T.Chhay                                                                                     NPIC




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Department of Civil Engineering                                        viTüasßanCatiBhubec©keTskm<úCa


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T.Chhay                                                                                    NPIC




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Department of Civil Engineering                                         viTüasßanCatiBhubec©keTskm<úCa


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T.Chhay                                                                                        NPIC



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Department of Civil Engineering                                                    viTüasßanCatiBhubec©keTskm<úCa


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T.Chhay                                                                                   NPIC




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Department of Civil Engineering                                                   viTüasßanCatiBhubec©keTskm<úCa


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T.Chhay                                                                                 NPIC




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Department of Civil Engineering                                          viTüasßanCatiBhubec©keTskm<úCa


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T.Chhay                                                                                      NPIC




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Department of Civil Engineering                                             viTüasßanCatiBhubec©keTskm<úCa


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T.Chhay                                                                                         NPIC




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Department of Civil Engineering                                             viTüasßanCatiBhubec©keTskm<úCa


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T.Chhay                                                                          NPIC




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Department of Civil Engineering                                          viTüasßanCatiBhubec©keTskm<úCa


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T.Chhay                                                                                  NPIC




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Department of Civil Engineering                                          viTüasßanCatiBhubec©keTskm<úCa


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T.Chhay                                                                            NPIC




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Department of Civil Engineering                                            viTüasßanCatiBhubec©keTskm<úCa


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T.Chhay                                                                                     NPIC




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Department of Civil Engineering                                            viTüasßanCatiBhubec©keTskm<úCa


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T.Chhay                                                                                        NPIC




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Department of Civil Engineering                                             viTüasßanCatiBhubec©keTskm<úCa


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T.Chhay                                                                                         NPIC




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Department of Civil Engineering                                         viTüasßanCatiBhubec©keTskm<úCa


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T.Chhay                                                                                     NPIC




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Department of Civil Engineering                                                viTüasßanCatiBhubec©keTskm<úCa


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T.Chhay                                                                                    NPIC




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Department of Civil Engineering                                   viTüasßanCatiBhubec©keTskm<úCa


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T.Chhay                                                                                        NPIC




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Xiv retaining walls

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Xiv retaining walls

  1. 1. T.Chhay NPIC XIV. CBa¢aMgTb; Retaining Wall 1> esckþIepþIm Introduction CBa¢aMgTb;CaeRKOgbgÁúMEdlRtUv)aneRbIedIm,Ipþl;lnwgdl;dI b¤sMPar³epSgeTot nigedIm,IkarBarva M BICMralFmμCatirbs;va. kñúgn½yenH CBa¢aMgTb;rkSadIEdlmankMritkMBs;xusKñaedayépÞTaMgBIrrbs;va. sM Par³EdlRtUv)anTb;enAnIv:Ux<s;CagGnuvtþkMlaMgeTAelICBa¢aMgTb;EdlGacbNþaleGayvaRkLab; (overturning) b¤)ak; (failure). CBa¢aMgTb;RtUv)aneRbIenAkñúgsMNg;s<anCa abutment/ enAkñúgsMNg;Ca basement walls/ nigenAkñúg embankments. vak¾RtUv)aneRbIedIm,ITb;sarFaturav dUcCaGagTwk nigGag sewage-treatment tank. 2> RbePTCBa¢aMgTb; Types of Retaining Walls CBa¢aMgTb;RtUv)ancat;cMNat;fñak;dUcxageRkam ¬eyagtamrUb 14>1¦³ - Gravity walls CaTUeTArYmmanebtugsuT§ b¤dæ edayGaRs½yeTAelITMgn;pÞal;rbs;vaedIm,I pþl;lMnwgRbqaMgkarrujénsMPar³EdlRtUvTb;. CBa¢aMgenHmanTMhMFMEdlkugRtaMgTajminekIt manenAkñúgebtug b¤dæbNþalmkBIkMlaMgrujelICBa¢aMgeT. kMBs;sMrab;Gnuvtþkñúg gravity walls minRtUvFMCag 3m . - Semigravity walls Ca gravity walls Edlman)atFMedIm,Ipþl;lT§PaBlMnwgrbs;CBa¢aMg nig edIm,IkarBarkarekIteLIgénkugRtaMgTajenAelI)at. brimaNEdkd¾tictYcRtUveRbIenAkñúg)at b¤ enAkñúgCBa¢aMgenAeBlxøH edIm,Ikat;bnßymuxkat;d¾FMrbs;CBa¢aMg. - Cantilever retaining wall CaCBa¢aMgebtugGarem:EdlCaTUeTARtUv)aneRbIEdlmankMBs;BI 2.4m eTA 6m . vaCaRbePTFmμtabMputéneRKagsMNg;Tb; edaysarlkçN³esdækic© nig lkçN³samBaØrbs;va. CBa¢aMg cantilever retaining wall CaeRcInRbePTRtUv)anbgðajkñúgrUb 14>1. - Counterfort retaining walls mankMBs;x<s;Cag 6m begáItm:Um:g;Bt;FMenA)aténCBa¢aMgTb; EdleFVIeGaykarKNnaénCBa¢aMgKμanlkçN³esdækic©. dMeNaHRsaymYyenAkñúgkrNIenHKWkarbEnßmnUvCBa¢aMgTTwg (counterfort) CBa¢aMgTb; 315
  2. 2. Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa EdlcgP¢ab;CBa¢aMgeTAnwg)at. Counterfort mannaTICaGgát;rgkarTajEdlRTCBa¢aMgbBaÄr. karKNnaCBa¢aMgenHmanlkçN³esdækic©edaysarEtCBa¢aMgRtUv)anKitCakMralxNнCab;Edlman KMlattamTisedkcenøaH counterfort. kMralxNнRtUv)anKNnadUckMralxNнEdlRTenAelITMr bIRCug ¬rUbTI 14>1 h ¦. - Buttressed retaining wall manTMrg;RsedogKñanwg nounterfort wall Edrb:uEnþkñúgkrNIenH CBa¢aMgTTwgmanTItaMgsßitenAmuxmçageTotEdleyIgemIleXIj ehIyCBa¢aMgTTwgenHmannaTICa Ggát;rgkarsgát; ¬rUbTI 14>1 i ¦. CBa¢aMgEbbenHmanlkçN³esdækic©enAeBlEdlvamankMBs; x<s;Cag 6m . vaminmankareBjniymeT edaysarEteKemIleXIjCBa¢aMgTTwg (buttress). Retaining Walls 316
  3. 3. T.Chhay NPIC - CaCBa¢aMgTb;enAEpñkxagelIEdlRtUveRbIedIm,IRTkMrals<an. CBa¢aMgRtUv)an Bridge abutment snμt;fabgáb;enAEpñkxageRkamenAnwg)at nigRTedayTMrsamBaØenAEpñkxagelI. - Basement walls Tb;sMBaFdIBIépÞmçagrbs;CBa¢aMg niglatsn§wgtamTisQrBIkMralxNнCan; eRkamdIeTAkMralxNнCan;TImYy. CBa¢aMgGacRtUv)ansnμt;bgáb;enA)at nigRTedayTMrsamBaØ b¤Tb;edayEpñk (partially restrained) enAEpñkxagelI. 3> kMlaMgenAelICBa¢aMgTb; Forces on Retaining Walls CaTUeTACBa¢aMgTb;rgnUvbnÞúkTMnajEpndI nigsMBaFdIEdlbNþalmkBIsMPar³Tb;enAelICBa¢aMg. bnÞúkTMnajEpndIEdlbNþalmkBITMgn;rbs;sMPar³RtUv)ankMNt;edaykarKNnaedaypÞal; niggay RsYl. GaMgtg;sIuet nigTisedArbs;sMBaFdIenAelICBa¢aMgTb;GaRs½yelIRbePT niglkçNdIEdlRtUv)an Tb; nigktþaepSgeTot EdleKminGacKNna)anRtwmRtUvdUcbnÞúkTMnajEpndIeT. eKGackMNt;sMBaFdI manGMeBIelICBa¢aMgTb;tamRTwsþI nigviFIsaRsþEdlmanBnül;kñúgmuxviC¢aemkanicdI. sßanPaBlMnwgrbs; CBa¢aMgTb; nigT§iBlénkMlaMgDINamiceTAelICBa¢aMgk¾manEcgkñúgmuxviC¢aenHEdr. dIRtsuH (granular material) dUcCaxSac; manlkçN³emkanicxusBIdIs¥it (cohesive material) dUcCadIdæ b¤BIbnSMénRbePTdITaMgBIr. eTaHCaGaMgtg;sIuetsMBaFdIenAelICBa¢aMgTb;manlkçN³sμúKsμaj eK)ansnμt;karBRgaysMBaFdImkelICBa¢aMgTb;manlkçN³CabnÞat;. GaMgtg;sIuetsMBaFekIneLIgsma- maRtCamYynwgCMerA ehIytMélrbs;vaCaGnuKmn_eTAnwgkMBs;CBa¢aMg/ TMgn;dI nigRbePTdI. GaMgtg;sIuetdI p enACMerA h BIeRkamépÞdIRtUv)anKNnadUcxageRkam³ p = Cwh ¬!$>!¦ Edl w CaTMgn;maDdI nig C CaemKuNEdlGaRs½yeTAnwglkçN³rUbrbs;dI. tMélrbs;emKuN C ERbRbYlBI 0.35 sMrab;dIRtsuH (loose granular soil) dUcCaxSac; eTA 1.0 sMrab;dIs¥it (cohesive soil) dUcCadIdæesIm. RbsinebICBa¢aMgTb;EtUv)ansnμt;rwgdac;xat enaHkrNIsMBaFdIenAes¶omnwgekIt eLIg. eRkamsMBaFdI CBa¢aMgGacdabb¤rMdiledaybrimaNtictYcBIdI ehIysMBaFdIskmμnwgekIteLIgdUc bgðajenAkñúgrUbTI 14>2. RbsinebICBa¢aMgrMkileq<aHeTAdI enaHsMBaFdIGkmμnwgekItman. TaMgsMBaFdI skmμ nigsMBaFdIGkmμRtUv)ansnμt;faERbRbYlCabnÞat;CamYynwgCMerACBa¢aMg ¬rUbTI 14>2¦. sMrab;dI RtsuH (granular) s¶Üt/ Gt;s¥it (noncohesive) RtUv)ansnμt;fasMBaFBRgaymanragCabnÞat; (linear) ÉdIs¥it b¤dIxSac;Eq¥tTwkmanlkçN³epSg KWsMBaFBRgaymanlkçN³minEmnbnÞat; (nonlinear). dUc CBa¢aMgTb; 317
  4. 4. Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa enH CaTUeTAeKeRbIdIRtsuHCasMPar³cak;bMeBjedIm,Ipþl;nUvdüaRkamsMBaFbnÞat; nigmü:ageTotpþl; lT§PaBkñúgkarbgðÚrTwkBICBa¢aMgxageRkay. sMrab;sMBaFbnÞat; GaMgtg;sIuetsMBaFskmμ nigsMBaFGkmμRtUv)anKNnadUcxageRkam³ Pa = C a wh ¬!$>@¦ Pp = C p wh ¬!$>#¦ Edl Ca nig C p CaemKuNénsMBaFskmμ nigsMBaFGkmμerogKña. 4> sMBaFdIGkmμ nigsMBaFdIskmμ Active and Passive Soil Pressures RTwsþId¾samBaØCaeKBIrEdlRtUv)aneRbICaTUeTAkñúgkarKNnasMBaFdIKW Rankine nig Coulomb. a. sMrab;viFIrbs; Rankine CBa¢aMgTb;RtUv)ansnμt;fa yield RKb;RKan;edIm,IbegáItnUvsßanPaBlM nwg)øasÞic enAkñúgdMudIenAépÞCaBa¢aMg. dIEdlenAes¶ómenArkSakñúgsßanPaBeGLasÞic. RTwsþIenH GnuvtþCacMbgcMeBaHdIKμanPaBs¥it (cohesiveless)/ dIEdlminGacsgát;)an (incompressible)/ dIEdlmanlkçN³sac;mYy (homogeneous) nigminKitnUvkMlaMgkkitrvagdI nigCBa¢aMg. sMBaF dIskmμenACMerA h manGMeBIelICBa¢aMgTb;edayQrelIRTwsþI Rankine RtUv)ankMNt;dUcxag eRkam³ ⎛ 1 − sin φ ⎞ Pa = C a wh = wh⎜ ⎜ 1 + sin φ ⎟ ⎟ ¬!$>$¦ ⎝ ⎠ Retaining Walls 318
  5. 5. T.Chhay NPIC ⎛ 1 − sin φ ⎞ Edl Ca = ⎜ ⎜ 1 + sin φ ⎟ ⎟ ⎝ ⎠ mMukkitkñúgrbs;dI ¬tarag !$>!¦ φ= wh 2 ⎛ 1 − sin φ ⎞ sMBaFskmμsrub Ha = ⎜ 2 ⎜ 1 + sin φ ⎟ ⎟ ¬!$>%¦ ⎝ ⎠ tarag !$>! tMélén w nig φ RbePTdIcak;bMeBj TMgn;maD ¬ kg / m 3 ¦ mMukkitkñúg φ Soft clay 1440 − 1920 0 o − 15 o Medium clay 1600 − 1920 15 o − 30 o Dry loose silt 1600 − 1920 27 o − 30 o Dry dense silt 1760 − 1920 30 o − 35 o Loose sand and gravel 1600 − 2100 30 o − 40 o Dense sand and gravel 1920 − 2100 25 o − 35 o Dry loose sand, graded 1840 − 2100 33o − 35 o Dry dense sand, graded 1920 − 2100 42 o − 46 o kMlaMgpÁÜb H a GnuvtþGMeBIenAkMBs; h / 3 BI)at ¬rUbTI !$>@¦. enAeBlEdldIrgbnÞúkbEnßmeday mMu δ EdlpÁúMCamYyGkS½edk enaH CBa¢aMgTb; 319
  6. 6. Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa ⎛ cos δ − cos 2 δ − cos 2 φ ⎞ C a = cos δ ⎜ ⎜ ⎟ ⎟ ¬!$>^¦ ⎝ cos δ + cos δ − cos φ 2 2 ⎠ wh 2 Pa = C a wh nig H a = Ca 2 kMlaMgpÁÜb H a eFVIGMeBIenAkMBs; h / 3 nigeRTtedaymMu δ eTAnwgbnÞat;edk ¬rUbTI 14>3¦. tM él Ca EdlsMEdgedaysmIkar !$>^ sMrab;tMélepSg²én δ nig φ RtUv)anbgðajenAkñúgta rag !$>@. tarag !$>@ tMélrbs; C a φ ¬mMukkitkñúg¦ δ 28 o 30 o 32 o 34 o 36 o 38 o 40 o 0o 0.361 0.333 0.307 0.283 0.260 0.238 0.217 10 o 0.380 0.350 0.321 0.294 0.270 0.246 0.225 20 o 0.461 0.414 0.374 0.338 0.306 0.277 0.250 25 o 0.573 0.494 0.434 0.385 0.343 0.307 0.275 30 o 0. 0.866 0.574 0.478 0.411 0.358 0.315 sMBaFdIGkmμekItmanenAeBlEdlCBa¢aMgTb;rMkil nigsgát;dI. sMBaFdIGkmμenAkMBs; h' enAelI CBa¢aMgTb;CamYynwgdIcak;bMeBjtamTisedkRtUv)ankMNt;dUcxageRkam³ ⎛ 1 + sin φ ⎞ Pp = C p wh = wh⎜ ⎜ 1 − sin φ ⎟ ⎟ ¬!$>&¦ ⎝ ⎠ ⎛ 1 + sin φ ⎞ 1 Edl Cp = ⎜ ⎜ 1 − sin φ ⎟ = C ⎟ ⎝ ⎠ a sin φ sMBaFGkmμsrubKW H p = wh ⎛ 1 + sin φ ⎞ 2 2 ⎝ ⎜ ⎜1− ⎟ ⎟ ¬!$>*¦ ⎠ kMlaMgpÁÜb H p manGMeBIenA h' / 3 BI)at ¬rUbTI 14>2¦. enAeBldIrgnUvbnÞúkbEnßmedaymMu ⎛ cos δ + cos 2 δ − cos 2 φ ⎞ δ eTAnwgbnÞat;edk enaH C p = cos δ ⎜ ⎜ ⎟ ⎟ ¬!$>(¦ ⎝ cos δ − cos δ − cos φ 2 2 ⎠ wh 2 Pp = C p wh nig H p = Cp 2 H p manGMeBIenA h' / 3 ehIyeRTtedaymMu δ eTAnwgbnÞat;edk ¬rUbTI 14>4¦. tMél C p Edl sMEdgedaysmIkar !$>( sMrab;tMélepSg²én δ nig φ RtUv)anbgðajenAkñúgtarag !$>#. Retaining Walls 320
  7. 7. T.Chhay NPIC tMélén φ nig w ERbRbYleTAtamRbePTdIcak;bMeBj. tamkarENnaM tMélFmμtarbs; φ nig w RtUv)aneGay enAkñúgtarag !$>!. tarag !$># tMélrbs; C p φ ¬mMukkitkñúg¦ δ 28 o 30 o 32 o 34 o 36 o 38 o 40 o 0o 2.77 3.00 3.25 3.54 3.85 4.20 4.60 10 o 2.55 2.78 3.02 3.30 3.60 3.94 4.32 20 o 1.92 2.13 2.36 2.61 2.89 3.19 3.53 25 o 1.43 1.66 1.90 2.14 2.40 2.68 3.00 30 o 0. 0.87 1.31 1.57 1.83 2.10 2.38 b. sMrab;RTwsþIrbs; Coulomb/ sMBaFdIskmμRtUv)ansnμt;faCalT§pléndMudI (wedge of soil) rGilRbqaMgmkelIépÞCBa¢aMgTb;. dUcenHRTwsþI Coulomb KWsMedAeTARTwsþI wedge. enAeBl EdlkMlaMgkkitRtUv)anKitenAkñúgCBa¢aMgTb; eK)ansnμt;faépÞrGilCabøgerobesμI EtkarBitva manlkçN³ekagbnþic. kMhusenAkñúgkarsnμt;enHRtUv)anecalenAkñúgkarKNnasMBaFdIskmμ . smIkar Coulomb edIm,IKNnasMBaFdIskmμ nigsMBaFdIGkmμmandUcxageRkam³ sMBaFdIskmμKW Pa = Ca wh CBa¢aMgTb; 321
  8. 8. Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa cos 2 (φ − θ ) Edl Ca = ¬!$>!0 a ¦ sin (φ + β )sin (φ − δ ) ⎤ 2 ⎡ cos 2 θ cos(θ + β )⎢1 + ⎥ ⎣ cos(θ + β ) cos(θ − β ) ⎦ Edl φ=mMukkitkñúgrbs;dI θ = mMuénépÞsMBaFdImkGkS½Qr β = mMukkittambeNþayépÞCBa¢aMg ¬mMurvagdInigebtug¦ δ = mMuénbnÞúkbEnßm (surcharge) eTAGkS½edk sMBaFdIskmμsrubKW wh 2 h H a = Ca = Pa 2 2 enAeBlEdlépÞCBa¢aMgmanlkçN¤bBaÄrRtg; enaH θ = 0o nigRbsinebI β = δ enaH Ca enAkñúg smIkar ¬!$>!0 a ¦ køayeTACasmIkar ¬!$>^ ¦ rbs; Rankine. sMBaFdIGkmμKW Pp = C p wh cos 2 (φ + θ ) Edl C p = ¬!$>!0 a ¦ sin (φ + β )sin (φ + δ ) ⎤ 2 ⎡ cos 2 θ cos(θ − β )⎢1 − ⎥ ⎣ cos(θ + β ) cos(θ − β ) ⎦ tMélrbs; φ nig w ERbRbYleTAtamRbePTdIcak;bMeBj. tamkarENnaM tMélFmμtarbs; φ nig w RtUv)aneGay enAkñúgtarag !$>!. c. enAeBlEdldIEq¥tTwk rn§es<atrbs;dIeBjeTAedayTwk EdlbegáItCasMBaFGIuRdUsþaTic. enAkñúg krNIenHTMgn;maDdIEdllicTwk (submerged unit weight)RtUv)aneRbI. TMgn;maDdIlicTwk Ca TMgn;maDdIEdl)andkTMgn;maDTwk. T§iBlrbs;sMBaFTwkGIuRdUsþaTicRtUvEtKitenAkñúgkar KNnaCBa¢aMgTb;EdlRbQmnwgRsTab;Twkx<s; nigdIlicTwk. eKGaceRbImMukkitkñúgEdl)an bgðajenAkñúgtarag !$>!. 5> T§iBlénbnÞúkbEnßm Effect of Surcharge bnÞúkepSg²énbnÞúkRtUv)andak;enAelIépÞéndIcak;bMeBjBIxageRkayCBa¢aMgTb;. RbsinebIbnÞúk CabnÞúkBRgayesμI kMBs;smmUlrbs;dI hs RtUv)ansnμt;famanGMeBIeTAelICBa¢aMgedIm,IbegáInsMBaF. sMrab;CBa¢aMgdUcbgðajenAkñúgrUbTI 14>5 sMBaFedkEdlbNþalBIbnÞúkbEnßmmantMélefreBjkMBs;rbs; CBa¢aMgTb;. Retaining Walls 322
  9. 9. T.Chhay NPIC hs = ws w ¬!$>!!¦ Edl kMBs;smmUlrbs;dI hs = ws = sMBaFbnÞúkelIs w = TMgn;maDdI sMBaFsrubKW H a = H a1 + H a2 = Ca w⎛ h2 + hhs ⎞ 2 ⎜ ⎜ ⎟ ⎟ ¬!$>!@¦ ⎝ ⎠ enAkñúgkrNIbnÞúkBRgayesμIedayEpñkmanGMeBIenAcMgaymYyBICBa¢aMgTb; enaHvamanEtsMBaFén bnÞúkbEnßmsrubmYyEpñkmanT§iBleTAelICBa¢aMg ¬rUbTI !$>^¦. vaCakarGnuvtþn_TUeTAedaysnμt;fakMBs;RbsiT§PaBénbnÞúkbEnßmKW h' Edlvas;BIcMnuc B eTA)at rbs;CBa¢aMgTb;. bnÞat; AB pÁúMmMu 45o CamYyGkS½edk. kñúgkrNIbnÞúkkg;LanmanGMeBIenAcMgaymYyCBa¢aMg bnÞúkRtUv)anBRgayelIépÞkMNt;mYy EdlCaTUeTAkMNt;eday specification EdleKTTYlsÁal;dUcCa AASHTO nig AREA. CBa¢aMgTb; 323
  10. 10. Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa 6> kMlaMgkkitenAelI)atCBa¢aMgTb; Friction on the Retaining Wall Base bgÁúMkMlaMgtamTisedkénkMlaMgTaMgGs;manGMeBIelICBa¢aMgTb;)anrujCBa¢aMgtamTisedAedk. )atCBa¢aMgTb;RtUvEtFMRKb;RKan;edIm,ITb;nwgkarrGilrbs;CBa¢aMg. emKuNkMlaMgkkitEdlRtUv)aneRbIKWCa emKuNkMlaMgkkiténdIenAelICBa¢aMgsMrab; coarse granular soils nigCaersIusþg;kMlaMgkat;TTwgéndIs¥it. emKuNkMlaMgkkit μ EdlGacTTYlyksMrab;RbePTdIepSg²mandUcxageRkam³ - Coarse-grained soils without silt, μ = 0.55 - Coarse-grained soils with silt, μ = 0.45 - Silt, μ = 0.35 - Sound rock, μ = 0.60 kMlaMgkkitsrub F enAelI)atedIm,ITb;nwgkarrGilKW F = μR + H p ¬!$>!#¦ Edl μ = emKuNkMlaMgkkit R = kMlaMgbBaÄrmanGMeBIelI)at H p = kMlaMgTb;Gkmμ emKuNsuvtßiPaBRbqaMgnwgkarrGilKW emKuNsuvtßiPaB = HF = μRH+ H p ≥ 1.5 ¬!$>!$¦ ah ah Edl H ah CabgÁúMkMlaMgedkénsMBaFskmμ H a . emKuNsuvtßiPaBRbqaMgnwgkarrGilminKYr tUcCag 1.5 RbsinebIkMlaMgTb;Gkmμ H p RtUv)anecal nigminKYrtUcCag 2.0 RbsinebI H p RtUv)an ykmkKitBicarNakñúgkarKNna. 7> sßanPaBlMnwgRbqaMgnwgkarRkLab; Stability against Overturning bgÁúMkMlaMgedkénsMBaFskmμ H a nwgeFVIeGayCBa¢aMgTb;RkLab;eFobcMnuc 0 ¬rUbTI 14>7¦. m:U m:g;eFVIeGayRkLab; (overturning moment) M 0 = H a h / 3 . TMgn;rbs;ebtug nigdIbegáItCam:Um:g;Edl eFVIeGaymanlMnwg (balancing moment or rightening moment) edIm,ITb;Tl;nwgm:Um:g;eFVIeGayRk Lab;. m:Um:g;eFVIeGaymanlMnwgsMrab;krNICBa¢aMgdUcbgðajkñúgrUbTI 14>7 KW M b = w1 x1 + w2 x 2 + w3 x3 = ∑ wx emKuNsuvtßiPaBRbqaMgnwgkarRkLab;KW Retaining Walls 324
  11. 11. T.Chhay NPIC emKuNsuvtßiPaB = M b = ∑ ws ≥ 2.0 M H h ¬!$>!%¦ 0 a 3 emKuNsuvtßiPaBenHminRtUvKYrtUcCag 2.0 eT. kMlaMgpÁÜbénkMlaMgTaMgGs;manGMeBIelICBa¢aMgTb; R A RbsBVenA)atCBa¢aMgTb;Rtg;cMnuc C ¬rUb TI 14>7¦. CaTUeTA cMnuc C minRtYtsIuKñaCamYyGkS½rbs;)atCBa¢aMg dUcenHvabegáIt)anCakMlaMgcakp©it enAelIeCIgtag. vaCakarRbesIredayrkSacMnuc C enAkñúgEpñkkNþalénRbEvgmYyPaKbIén)atCBa¢aMg edIm,IeFVIeGay)atCBa¢aMgTaMgmUlsßiteRkamsMBaFdI. ¬krNIeCIgtageRkambnÞúkcakp©itRtUv)anBnül;kñúg emeronTI 13¦. CBa¢aMgTb; 325
  12. 12. Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa 8> smamaRténCBa¢aMgTb; Proportions of Retaining Walls karKNnaCBa¢aMgTb;cab;epþImCamYynwgkarmuxkat;sakl,gEdlmanTMhMRbhak;RbEhl. bnÞab;mkmuxkat;snμt;enaHRtUv)anepÞógpÞat;sßanPaBlMnwg nigPaBRKb;RKan;rbs;eRKOgbgÁúM. xageRkam Cac,ab;EdlGaceRbIedIm,IkMNt;xñatRbhak;RbEhlénEpñkepS²rbs;CBa¢aMgTb; cantilever³ a. kMBs;rbs;CBa¢aMg³ kMBs;srubrbs;CBa¢aMgesμInwgPaBxusKñaénkMritkMBs;bUknwg 900mm eTA 1200mm EdlCakarKNnaCMerAénCMrabTwkkk (frost penetration depth) sMrab;rdæPaKxag eCIgrbs;RbeTsGaemrik. b. kMras;CBa¢aMg³ GaMgtg;sIueténsMBaFekIneLIgeTAtamCMerArbs;CBa¢aMg ehIytMélGtibrmarbs; vasßitenA)atCBa¢aMg. dUcenH m:m:g;Bt;Gtibrma nigkMlaMgkat;TTwgGtibrmaenAkñúgCBa¢aMgekIt U manenAnwg)atrbs;va. kMras;CBa¢aMgenA)atRtUv)ankMNt;esμInwg 1 / 12 eTA 1 / 10 énkMBs;CBa¢aMg h . kMras;rbs;CBa¢aMgenAkMBUlRtUv)ansnμt; 200mm nig 300mm . edaysarCBa¢aMgTb;RtUv KNnasMrab;Tb;sMBaFdIskmμ edIm,IeFVIeGaymanPaBdabrbs;CBa¢aMgtUc vaCakarRbesIredIm,I pþl;nUvépÞCBa¢aMgmanCMralGb,brmakñúgkMrit 25mm kñúgkMBs; 1m . sMrab;CBa¢aMgTabEdlman kMBs; 3m eKGacykkMras;CBa¢aMgefr)at. c. RbEvgeCIgtag³ karkMNt;dMbUgsMrab;RbEvg)atesμInwg 2 / 5 eTA 2 / 3 énkMBs;CBa¢aMg h . Retaining Walls 326
  13. 13. T.Chhay NPIC d. kMras;rbs;)at³ kMras;)atxageRkamRtUv)ankMNt;esμIkMras;CBa¢aMgenA)at EdlesμInwg 1 / 12 eTA énkMBs;CBa¢aMg. kMras;Gb,brmaRtUv)ankMNt;RbEhl 300mm . )atCBa¢aMgGacmankM- 1 / 10 ras;esμI b¤sþÜcenAcugTaMgsgçag Edlmanm:Um:g;Bt;sUnü. smamaRtrbs;CBa¢aMg cantilever retaining wall RtUv)anbgðajenAkñúgrUbTI 14>8. 9> tMrUvkarsMrab;KNna Design Requirement ACI Code, Chapter 14 pþl;nUvviFIsaRsþsMrab;KNnalT§PaBRTRTg;rbs;CBa¢aMg. tMrUvkarcMbg dUcxageRkam³ a. kMras;Gb,brmaénCBa¢aMgKW 1 / 25 énkMBs; b¤énRbEvgCBa¢aMg ykmYyNaEdltUcCageK b:uEnþ minRtUvtUcCag 100mm . b. RkLaépÞGb,brmaénEdkedkenAkñúgCBa¢aMgKW 0.0025bh Edl bh CaRkLaépÞebtugCBa¢aMg. tMélenHRtUv)ankat;bnßyRtwm 0.002bh RbsinebIeKeRbIEdk DB16 b¤EdkEdlmanmuxkat; tUcCagenH nigman f y ≥ 400MPa . sMrab;EdksMNaj;pSar ¬EdkmUl b¤EdkfñaMgGMeBA¦ Rk LaépÞEdkGb,brmaKW 0.002bh . c. RkLaépÞGb,brmaénEdkQrKW 0.0015bh b:uEnþvaRtUv)ankat;bnßyRtwm 0.0012bh RbsinebI Edk DB16 b¤EdkEdlmanGgát;p©ittUcCagenHCamYynwg f y ≥ 400MPa RtUv)aneRbI. sMrab; EdksMNaj;pSar ¬EdkmUl b¤EdkfñaMgGMeBA¦ brimaNEdkGb,brmaKW 0.0012bh . d. KMlatGtibrmaénEdkbBaÄr nigEdkedkKWtMéltUcCageKkñúgcMeNam 450mm b¤kMras;CBa¢aMgbI dg. e. RbsinkMras;CBa¢aMgFMCag 250mm enaHEdkbBaÄr nigEdkedkKYrEtdak;BIrRsTab;RsbKñanwgépÞ xagkñúg nigxageRkA dUcxageRkam³ sMrab;épÞCBa¢aMgxageRkA y:agtic1 / 2 énbrimaNEdk As ¬b:uEnþminRtUveRcInCag 2 As / 3 ¦ KYr mankMras;karBarEdkGb,brma 50mm b:uEnþminRtUvFMCag 1 / 3 énkMras;CBa¢aMg. enHedaysar épÞCBa¢aMgxageRkARbQmnwglkçxNÐGakasFatuepSgKña nigbMErbMrYlsItuNðPaB. sMrab;épÞCBa¢aMgxagkñúg EdktMrUvkarenAkñgTisedAnImYy²KYrmankMras;karBarEdkGb,brma ú 20mm b:uEnþminRtUvFMCag 1 / 3 énkMras;CBa¢aMg. EdkGb,brmaenAkñúgeCIgtagCBa¢aMg eyagtam ACI Code, Section 10.5.3 KWfaEdktMrUvkarsM rab;EdkrYmmaD nigEdksItuNðPaB Edlfa 0.0018bh enAeBl f y = 400MPa nig 0.0020bh CBa¢aMgTb; 327
  14. 14. Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa enAeBl f y = 280MPa b¤ f y = 350MPa . edaysarbrimaNEdkGb,brmamantMéltUc eBk enAkñúgkarGnuvtþeKRtUvtMeLIgvadl;brimaNEdkGb,brma As sMrab;karBt;³ A = s min 4f f' c b d nig ≥ w 1.4 f b d w ¬!$>!^¦ y y 10> karbgðÚrTwk Drainage sMBaFdIEdl)anerobrab;BIxagedImmin)anrab;bBa©ÚlsMBaFGIuRdUsþaTic. RbsinebITwkRbmUlpþúMenA xageRkayCBa¢aMgTb; sMBaFTwkRtUvEtrab;bBa©ÚlkñúgkarKNna. épÞ b¤RsTab;TwkeRkamdIGacRCabenAkñúg dIcak; nigbegáItkrNIdIlicTwk. edIm,IeCosvagsMBaFGIRu dUsþaTic karbgðÚrTwkKYrRtUvdak;enABIeRkayCBa¢aMg. RbsinebIdIGt;manPaBs¥itbgðÚrTwk)anl¥RtUv)aneRbIsMrab;cak;bMeBj CBa¢aMgGacRtUv)anKNnasMrab;Et sMBaFdIsuT§. RbBn§½karbgðÚrTwkGacrYmmanmYy b¤bnSMénkarerobrab;xageRkam³ - rn§Rbehag (weep holes) enAkñúgCBa¢aMgTb;manGgát;p©it 100mm b¤FMCagenH nigmanKMlat RbEhl 1.5m enAkNþalGkS½edk nigGkS½Qr ¬rUbTI 14>9 a ¦. - TIbRbehag (perforated pipe) EdlmnaGgát;p©it 200mm dak;tambeNþayénCBa¢aMgBT§½CMu vijedayxSac; b¤fμbMEbk ¬rUbTI 14>9 b ¦. - labépÞCBa¢aMgxagcak;bMeBjCamYy asphalt edIm,IkarBarkarRCabTwk. - viFIepSgeTotedIm,IbgðÚrTwk ]TahrN_14>1³ muxkat;sakl,grbs;CBa¢aMgTb;ebtugsuT§ semigravity RtUv)anbgðajenAkñúgrUbTI 14>10. CBa¢aMgenHcaM)ac;RtUvkarRtYtBinitüsuvtßiPaBTb;nwgkarRkLab;/ karrGil nigRTRTg;nUvsMBaFBI eRkameCIgtag. eKeGay³ TMgn;maDdIcak;bMeBj 17.6kN / m3 / mMukkitkñúg φ = 35o / emKuNkkitrvag ebtug nigdI μ = 0.5 / sMBaFdIGnuBaØatKW 120kN / m 2 nig f 'c = 20MPa . Retaining Walls 328
  15. 15. T.Chhay NPIC dMeNaHRsay³ 1> edayeRbIsmIkar Rankine 1 − sin φ 1 − 0.574 Ca = = = 0.271 1 + sin φ 1 + 0.574 sMBaFGkmμenAEpñkxagmuxKWsMrab;kMBs; 300mm EdlCatMéltUcGacecal)an. C a wh 2 0.271× 17.6 × 3.32 Ha = = = 26kN 2 2 CBa¢aMgTb; 329
  16. 16. Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa Ha eFVIGMeBIenAcMgay h / 3 = 1.1m BI)at. 2> m:Um:g;eFVIeGayRkLab; (overturning moment) KW M 0 = 26 ×1.1 = 28.6kN .m 3> KNnam:Um:g;eFVIeGaymanlMnwg (balancing moment) M b edayKiteFobcMnuc 0 ¬rUbTI 14>10¦³ TMgn; (kN ) édXñas; (m) m:Um:g; (kN .m) w1 = 0.3 × 3 × 24 = 21.6 0 .4 8.64 w2 = × 3 × (1.05 − 0.3) × 24 = 27 1 0 .8 21.6 2 w3 = 0.3 × 1.6 × 24 = 11.52 0 .8 9.22 w4 = × 3 × (1.05 − 0.3) × 17.6 = 19.8 1 1.05 20.79 2 w5 = 0.3 × 3 × 17.6 = 15.84 1.45 23 ∑ w = R = 95.76kN M b = ∑ M = 83.25kN 4> emKuNsuvtßiPaBRbqaMgnwgkarRkLab;KW 83.25 / 28.6 = 2.91 > 2.0 5> kMlaMgRbqaMgkarrGil F = μR = 0.5 × 95.76 = 47.88kN emKuNsuvtßiPaBTb;nwgkarrGilKW F / H a = 47.88 / 26 = 1.84 > 1.5 6> KNnasMBaFdIeRkam)at a. cMgayrbs;kMlaMgpÁÜbBIcMnuc 0 M b − M 0 83.25 − 28.6 x= = = 0.57 m R 95.76 cMNakp©itKW e = 0.8 − 0.57 = 0.23m . kMlaMgpÁÜb R manGMeBIenAkñúgEpñkkNþalénmYyPaKbI RbEvgeCIgtag nigmancMNakp©it e = 0.23m BIGkS½rbs;)at ¬rUbTI 14>10¦. b. sMrab;eCIgtagRbEvg 1m nigRbEvgeCIgtagRbsiT§PaB 1.6m m:Um:g;niclPaB I = 1×1.63 /12 = 0.34m 4 / RkLaépÞ A = 1.6m 2 c. sMBaFdIenAcugTaMgBIrrbs;eCIgtagKW q1, q2 = R / A ± Mc / I . m:Um:g; M KW R ⋅ e = 95.76 × 0.23 = 22kN .m nig c = 0.8m 95.76 22 × 0.8 q1 = + = 111.6kN 1.6 0.34 95.76 22 × 0.8 q2 = − = 8.1kN 1.6 0.34 Retaining Walls 330
  17. 17. T.Chhay NPIC 7> RtYtBinitükugRtaMgBt;enAkñúgebtugRtg;cMnuc A a. sMBaFdIRtg;cMnuc A ¬BIFrNImaRt¦KW ⎛ 1.35 ⎞ q A = 8.1 + ⎜ ⎟(111.6 − 8.1) = 95.4kN ⎝ 1.6 ⎠ b. m:Um:g; M A RtUv)anKNnaenARtg; A bNþalmkBIkugRtaMgctuekaNEkg nigkugRtaMg RtIekaN 95.4 × 0.25 2 16.2 × 0.25 ⎛ 2⎞ MA = + ⎜ 0.25 × ⎟ = 3.32kN .m 2 2 ⎝ 3⎠ c. kugRtaMgBt;enAkñúgebtugKW Mc 3.32 × 0.15 = −3 ⋅10 − 3 = 0.221MPa I 2.25 ⋅10 Edlc= = h 0.3 2 2 = 0.15m nig I = 1× 0.33 / 12 = 2.25 ⋅10 −3 m 4 d. m:UDuldac;rbs;ebtug (modulus of rupture of concrete) KW 0.623 f 'c = 2.8MPa > 0.221MPa emKuNsuvtßiPaBRbqaMgnwgkareRbHKW 02221 = 12.67 . dUcenH . .8 muxkat;manlkçN³RKb;RKan;. eKmincaM)ac;esñInUvmuxkat;epSgeTotedIm,IRtYtBinitüeT. ]TahrN_14>2³ KNnaCBa¢aMgTb; cantilever edIm,ITb;dIRcaMgkMBs; 5m . enAelIdIEdlTb;manbnÞúk bEnßm 9.25kN / m 2 . eKeGay³ TMgn;maDdIcak;bMeBj 18.5kN / m3 / mMukkitkñúg φ = 35o / emKuNkkit rvagebtug nigdI μ = 0.5 / emKuNkkitrvagRsTab;dI μ = 0.7 / lT§PaBRTdIGnuBaØat 200kN / m 2 / f 'c = 20MPa nig f y = 400MPa . dMeNaHRsay³ 1> kMNt;TMhMrbs;CBa¢aMgTb;edayeRbITMnak;TMngRbhak;RbEhlEdl)anbgðajenAkñúgrUbTI 14>8 a. kMBs;CBa¢aMg³ edaybgáb;CBa¢aMgTb; 900mm enaHkMBs;rbs;CBa¢aMgTb; h = 5 + 0.9 = 5.9m b. kMras;)at³ snμt;kMras;)atesμI 0.08h = 0.08 × 5.9 = 0.472m yk 0.45m . kMBs;rbs;tY CBa¢aMg 5.45m c. RbEvgeCIgtag³ RbEvgeCIgtagERbRbYlcenøaH 0.4h nig 0.67 h . edaysnμt;yktMél mFüm enaHRbEvgeCIgtagesμI 0.53h = 0.53 × 5.9 = 3.127m yk 3.2m . CBa¢aMgTb; 331
  18. 18. Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa RbEvg)atenABImuxtY CBa¢aMgERbRbYlcenøaH 0.17h nig 0.125h . snμt;RbEvg)atxagmux esμI 0.17 × 5.9 = 1m . d. kMras;CBa¢aMg³ kMras;Gtibrmarbs;CBa¢aMgsßitenAKl;EdlERbRbYlcenøaH 0.08h eTA 0.1h . eRCIserIskMras;CBa¢aMgGtibrmaesμInwgkMras;eCIgtagKW 0.45m . kMras;Gb,brmarbs;CBa¢aMg sßitenAkMBUlrbs;CBa¢aMg edaykMNt;yk 0.3m . CMralGb,brmarbs;épÞCBa¢aMgKW 25mm / m . sMrab;CBa¢aMgEdlmankMBs; 5.45m enaHRbEvgsþÜcesμInwg 5.45 × 0.025 = 0.136m EdltUcCagRbEvgsþÜcEdlman 0.45 − 0.3 = 0.15m . TMhMrbs;CBa¢aMg Edl)anesñIeLIgRtUv)anbgðajenAkñúg rUbTI14>11. 2> tamsmIkar Rankine ³ 1 − sin φ 1 − 0.574 Ca = = = 0.271 1 + sin φ 1 + 0.574 3> emKuNsuvtßiPaBRbqaMgnwgkarRkLab;GacRtUv)ankMNt;dUcxageRkam³ a. KNnakMlaMgKμanemKuNBitR)akdEdlmanGMeBIelICBa¢aMgTb;. dMbUg kMNt;nUvral;kMlaMg EdleFVIeGayCBa¢aMgRkLab;³ Retaining Walls 332
  19. 19. T.Chhay NPIC hs ¬EdlbNþalBIbnÞúkelIs¦ = ws = 1825 = 0.5m w 9. .5 p1 = C a whs = 0.271× 18.5 × 0.5 = 2.5kN / m 2 p2 = C a wh = 0.271× 18.5 × 5.9 = 29.58kN / m 2 H a 2 = 2.5 × 5.9 = 14.75kN édXñas; = 5.9 2 = 2.95m 1 H a 2 = 29.58 × 5.9 = 87.26kN 2 édXñas; = 5.9 3 = 1.97m b. m:Um:g;EdleFVIeGayRkLab; (overturning moment) KW 14.75 × 2.95 + 87.26 × 1.97 = 215.4kN.m c. m:Um:g;eFVIeGaymanlMnwgEdlRbqaMgnwgkarRkLab; ¬emIlrUbTI 14>12¦ CBa¢aMgTb; 333
  20. 20. Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa kMlaMg (kN ) édXñas; (m) m:Um:g; (kN .m) w1 = 0.3 × 5.45 × 25 = 40.875 1 .3 53.14 1 w2 = 0.15 × 5.45 × 25 = 10.22 1 .1 11.24 2 w3 = 3.2 × 0.45 × 25 = 36 1 .6 57.6 w4 = 1.75 × 5.45 × 18.5 = 176.44 2.375 419 ∑ w = R = 263.5kN ∑ M = 541kN .m emKuNsuvtßiPaBRbqaMgnwgkarRkLab;KW 215.4 = 2.51 > 2 541 4> KNnasMBaFdIeRkameCIgtag. Kitm:Um:g;eFobcMnuc 0 ¬rUbTI 14>12¦ edIm,IkMNt;TItaMg kMlaMgpÁÜb R énkMlaMgbBaÄr x= ∑ M − ∑ Hy = balancing M − overturning M = 541 − 215.4 R R 263.5 3.2 = 1.236m > = 1.066m 3 cMNakp©itKW e = 3.2 / 2 − 1.236 = 0.364m . kMlaMgpÁÜb R manGMeBIenAkñúgEpñkkNþalén RbEvgmYyPaKbIéneCIgtag nigmancMNakp©it e = 0.476m BIGkS½rbs;eCIgtag. sMrab; RbEvgbeNþay 1m rbs;eCIgtag RkLaépÞ = 1× 3.2 = 3.2m 2 3.23 m:Um:g;niclPaB I = 1× 12 = 2.73m 4 R R ⋅ e ⋅ C 263.5 263.5 × 0.364 × 1.6 q1 = + = + = 138.56kN / m 2 < 200kN / m 2 A I 3.2 2.73 R R ⋅ e ⋅ C 263.5 263.5 × 0.364 × 1.6 q2 = − = − = 26.13kN / m 2 A I 3.2 2.73 sMBaFdIKWRKb;RKan; 5> KNnaemKuNsuvtßiPaBRbqaMgnwgkarrGil. emKuNsuvtßiPaBGb,brmaRtUvesμI 1.5 . kMlaMgeFVIeGayrGil = H a1 + H a2 = 14.75 + 87.26 = 102kN kMlaMgTb;kMueGayrGil = μR = 0.5 × 253.5 = 126.75kN emKuNsuvtßiPaBRbqaMgnwgkarrGil = 126.75 = 1.24 < 1.5 102 kMlaMgTb;RbqaMgnwgkarrGilEdlmanmin)anpþl;suvtßiPaBRKb;RKan;RbqaMgnwgkarrGileT. enA kñúgkrNIenH key RtUv)anbegáItedIm,IbegáItsMBaFGkmμFMRKb;RKan;edIm,ITb;nwgkMlaMgd¾FMEdleFVI Retaining Walls 334
  21. 21. T.Chhay NPIC eGayrGil. tYnaTIepSgeTotrbs; key KWpþl;nUvRbEvgbgáb;RKb;RKan;sMrab;Edk dowel rbs;tY CBa¢aMg. dUcenH key RtUv)andak;enATItaMgEdlépÞxagmuxrbs;vamancMgay 150mm BIépÞxag eRkayrbs;CBa¢aMg ¬rUbTI14>13¦. enAkñúgkarKNnasMBaFGkmμ dIenABIelIeCIgtagEpñkxag muxRtUv)anecalkñúgkMBs; 300mm . dUcenHenAkñúg]TahrN_enHkMBs;dIKItBI)ateCIgtagesμI 600mm . snμt; key mankMBs; t = 450mm nigTTwg b = 450mm . 1 + sin φ 1 1 Cp = = = = 3.69 1 − sin φ C a 0.271 H p = C p w(h'+t )2 = 3.69 × 18.5(0.6 + 0.45)2 = 37.63kN 1 1 2 2 LÚvkarrGilGacnwgekItmanenAelIépÞ AC / CD nig EF ¬rUbTI14>13¦. épÞrGil AC CaépÞrGilrvagRsTab;dInigRsTab;dIEdlmanemKuNkMlaMgkkitkñúg = tan φ = tan 35o = 0.7 . cMENkÉépÞrGil CD nig EF CaépÞrGilrvagebtugnigRsTab;dIEdlmanemKuNkMlaMgkkitkñúg esμI 0.5 dUcEdl)aneGayenAkñúgsmμtikmμrbs;]TahrN_. CBa¢aMgTb; 335
  22. 22. Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa ersIusþg;kMlaMgkkitKW F = μ1R1 + μ 2 R2 . ⎛ 138.56 + 92.89 ⎞ R1 = Rbtikmμén AC = ⎜ ⎟ × 1.3 = 150.4kN ⎝ 2 ⎠ R2 = R − R1 = 263.5 − 150.4 = 113.1kN ⎛ 92.89 + 26.13 ⎞ R2 = Rbtikmμén CDF = ⎜ ⎝ 2 ⎟ × 1.9 = 113.1kN ⎠ F = 0.7 × 150.4 + 0.5 × 113.1 = 161.83kN kMlaMgTb;srubKW F + H p = 161.83 + 37.63 = 199.5kN emKuNsuvtßiPaBRbqaMgnwgkarrGilKW 199.5 = 1.96 < 1.5 b¤ 161.83 = 1.59 < 1.5 102 102 emKuNsuvtßiPaBFMCag 1.5 EdlRtUv)anENnaMenAeBlEdlsMBaFGkmμRbqaMgnwgkarrGilmin RtUv)anKitbBa©Úl. 6> KNnatYCBa¢aMg. karKNnaénGgát;ebtugGarem:GaceFVI)anedayeRbI ACI Code alternative design method, appendix B and C. a. Edkem (main reinforcement)³ kMlaMgtamTisedkEdlGnuvtþmkelICBa¢aMgRtUv)anKNna edayeRbIemKuN 1.6 . muxkat;eRKaHfñak;sMrab;m:Um:g;Bt;KWsßitenARtg;)aténCBa¢aMg ¬kMBs; h = 5.45m ¦ KNnakMlaMgemKuN P = 1.6(C a whs ) = 1.6(0.271× 18.5 × 0.5) = 4.01kN / m 2 1 P2 = 1.6(C a wh ) = 1.6(0.271× 18.5 × 5.45) = 43.72kN / m 2 H a1 = 4.01× 5.45 = 21.85kN édXñas;= 5.45 2 = 2.725m 1 H a 2 = 43.72 × 5.45 = 119.14kN 2 édXñas; = 5.45 3 = 1.82m Mu ¬enA)atrbs;CBa¢aMg¦ = 21.85 × 2.725 + 119.14 ×1.82 = 276.4kN .m kMras;srubEdleRbIKW 450mm / b = 1m nig d = 0.45 − (concrete cover) − (half the bar diameter) = 0.387m Mu 276.4 ⋅10 6 Ru = = = 1.85MPa bd 2 1000 × 387 2 0.85 f 'c ⎡ ⎤ PaKryEdk ρ= ⎢1 − 1 − 2 Ru φ 0.85 f 'c ⎥ = 0.0058 fy ⎣ ⎢ ⎥ ⎦ Retaining Walls 336
  23. 23. T.Chhay NPIC As = 0.0058 × 1000 × 387 = 2244.6mm 2 eRbI DB25 KMlat 200mm ¬ As = 2454.4mm 2 ¦. EdkbBaÄrGb,brma As eyagtam ACI Code, Section 14.3 KW As = 0.0015 × 450 × 1000 = 675mm 2 < 2454.4mm 2 edaysarEtm:Um:g;fycuHtamkMBs;rbs;CBa¢aMg As KYrRtUv)ankat;bnßyeTAtamm:Um:g;Edl ekItmanenAelICBa¢aMg. CakarGnuvtþn_ eKKYreRbI As b¤KMlatmYy sMrab;Bak;kNþalCBa¢aMg xageRkam nig As b¤KMlatmYyepSgeTot sMrab;Bak;kNþalCBa¢aMgxagelI. edIm,IKNna m:Um:g;enAkMBs;Bak;kNþalCBa¢aMg ¬ 2.725m BIkMBUl¦ P = 1.6(C a whs ) = 1.6(0.271× 18.5 × 0.5) = 4.01kN / m 2 1 P2 = 1.6(C a wh ) = 1.6(0.271× 18.5 × 2.725) = 21.86kN / m 2 H a1 = 4.01× 2.725 = 10.93kN édXñas; = 2.725 2 = 1.36m 1 H a 2 = 21.86 × 2.725 = 29.78kN 2 édXñas; = 2.725 3 = 0.91m Mu ¬enAkMBs;Bak;kNþal¦ = 10.93 ×1.36 + 29.78 × 0.91 = 41.96kN .m kMras;srubenAkMBs;Bak;kNþalKW 300 + 450 = 375mm / b = 1m nig 2 d = 0.375 − 0.05 − 0.013 = 0.312m Mu 41.96 ⋅10 6 Ru = 2 = = 0.43MPa bd 1000 × 312 2 0.85 f 'c ⎡ 2 Ru ⎤ PaKryEdk ρ= ⎢1 − 1 − ⎥ = 0.0013 φ 0.85 f 'c ⎥ fy ⎣ ⎢ ⎦ As = 0.0013 × 1000 × 312 = 405.6mm 2 As min = 0.0015 × 1000 × 375 = 562.5mm 2 > 405.6mm 2 eRbIEdk DB12 KMlat 200mm ¬ As = 565.5mm 2 ¦. b. EdksItuNðPaB nigEdkrYmmaD³ EdkedkGb,brmaenA)atCBa¢aMgGaRs½ynwg ACI Code, Section 14.3 KW As min = 0.002 × 1000 × 450 = 900mm 2 ¬sMrab;mYyPaKbIBI)at¦/ edaysnμt;eRbIEdk DB16 b¤tUcCagenH. As min = 0.002 × 1000 × 400 = 800mm 2 CBa¢aMgTb; 337
  24. 24. Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa ¬sMrab;BIPaKbIBIkMBUl¦. edaysar épÞxagmuxrbs;CBa¢aMgrgnUvbMErbMrYlsIuNðPaB dUcenH eKeRbI mYyPaKBIreTAmYyPaKbIénEdkedk enAépÞxageRkArbs;CBa¢aMg nigdak;nUvbrimaN dUcKñaenAépÞxagkñúg. 0.5 As = 0.5 × 900 = 450mm 2 eRbIEdk DB12 KMlat 200mm ¬ As = 565.5mm 2 ¦enATaMgépÞxagkñúg nigépÞxageRkA rbs;CBa¢aMg. eRbIEdk DB12 KMlat 300mm edIm,IRTEdkedkrYmmaD nigEdksItuNðPaB. c. Edk dowel sMrab;EdkbBaÄr³ RbEvgf<k;rbs;Edk DB25 eTAkñúgeCIgtagRtUvEtman RbEvg y:agticbMput 550mm . eRbIRbEvgEdkbgáb; 600mm eTAkñúgeCIgtag nig key BIeRkamtY CBa¢aMg. d. KNnasMrab;kMlaMgkat;TTwg³ muxkat;eRKaHfñak;sMrab;kMlaMgkat;TTwgsßitenAcMgay d = 0.387 mm BI)attYCBa¢aMg. enARtg;muxkat;enH cMgayBIkMBUlesμI 5.45 − 0.387 = 5.063m P = 1.6(C a whs ) = 1.6(0.271× 18.5 × 0.5) = 4.01kN / m 2 1 P2 = 1.6(C a wh ) = 1.6(0.271× 18.5 × 5.063) = 40.61kN / m 2 H a1 = 4.01× 5.063 = 20.3kN 1 H a 2 = 40.61× 5.063 = 102.8kN 2 H = H a1 + H a 2 = 123.1kN φVc = φ 0.17 f 'c bd = 0.75 × 0.17 20 × 1000 × 387 ⋅10 −3 = 220.7kN > 123.1kN 7> KNnaeCIgtagEpñkxageRkayCBa¢aMg³ emKuNbnÞúk 1.2 RtUv)aneRbIsMrab;KNnam:Um:g;Bt;emKuN nigkMlaMgkat;TTwgEdlekItBIdIcak;bMeBjnigebtug. cMENkÉemKuNbnÞúk 1.6 RtUv)aneRbI sMrab;bnÞúkbEnßm. sMBaFdIeLIgelIRtUv)anecaledaysarvanwgkat;bnßyT§iBléndIcak;bMeBj nigebtugeTAelI eCIgtagEpñkxageRkayCBa¢aMg. eyagtamrUbTI 14>12 bnÞúksrubenAelIeCIg tagEpñkxageRkayrbs; CBa¢aMgKW Vu = 1.2(5.45 × 1.75 × 18.5 + 0.45 × 1.75 × 25) + 1.6 × 0.5 × 1.75 × 18.5 = 261.3kN Mu ¬enARtg;épÞCBa¢aMg¦= Vu 1.75 2 = 228.64kN .m Retaining Walls 338
  25. 25. T.Chhay NPIC CaTUeTAmuxkat;eRKaHfñak;sMrab;kMlaMgkat;TTwgsßitenAcMgay d BIépÞCBa¢aMgenAeBlEdlkMlaMg RbtikmμbegáItkMlaMgsgát;enAtMbn;xagcugrbs;Ggát;. kñúgkrNIenH muxkat;eRKaHfñak;RtUv)anKit faekItmanenAnwgépÞCBa¢aMg edaysarEtkMlaMgTaj minEmnkMlaMgsgát;ekItmanenAkñúgebtug. Vu = 261.3kN φ2 2 φVc = f 'c bd = 0.75 × 20 × 1000 × 362 ⋅10 − 3 = 202.4kN < 261.3kN 12 12 edaysar φVc < Vu = 216.3kN enaHmuxkat;RtUv)antMeLIgedayGRta 261.3 / 202.4 b¤k¾Edk kMlaMgkat;TTwgRtUv)andak;. d caM)ac; = 261.3 × 362 = 467mm 202.4 kMras;eCIgtagsrubcaM)ac; = 467 + 75 + 13 = 555mm ykkMras;eCIgtagesμI 560mm nig d = 472mm 228.64 ⋅10 6 Ru = = 1.03MPa ρ = 0.0031 1000 × 472 2 As = 1463.2mm 2 EdkrYmmaDGb,brma As = 0.0018 ×1000 × 560 = 1008mm 2 EdkrgkarBt;Gb,brma As = 0.0033 ×1000 × 472 = 1557.6mm 2 eRbIEdk DB20 manKMlat 200mm ¬ As = 1570.8mm 2 ¦. RbEvgEdkbgáb;sMrab; DB20 esμI nwg 1.4ld = 1100mm . dUcenHEdkRtUv)andak;bgðÜscUleTAkñúgEpñkxagmuxrbs;eCIgtageday RbEvg 1100mm . EdkrYmmaD nigEdksItuNðPaBsMrab;TisedAEvgmincaM)ac;RtUv)andak;enAkñúgeCIgtagEpñkxagmux nigEpñkxageRkayrbs;eCIgtageT. b:uEnþCakarGnuvtþn_ eKRtUvdak;brimaNEdkGb,brmaenAkñúg TisedAenH edayeRbI DB12 @ 300 . 8> KNnaeCIgtagEpñkxagmuxCBa¢aMg³ Epñkxagmuxrbs;eCIgtageFVIkardUcCaFñwm cantilever Edl rgnUvsMBaFdIeLIgelICamYynwgbnÞúkemKuN 1.6 edaysarvaekIteLIgCadMbUledaykMlaMgxag. muxkat;eRKaHfñak;sMrab;kMlaMgkat;TTwgsßitenAcMgay d BIépÞxagmuxrbs;CBa¢aMg edaysarEt RbtikmμenAkñúgTisedAénkMlaMgkat;TTwgbegáItkMlaMgsgát;enAkñúgEpñkxagmuxrbs;eCIgtag. eyagtamrUbTI 14>13 Epñkxagmuxrbs;eCIgtagrgnUvsMBaFeLIgelIedaysardI nigsMBaFcuH eRkamedaysarbnÞúkpÞal;rbs;kMraleCIgtagEpñkxagmux. CBa¢aMgTb; 339
  26. 26. Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa ⎛ 138.56 + 120 ⎞ Vu = 1.6⎜ ⎟0.528 − 1.2(0.56 × 25)0.528 = 100.3kN ⎝ 2 ⎠ vamantMéltUcCag φVc = 263.8kN . ⎡103.43 2 2⎤ ⎡ 12 ⎤ M u = 1.6⎢ 1 + (138.56 − 103.43) × 1× 0.5 × ⎥ − 1.2⎢0.56 × 25 ⎥ = 93.1kN .m ⎣ 2 3⎦ ⎢ ⎣ 2⎥⎦ Mu 93.1 ⋅10 6 Ru = = = 0.42MPa ρ = 0.00125 bd 2 1000 × 472 2 As = 0.00125 × 1000 × 472 = 590mm 2 Retaining Walls 340
  27. 27. T.Chhay NPIC EdkGb,brmasItuNðPaB nigrYmmaD As = 0.0018 ×1000 × 560 = 1008mm 2 EdkGb,brmargkarBt; As = 0.0033 ×1000 × 472 = 1557.6mm 2 eRbIEdk DB20 manKMlat 200mm dUcKñanwgEpñkxagmuxCBa¢aMg. RbEvgEdkbgáb;sMrab;Edk DB 20 esμInwg 650mm . bgðÜsEdkcUleTAkñúgEpñkxageRkayCBa¢aMgRbEvg 650mm . bøg;srés EdklMGitRtUv)anbgðajenAkñúgrUbTI 14>14. 9> Shear keyway rvagCBa¢aMg nigeCIgtag³ enAkñúgkarsagsg;CBa¢aMgTb; eCIgtagRtUv)ancak;mun bnÞab;mkeTIbEpñkxagelIRtUv)ancak;bnþ. Construction joint RtUv)aneRbIenA)atCBa¢aMg. épÞ tMNrRtUv)anykmanragCa keyway dUcbgðajenAkñúgrUbTI 14>15 b¤RtUvTukeGaymanlkçN³ KeRKIm ¬rUbTI 14>14¦. tMNrRtUvmanlT§PaBbBa¢ÚnkMlaMgkat;TTwgBItYCBa¢aMgeTAeCIgtag. 10> enAkñúgkarKNnaenH eKcaM)ac;RtUvdak;RbBn§½bgðÚrTwkBIdIcak;bMeBjeGay)anRtwmRtUv BIeRBaHsM BaFdIEdleRbIKWsMrab;dIcak;bMeBjEdlbgðÚrTwkecj. Weep holes KYrRtUv)andak;enAkñúgCBa¢aMg EdlmanGgát;p©it 100mm manKMlat 1.5m tamTisedAedk nigTisedAbBaÄr. 11> CBa¢aMgCan;eRkamdI Basement Walls CBa¢aMgCan;eRkamdIRtUv)aneKsnμt;fasßitenAcenøaHkMralxNнCan;eRkamdI nigkMralxNнCan;pÞal;dI. eKmanBIrkrNIkñúgkarKNnaCBa¢aMgCan;eRkamdI. TImYy enAeBlEdlCBa¢aMgRtUv)ansg;enABIelIkMralxNнCan;eRkamdI CBa¢aMgnwgrgnUvsMBaFdItam Tisedk nigminrgbnÞúkbBaÄreRkABIbnÞúkpÞal;xøÜn. kñúgkrNIenH CBa¢aMgmannaTICa cantilever ehIybri- maNEdkRKb;RKan;KYrRtUv)andak;sMrab;karKNnaCBa¢aMg cantilever. krNIenHGaceCosvag)aneday tMeLIgkMralxNнCan;eRkamdI nigkMralxNнCan;TImYymuxnwgcak;bMeBjdI. TIBIr enAeBlEdlkMralxNнCan;TImYy nigkMralxNнCan;epSgeTotRtUv)ansg; ehIysMNg; RtUv)andak;bnÞúkeBj enaHCBa¢aMgCan;eRkamdImannaTICaCBa¢aMg propped cantilever EdlrgnUvsMBaFdI k¾dUcCasMBaFbBaÄr. sMrab;mMukkitkñúg φ = 35o enaHemKuNsMBaFskmμ Ca = 0.271 . sMBaFsIedkenAnwg)atKW Pa = C a wh . sMrab; w = 17.6kN / m 3 nigCBa¢aMgmankMBs;mFüm h = 3m enaH Pa = 0.271× 17.6 × 3 = 14.31kN / m 2 32 H a = 0.271× 17.6 × 2 = 21.46kN / m énCBa¢aMg CBa¢aMgTb; 341
  28. 28. Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa Ha eFVIGMeBIenARtg; h / 3 = 3 / 3 = 1m BI)at. sMBaFbEnßmRbEhl 9.6kN / m 2 RtUv)anKitfa manenAelIdIxageRkayCBa¢aMg enaH 9.6 hs = = 0.55m 17.6 Ps = C a whs = 0.271× 17.6 × 0.55 = 2.62kN / m 2 H s = (Ca whs )h = 2.62 × 3 = 7.86kN / m énCBa¢aMg H s énbnÞúkbEnßmeFVIGMeBIenA h / 2 = 1.5m BI)at. kñúgkarKNnaelIkmun eK)ansnμt;fadIcak;bMeBjmanlkçN³s¶Üt b:uEnþsMrab;krNIenHeKcaM)ac; RtUvKitBIsMBaFTwkenABIeRkayCBa¢aMg. sMBaFTwkGtibrmaekItmanenAeBlkMBs;CBa¢aMgTaMgmUlrbs; CBa¢aMgCan;eRkamdIrgnUvsMBaFTwk. Pw = 10 × 3 = 30kN / m 2 wh 2 32 Hw = = 10 = 45kN / m énCBa¢aMg 2 2 sMBaFGtibrmaminGacmanvtþmanenABIeRkayCBa¢aMgCab;rhUteT. dUcenH RbsinebIdIesImyUr² mþg enaHeKGacyksMBaFTwkRtwm 50% mkKit. Pw 30 = = 15kN / m 2 2 2 H H ' w = w = 22.5kN / m 2 énCBa¢aMg H ' w eFVIGMeBIenA h / 3 = 3 / 3 = 1m BI)at. TwkGacRtUv)ankarBarBIkarRbmUlpþúMRbqaMgnwgCBa¢aMg edayerobcMkarbgðÚrenAEpñkxageRkaménCBa¢aMg. bEnßmBIelIkarerobcMRbBn§½bgðÚr CBa¢aMgEpñkxageRkARtUvlabfñaMkarBarCMrabTwk (waterproofing or damp-proofing membrane) . ACI Code, Section 14.5 kMNt;fakMras;Gb,brmaénCBa¢aMgeRkam dIEpñkxageRkA nigRKwHrbs;vaKW 190mm . CaTUeTA kMras;Gb,brmarbs;CBa¢aMgRTesμInwgtMéltUcCageK kñúgcMeNam 1/ 25 énkMBs; b¤1/ 25 éRbEvgCBa¢aMg b¤ 100mm . ]TahrN_14>3³ kMNt;kMras; nigbrimaNEdkcaM)ac;sMrab;CBa¢aMgTb;Can;eRkamdIdUcbgðajkñúgrUbTI 14>16. eKeGay³ TMgn;maDdIcak;bMeBj 17.6kN / m3 / mMukkitkñúg φ = 35o / f 'c = 20MPa nig f y = 400MPa . dMeNaHRsay³ Retaining Walls 342
  29. 29. T.Chhay NPIC 1> CBa¢aMgmanElVgtamTisQr nigRtUv)ancat;TukfamanTMrbgáb;enA)at nigTMr propped enA kMBUl. edaycat;TukRbEvgElVg L = 2.925m dUcbgðajkñúgrUbTI 14>16. sMBaFxag epSg²EdlmanGMeBIelICBa¢aMgkñúgRbEvg 1m mandUcteTA³ sMBaFEdlekItBIsMBaFdI Pa = 14.31kN / m nig H a = 21.46kN sMBaFEdlekItBIsMBaFTwk Pw = 15kN / m nig H w = 22.5kN sMBaFEdlekItBIbnÞúkelIs Ps = 2.62kN / m nig H s = 7.86kN H a nig H w KWbNþalmkBIbnÞúkBRgayrayRtIekaN b:uEnþ H s )anBIbnÞúkBRgayesμI. BI rUbTI 14>16 nigedayeRbIemKuNm:Um:g;énFñwm propped EdlrgbnÞúkRtIekaN nigbnÞúk BRgayesμI CamYynwgemKuNbnÞúk = 1.6 (ACI Code, Appendix C) M u = 1.6(H a + H w ) L L + 1.6 H s 7.5 8 = 1.6(21.46 + 22.5) 2.925 2.925 + 1.6 × 7.86 × = 32.03kN.m 7.5 8 ⎛ 21.46 + 22.5 7.86 ⎞ 32.03 RB = 1.6⎜ + ⎟− = 18.78kN ⎝ 3 2 ⎠ 2.925 R A = 1.6(21.46 + 22.5 + 7.86 ) − 18.78 = 64.13kN m:Um:g;viC¢manGtibrmaEdlekItmanenAmuxkat;EdlmankMlaMgkat;sUnü ⎛ 14.31 + 15 ⎞ x 2 Vu = 18.78 − 1.6(2.62 x ) − 1.6⎜ ⎟ =0 ⎝ 2.925 ⎠ 2 x = 1.291m ⎛ 2.62 2 12.94 1.291 ⎞ 2 M c = 18.78 × 1.291 − 1.6⎜ 1.291 + ⎟ = 15kN .m ⎜ 2 2 3 ⎟ ⎝ ⎠ 2> edaysnμt; ρ = 0.01 enaH Ru = 3MPa Mu 30.03 ⋅ 10 6 d= = = 100mm Ru b 3 × 1000 kMras;srub = 100 + 40 + 6 = 146mm . eRbIkMras; 190mm dUcenH d = 144mm Mu 30.03 ⋅10 6 Ru = = = 1.45MPa bd 2 1000 ×144 2 PaKryEdk ρ = 0.0045 nig As = 0.0045 ×1000 ×144 = 648mm 2 As Gb,brma = 0.0015bh = 0.0015 × 1000 × 190 = 285mm 2 As Gb,brmargkarBt; = 0.0033 ×1000 ×144 = 475.2mm 2 CBa¢aMgTb; 343
  30. 30. Department of Civil Engineering viTüasßanCatiBhubec©keTskm<úCa eRbIEdk DB16 manKMlat 300mm ¬ As = 670mm 2 ¦ 3> sMrab;m:Um:g;viC¢man M c = 15kN .m 15 ⋅10 6 Ru = = 0.72MPa ρ = 0.0022 1000 ×144 2 As = 0.0022 × 1000 × 144 = 316.8mm 2 < 670mm 2 eRbIEdk DB12 manKMlat 250mm ¬ As = 452mm 2 ¦ 4> m:Um:g;sUnüekItmanenAcMgay 2.288m BIkMBUl nig 0.637m BI)at. RbEvgRCYsrbs;Edk DB16 KW 360mm ¬tMbn;sgát;¦. dUcenH dak;Edkem DB16 RbEvg 637 mm + 360mm = 997 mm b¤ 1000mm BI)at rYcbnÞab;mkeRbIEdk DB12 KMlat 300mm enAépÞxageRkA. sMrab;épÞxagkñúg eRbIEdk DB12 KMlat 250mm . Retaining Walls 344
  31. 31. T.Chhay NPIC 5> brimaNEdkbeNþay³ eRbIPaKryEdkGb,brma ρ = 0.002 ¬ACI Code, Section 14.3¦ b¤ As = 0.002 × 1000 × 190 = 380mm2 . eRbI DB12 KMlat 300mm enAépÞTaMgsgçag. 6> RbsinebIm:Um:g;Bt;enA)aténCBa¢aMgmantMélFM enaHeKcaM)ac;RtUvkarkMras;kMralxNнCBa¢aMg FM ]TahrN_ 300mm b¤FMCagenH. enAkñúgkrNIxøHeKGaceRbI haunch dUcbgðajkñúgrUbTI 14>17. eKeFVIEbbenHedIm,Ikat;bnßykMras;CBa¢aMg edaysarEtm:Um:g;RtUv)anKNnaenAelI muxkat;BIelI haunch Etmþg. 7> kMralxNнCan;eRkamdIGacmankMras;FMCagkMras;CBa¢aMg nigGacRtUv)anBnøÚtecjeRkAhYs épÞCBa¢aMgRbEhl 250mm b¤FMCagenHRbsinebIcaM)ac;. CBa¢aMgTb; 345

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