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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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