated retained soil; Fsat_v = γG × Asat × (γsr - γw) = 39.8 kN/m Water; Fwater_v = γG × Awater × γw = 31.4 kN/m Moist retained soil; Fmoist_v = γG × Amoist × γmr = 258.9 kN/m Base soil; Fpass_v = γG × Apass × γmb = 10.1 kN/m
  11. 11. GEODOMISI Ltd. - Dr. Costas Sachpazis Civil & Geotechnical Engineering Consulting Company for Structural Engineering, Soil Mechanics, Rock Mechanics, Foundation Engineering & Retaining Structures. Tel.: (+30) 210 5238127, 210 5711263 - Fax.:+30 210 5711461 - Mobile: (+30) 6936425722 & (+44) 7585939944, costas@sachpazis.info Project: Retaining wall Analysis & Design, In accordance with EN1997-1:2004 incorporating Corrigendum dated February 2009 and the recommended values. Job Ref. Section Civil & Geotechnical Engineering Sheet no./rev. 1 Calc. by Dr. C. Sachpazis Date 04/04/2014 Chk'd by Date App'd by Date Total; Ftotal_v = Fstem + Fbase + Fsat_v + Fmoist_v + Fpass_v + Fwater_v + Fsur_v = 504.6 kN/m Horizontal forces on wall Surcharge load; Fsur_h = KA × cos(δr.d) × γQ × SurchargeQ × heff = 37.5 kN/m Saturated retained soil; Fsat_h = γG × KA × cos(δr.d) × (γsr - γw) × (hsat + hbase) 2 / 2 = 5.6 kN/m Water; Fwater_h = γG × γw × (hwater + dcover + hbase) 2 / 2 = 7.7 kN/m Moist retained soil; Fmoist_h = γG × KA × cos(δr.d) × γmr × ((heff - hsat - hbase) 2 / 2 + (heff - hsat - hbase) × (hsat + hbase)) = 136 kN/m Base soil; Fpass_h = -γGf × KP × cos(δb.d) × γmb × (dcover + hbase) 2 / 2 = -27 kN/m Total; Ftotal_h = max(Fsat_h + Fmoist_h + Fpass_h + Fwater_h + Fsur_h - (ab.d × b + Ftotal_v × tan(δbb.d)), 0 kN/m) = 0 kN/m Moments on wall Wall stem; Mstem = Fstem × xstem = 65 kNm/m Wall base; Mbase = Fbase × xbase = 173.3 kNm/m Surcharge load; Msur = Fsur_v × xsur_v - Fsur_h × xsur_h = 90.4 kNm/m Saturated retained soil; Msat = Fsat_v × xsat_v - Fsat_h × xsat_h = 139 kNm/m Water; Mwater = Fwater_v × xwater_v - Fwater_h × xwater_h = 108.2 kNm/m Moist retained soil; Mmoist = Fmoist_v × xmoist_v - Fmoist_h × xmoist_h = 708.7 kNm/m Base soil; Mpass = Fpass_v × xpass_v - Fpass_h × xpass_h = 13.6 kNm/m Total; Mtotal = Mstem + Mbase + Msat + Mmoist + Mpass + Mwater + Msur = 1298.1 kNm/m Check bearing pressure Distance to reaction; x = Mtotal / Ftotal_v = 2573 mm Eccentricity of reaction; e = x - lbase / 2 = -202 mm Loaded length of base; lload = 2 × x = 5145 mm Bearing pressure at toe; qtoe = Ftotal_v / lload = 98.1 kN/m 2 Bearing pressure at heel; qheel = 0 kN/m 2 Effective overburden pressure; q = (tbase + dcover) × γmb - (tbase + dcover + hwater) × γw = 6.7 kN/m 2 Design effective overburden pressure; q' = q / γγ = 6.7 kN/m 2
  12. 12. GEODOMISI Ltd. - Dr. Costas Sachpazis Civil & Geotechnical Engineering Consulting Company for Structural Engineering, Soil Mechanics, Rock Mechanics, Foundation Engineering & Retaining Structures. Tel.: (+30) 210 5238127, 210 5711263 - Fax.:+30 210 5711461 - Mobile: (+30) 6936425722 & (+44) 7585939944, costas@sachpazis.info Project: Retaining wall Analysis & Design, In accordance with EN1997-1:2004 incorporating Corrigendum dated February 2009 and the recommended values. Job Ref. Section Civil & Geotechnical Engineering Sheet no./rev. 1 Calc. by Dr. C. Sachpazis Date 04/04/2014 Chk'd by Date App'd by Date Bearing resistance factors; Nq = Exp(π × tan(φ'b.d)) × (tan(45 deg + φ'b.d / 2)) 2 = 6.698 Nc = (Nq - 1) × cot(φ'b.d) = 15.273 Nγ = 2 × (Nq - 1) × tan(φ'b.d) = 4.251 Foundation shape factors; sq = 1 sγ = 1 sc = 1 Load inclination factors; H = Ftotal_h = 0 kN/m V = Ftotal_v = 504.6 kN/m m = 2 iq = [1 - H / (V + lload × c'b.d × cot(φ'b.d))] m = 1 iγ = [1 - H / (V + lload × c'b.d × cot(φ'b.d))] (m + 1) = 1 ic = iq - (1 - iq) / (Nc × tan(φ'b.d)) = 1 Net ultimate bearing capacity; nf = c'b.d × Nc × sc × ic + q' × Nq × sq × iq + 0.5 × (γmb - γw) × lload × Nγ × sγ × iγ = 217.7 kN/m 2 Factor of safety; FoSbp = nf / max(qtoe, qheel) = 2.22 PASS - Allowable bearing pressure exceeds maximum applied bearing pressure RETAINING WALL DESIGN In accordance with EN1992-1-1:2004 incorporating Corrigendum dated January 2008 and the recommended values Concrete details - Table 3.1 - Strength and deformation characteristics for concrete Concrete strength class; C20/25 Characteristic compressive cylinder strength; fck = 20 N/mm 2 Characteristic compressive cube strength; fck,cube = 25 N/mm 2 Mean value of compressive cylinder strength; fcm = fck + 8 N/mm 2 = 28 N/mm 2 Mean value of axial tensile strength; fctm = 0.3 N/mm 2 × (fck / 1 N/mm 2 ) 2/3 = 2.2 N/mm 2 5% fractile of axial tensile strength; fctk,0.05 = 0.7 × fctm = 1.5 N/mm 2 Secant modulus of elasticity of concrete; Ecm = 22 kN/mm 2 × (fcm / 10 N/mm 2 ) 0.3 = 29962 N/mm 2 Partial factor for concrete - Table 2.1N; γC = 1.50 Compressive strength coefficient - cl.3.1.6(1); αcc = 1.00 Design compressive concrete strength - exp.3.15; fcd = αcc × fck / γC = 13.3 N/mm 2 Maximum aggregate size; hagg = 20 mm Reinforcement details Characteristic yield strength of reinforcement; fyk = 500 N/mm 2 Modulus of elasticity of reinforcement; Es = 200000 N/mm 2
  13. 13. GEODOMISI Ltd. - Dr. Costas Sachpazis Civil & Geotechnical Engineering Consulting Company for Structural Engineering, Soil Mechanics, Rock Mechanics, Foundation Engineering & Retaining Structures. Tel.: (+30) 210 5238127, 210 5711263 - Fax.:+30 210 5711461 - Mobile: (+30) 6936425722 & (+44) 7585939944, costas@sachpazis.info Project: Retaining wall Analysis & Design, In accordance with EN1997-1:2004 incorporating Corrigendum dated February 2009 and the recommended values. Job Ref. Section Civil & Geotechnical Engineering Sheet no./rev. 1 Calc. by Dr. C. Sachpazis Date 04/04/2014 Chk'd by Date App'd by Date Partial factor for reinforcing steel - Table 2.1N; γS = 1.15 Design yield strength of reinforcement; fyd = fyk / γS = 435 N/mm 2 Cover to reinforcement Front face of stem; csf = 40 mm Rear face of stem; csr = 50 mm Top face of base; cbt = 50 mm Bottom face of base; cbb = 75 mm Check stem design at base of stem Depth of section; h = 550 mm Rectangular section in flexure - Section 6.1 Design bending moment combination 1; M = 235.8 kNm/m Depth to tension reinforcement; d = h - csr - φsr / 2 = 488 mm K = M / (d 2 × fck) = 0.050 K' = 0.196 K' > K - No compression reinforcement is required Lever arm; z = min(0.5 + 0.5 × (1 – 3.53 × K) 0.5 , 0.95) × d = 463 mm Depth of neutral axis; x = 2.5 × (d – z) = 61 mm Area of tension reinforcement required; Asr.req = M / (fyd × z) = 1171 mm 2 /m Tension reinforcement provided; 25 dia.bars @ 200 c/c Area of tension reinforcement provided; Asr.prov = π × φsr 2 / (4 × ssr) = 2454 mm 2 /m Minimum area of reinforcement - exp.9.1N; Asr.min = max(0.26 × fctm / fyk, 0.0013) × d = 634 mm 2 /m Maximum area of reinforcement - cl.9.2.1.1(3); Asr.max = 0.04 × h = 22000 mm 2 /m max(Asr.req, Asr.min) / Asr.prov = 0.477 PASS - Area of reinforcement provided is greater than area of reinforcement required Crack control - Section 7.3 Limiting crack width; wmax = 0.3 mm Variable load factor - EN1990 – Table A1.1; ψ2 = 0.3 Serviceability bending moment; Msls = 152.3 kNm/m Tensile stress in reinforcement; σs = Msls / (Asr.prov × z) = 134 N/mm 2 Load duration; Long term Load duration factor; kt = 0.4 Effective area of concrete in tension; Ac.eff = min(2.5 × (h - d), (h – x) / 3, h / 2) = 156250 mm 2 /m Mean value of concrete tensile strength; fct.eff = fctm = 2.2 N/mm 2 Reinforcement ratio; ρp.eff = Asr.prov / Ac.eff = 0.016 Modular ratio; αe = Es / Ecm = 6.675 Bond property coefficient; k1 = 0.8
  14. 14. GEODOMISI Ltd. - Dr. Costas Sachpazis Civil & Geotechnical Engineering Consulting Company for Structural Engineering, Soil Mechanics, Rock Mechanics, Foundation Engineering & Retaining Structures. Tel.: (+30) 210 5238127, 210 5711263 - Fax.:+30 210 5711461 - Mobile: (+30) 6936425722 & (+44) 7585939944, costas@sachpazis.info Project: Retaining wall Analysis & Design, In accordance with EN1997-1:2004 incorporating Corrigendum dated February 2009 and the recommended values. Job Ref. Section Civil & Geotechnical Engineering Sheet no./rev. 1 Calc. by Dr. C. Sachpazis Date 04/04/2014 Chk'd by Date App'd by Date Strain distribution coefficient; k2 = 0.5 k3 = 3.4 k4 = 0.425 Maximum crack spacing - exp.7.11; sr.max = k3 × csr + k1 × k2 × k4 × φsr / ρp.eff = 441 mm Maximum crack width - exp.7.8; wk = sr.max × max(σs – kt × (fct.eff / ρp.eff) × (1 + αe × ρp.eff), 0.6 × σs) / Es wk = 0.177 mm wk / wmax = 0.59 PASS - Maximum crack width is less than limiting crack width Rectangular section in shear - Section 6.2 Design shear force; V = 153.5 kN/m CRd,c = 0.18 / γC = 0.120 k = min(1 + √(200 mm / d), 2) = 1.641 Longitudinal reinforcement ratio; ρl = min(Asr.prov / d, 0.02) = 0.005 vmin = 0.035 N 1/2 /mm × k 3/2 × fck 0.5 = 0.329 N/mm 2 Design shear resistance - exp.6.2a & 6.2b; VRd.c = max(CRd.c × k × (100 N 2 /mm 4 × ρl × fck) 1/3 , vmin) × d VRd.c = 207.2 kN/m V / VRd.c = 0.741 PASS - Design shear resistance exceeds design shear force Horizontal reinforcement parallel to face of stem - Section 9.6 Minimum area of reinforcement – cl.9.6.3(1); Asx.req = max(0.25 × Asr.prov, 0.001 × (tstem + lslf)) = 614 mm 2 /m Maximum spacing of reinforcement – cl.9.6.3(2); ssx_max = 400 mm Transverse reinforcement provided; 16 dia.bars @ 200 c/c Area of transverse reinforcement provided; Asx.prov = π × φsx 2 / (4 × ssx) = 1005 mm 2 /m PASS - Area of reinforcement provided is greater than area of reinforcement required Check base design at toe Depth of section; h = 450 mm Rectangular section in flexure - Section 6.1 Design bending moment combination 1; M = 48.9 kNm/m Depth to tension reinforcement; d = h - cbb - φbb / 2 = 367 mm K = M / (d 2 × fck) = 0.018 K' = 0.196 K' > K - No compression reinforcement is required Lever arm; z = min(0.5 + 0.5 × (1 – 3.53 × K) 0.5 , 0.95) × d = 349 mm Depth of neutral axis; x = 2.5 × (d – z) = 46 mm Area of tension reinforcement required; Abb.req = M / (fyd × z) = 323 mm 2 /m
  15. 15. GEODOMISI Ltd. - Dr. Costas Sachpazis Civil & Geotechnical Engineering Consulting Company for Structural Engineering, Soil Mechanics, Rock Mechanics, Foundation Engineering & Retaining Structures. Tel.: (+30) 210 5238127, 210 5711263 - Fax.:+30 210 5711461 - Mobile: (+30) 6936425722 & (+44) 7585939944, costas@sachpazis.info Project: Retaining wall Analysis & Design, In accordance with EN1997-1:2004 incorporating Corrigendum dated February 2009 and the recommended values. Job Ref. Section Civil & Geotechnical Engineering Sheet no./rev. 1 Calc. by Dr. C. Sachpazis Date 04/04/2014 Chk'd by Date App'd by Date Tension reinforcement provided; 16 dia.bars @ 200 c/c Area of tension reinforcement provided; Abb.prov = π × φbb 2 / (4 × sbb) = 1005 mm 2 /m Minimum area of reinforcement - exp.9.1N; Abb.min = max(0.26 × fctm / fyk, 0.0013) × d = 477 mm 2 /m Maximum area of reinforcement - cl.9.2.1.1(3); Abb.max = 0.04 × h = 18000 mm 2 /m max(Abb.req, Abb.min) / Abb.prov = 0.475 PASS - Area of reinforcement provided is greater than area of reinforcement required Crack control - Section 7.3 Limiting crack width; wmax = 0.3 mm Variable load factor - EN1990 – Table A1.1; ψ2 = 0.3 Serviceability bending moment; Msls = 35.3 kNm/m Tensile stress in reinforcement; σs = Msls / (Abb.prov × z) = 100.8 N/mm 2 Load duration; Long term Load duration factor; kt = 0.4 Effective area of concrete in tension; Ac.eff = min(2.5 × (h - d), (h – x) / 3, h / 2) = 134708 mm 2 /m Mean value of concrete tensile strength; fct.eff = fctm = 2.2 N/mm 2 Reinforcement ratio; ρp.eff = Abb.prov / Ac.eff = 0.007 Modular ratio; αe = Es / Ecm = 6.675 Bond property coefficient; k1 = 0.8 Strain distribution coefficient; k2 = 0.5 k3 = 3.4 k4 = 0.425 Maximum crack spacing - exp.7.11; sr.max = k3 × cbb + k1 × k2 × k4 × φbb / ρp.eff = 619 mm Maximum crack width - exp.7.8; wk = sr.max × max(σs – kt × (fct.eff / ρp.eff) × (1 + αe × ρp.eff), 0.6 × σs) / Es wk = 0.187 mm wk / wmax = 0.625 PASS - Maximum crack width is less than limiting crack width Rectangular section in shear - Section 6.2 Design shear force; V = 97.4 kN/m CRd,c = 0.18 / γC = 0.120 k = min(1 + √(200 mm / d), 2) = 1.738 Longitudinal reinforcement ratio; ρl = min(Abb.prov / d, 0.02) = 0.003 vmin = 0.035 N 1/2 /mm × k 3/2 × fck 0.5 = 0.359 N/mm 2 Design shear resistance - exp.6.2a & 6.2b; VRd.c = max(CRd.c × k × (100 N 2 /mm 4 × ρl × fck) 1/3 , vmin) × d VRd.c = 134.9 kN/m V / VRd.c = 0.722 PASS - Design shear resistance exceeds design shear force
  16. 16. GEODOMISI Ltd. - Dr. Costas Sachpazis Civil & Geotechnical Engineering Consulting Company for Structural Engineering, Soil Mechanics, Rock Mechanics, Foundation Engineering & Retaining Structures. Tel.: (+30) 210 5238127, 210 5711263 - Fax.:+30 210 5711461 - Mobile: (+30) 6936425722 & (+44) 7585939944, costas@sachpazis.info Project: Retaining wall Analysis & Design, In accordance with EN1997-1:2004 incorporating Corrigendum dated February 2009 and the recommended values. Job Ref. Section Civil & Geotechnical Engineering Sheet no./rev. 1 Calc. by Dr. C. Sachpazis Date 04/04/2014 Chk'd by Date App'd by Date Check base design at heel Depth of section; h = 450 mm Rectangular section in flexure - Section 6.1 Design bending moment combination 2; M = 238.1 kNm/m Depth to tension reinforcement; d = h - cbt - φbt / 2 = 388 mm K = M / (d 2 × fck) = 0.079 K' = 0.196 K' > K - No compression reinforcement is required Lever arm; z = min(0.5 + 0.5 × (1 – 3.53 × K) 0.5 , 0.95) × d = 358 mm Depth of neutral axis; x = 2.5 × (d – z) = 73 mm Area of tension reinforcement required; Abt.req = M / (fyd × z) = 1529 mm 2 /m Tension reinforcement provided; 25 dia.bars @ 200 c/c Area of tension reinforcement provided; Abt.prov = π × φbt 2 / (4 × sbt) = 2454 mm 2 /m Minimum area of reinforcement - exp.9.1N; Abt.min = max(0.26 × fctm / fyk, 0.0013) × d = 504 mm 2 /m Maximum area of reinforcement - cl.9.2.1.1(3); Abt.max = 0.04 × h = 18000 mm 2 /m max(Abt.req, Abt.min) / Abt.prov = 0.623 PASS - Area of reinforcement provided is greater than area of reinforcement required Crack control - Section 7.3 Limiting crack width; wmax = 0.3 mm Variable load factor - EN1990 – Table A1.1; ψ2 = 0.3 Serviceability bending moment; Msls = 107.7 kNm/m Tensile stress in reinforcement; σs = Msls / (Abt.prov × z) = 122.5 N/mm 2 Load duration; Long term Load duration factor; kt = 0.4 Effective area of concrete in tension; Ac.eff = min(2.5 × (h - d), (h – x) / 3, h / 2) = 125559 mm 2 /m Mean value of concrete tensile strength; fct.eff = fctm = 2.2 N/mm 2 Reinforcement ratio; ρp.eff = Abt.prov / Ac.eff = 0.020 Modular ratio; αe = Es / Ecm = 6.675 Bond property coefficient; k1 = 0.8 Strain distribution coefficient; k2 = 0.5 k3 = 3.4 k4 = 0.425 Maximum crack spacing - exp.7.11; sr.max = k3 × cbt + k1 × k2 × k4 × φbt / ρp.eff = 387 mm Maximum crack width - exp.7.8; wk = sr.max × max(σs – kt × (fct.eff / ρp.eff) × (1 + αe × ρp.eff), 0.6 × σs) / Es wk = 0.142 mm
  17. 17. GEODOMISI Ltd. - Dr. Costas Sachpazis Civil & Geotechnical Engineering Consulting Company for Structural Engineering, Soil Mechanics, Rock Mechanics, Foundation Engineering & Retaining Structures. Tel.: (+30) 210 5238127, 210 5711263 - Fax.:+30 210 5711461 - Mobile: (+30) 6936425722 & (+44) 7585939944, costas@sachpazis.info Project: Retaining wall Analysis & Design, In accordance with EN1997-1:2004 incorporating Corrigendum dated February 2009 and the recommended values. Job Ref. Section Civil & Geotechnical Engineering Sheet no./rev. 1 Calc. by Dr. C. Sachpazis Date 04/04/2014 Chk'd by Date App'd by Date wk / wmax = 0.475 PASS - Maximum crack width is less than limiting crack width Rectangular section in shear - Section 6.2 Design shear force; V = 89.9 kN/m CRd,c = 0.18 / γC = 0.120 k = min(1 + √(200 mm / d), 2) = 1.718 Longitudinal reinforcement ratio; ρl = min(Abt.prov / d, 0.02) = 0.006 vmin = 0.035 N 1/2 /mm × k 3/2 × fck 0.5 = 0.353 N/mm 2 Design shear resistance - exp.6.2a & 6.2b; VRd.c = max(CRd.c × k × (100 N 2 /mm 4 × ρl × fck) 1/3 , vmin) × d VRd.c = 186.3 kN/m V / VRd.c = 0.483 PASS - Design shear resistance exceeds design shear force Secondary transverse reinforcement to base - Section 9.3 Minimum area of reinforcement – cl.9.3.1.1(2); Abx.req = 0.2 × Abt.prov = 491 mm 2 /m Maximum spacing of reinforcement – cl.9.3.1.1(3); sbx_max = 450 mm Transverse reinforcement provided; 16 dia.bars @ 300 c/c Area of transverse reinforcement provided; Abx.prov = π × φbx 2 / (4 × sbx) = 670 mm 2 /m PASS - Area of reinforcement provided is greater than area of reinforcement required
  18. 18. GEODOMISI Ltd. - Dr. Costas Sachpazis Civil & Geotechnical Engineering Consulting Company for Structural Engineering, Soil Mechanics, Rock Mechanics, Foundation Engineering & Retaining Structures. Tel.: (+30) 210 5238127, 210 5711263 - Fax.:+30 210 5711461 - Mobile: (+30) 6936425722 & (+44) 7585939944, costas@sachpazis.info Project: Retaining wall Analysis & Design, In accordance with EN1997-1:2004 incorporating Corrigendum dated February 2009 and the recommended values. Job Ref. Section Civil & Geotechnical Engineering Sheet no./rev. 1 Calc. by Dr. C. Sachpazis Date 04/04/2014 Chk'd by Date App'd by Date

×