This document contains section notes on foundation engineering from a third year civil engineering course. It discusses terminology and sizing parameters for retaining walls, including factors related to height. It also describes two potential failure modes - overturning and sliding - and provides equations for calculating resisting and driving moments or forces to ensure adequate safety factors against each failure mode. Friction coefficients are provided for different soil types. The use of passive pressure is also mentioned to supplement friction forces if insufficient on their own.

1. *5;9*5;9*5;9*5;9 ͮ ϯƌĚ zĞĂƌ ʹ ŝǀŝů ŶŐŝŶĞĞƌŝŶŐ ĞƉ͘
ŽƵŶĚĂƚŝŽŶ ŶŐŝŶĞĞƌŝŶŐ ʹ ^ĞĐƚŝŽŶ EŽƚĞƐ
Ξ ŶŐ͘ ŚŵĂĚ DĂŚĞƌ ĚĂŵ
Gravity Retaining wall
Terminology and sizing
‫ܤ‬ ൌ ሺͲǤͷ ̱ ͲǤ͹ሻ ‫ܪ‬
ܽ ൌ ൬
ͳ
ͳʹ
൰ ‫ܪ‬ ൒ ͵Ͳ ܿ݉
ܶ ൌ ൬
ͳ
ͺ
̱
ͳ
͸
൰ ‫ܪ‬
‫ݐ‬ ൌ ൬
ͳ
ʹ
̱
ʹ
͵
൰ ܶ
‫ܦ‬ ൒ ͳ ݉

2. *5;9*5;9*5;9*5;9 ͮ ϯƌĚ zĞĂƌ ʹ ŝǀŝů ŶŐŝŶĞĞƌŝŶŐ ĞƉ͘
ŽƵŶĚĂƚŝŽŶ ŶŐŝŶĞĞƌŝŶŐ ʹ ^ĞĐƚŝŽŶ EŽƚĞƐ
Ξ ŶŐ͘ ŚŵĂĚ DĂŚĞƌ ĚĂŵ
Failure modes
1- Overturning
‫اﻟﺠﺬع‬ ‫دوران‬ ‫ﻳﺴﺒﺐ‬ ‫اﻟﱰﺑﺔ‬ ‫ﰲ‬ ‫اﳌﺘﻮﻟﺪ‬ ‫اﻟﺠﺎﻧﺒﻲ‬ ‫اﻟﻀﻐﻂ‬Stem‫ﻧﻘﻄﺔ‬ ‫ﺣﻮل‬B‫ﺣﻮل‬ ‫ﻛﻠﻪ‬ ‫اﻟﺤﺎﺋﻂ‬ ‫ودوران‬ ،
‫ﻧﻘﻄﺔ‬A.‫اﻟﺤﺎﺋﻂ‬ ‫ﻓﻮق‬ ‫اﻟﱰﺑﺔ‬ ‫ووزن‬ ‫ﻧﻔﺴﻪ‬ ‫اﻟﺤﺎﺋﻂ‬ ‫وزن‬ ‫اﻟﺪوران‬ ‫ﻫﺬا‬ ‫وﻳﻘﺎوم‬ .
Overturning moment ‫ܯ‬௢௩௘௥ ௧௨௥௡௜௡௚ = moment due to lateral earth forces.
Resisting moment ‫ܯ‬ோ௘௦௜௦௧௜௡௚ = moment due to weight of soil and weight of wall.
‫ﻫﻨﺎ‬ ‫ﻳﻜﻮن‬ ‫ان‬ ‫وﻻﺑﺪ‬‫اﳌﻘﺎوﻣﺔ‬ ‫واﻟﻌﺰوم‬ ‫اﳌﺆﺛﺮة‬ ‫اﻟﻌﺰوم‬ ‫ﺑني‬ ‫ﻣﻨﺎﺳﺐ‬ ‫اﻣﺎن‬ ‫ﻣﻌﺎﻣﻞ‬ ‫ك‬
ࡲǤ ࡻǤ ࡿࢇࢍࢇ࢏࢔࢙࢚ ࢕࢜ࢋ࢚࢛࢘࢘࢔࢏࢔ࢍ =
ࡹࡾࢋ࢙࢏࢙࢚࢏࢔ࢍ
ࡹ࢕࢜ࢋ࢘ ࢚࢛࢘࢔࢏࢔ࢍ
൒ 1.5

3. *5;9*5;9*5;9*5;9 ͮ ϯƌĚ zĞĂƌ ʹ ŝǀŝů ŶŐŝŶĞĞƌŝŶŐ ĞƉ͘
ŽƵŶĚĂƚŝŽŶ ŶŐŝŶĞĞƌŝŶŐ ʹ ^ĞĐƚŝŽŶ EŽƚĞƐ
Ξ ŶŐ͘ ŚŵĂĚ DĂŚĞƌ ĚĂŵ
2- Sliding
‫اﻟ‬ ‫ﺗﺤﺮك‬ ‫ﻳﺴﺒﺐ‬ ‫اﻟﱰﺑﺔ‬ ‫ﰲ‬ ‫اﳌﺘﻮﻟﺪ‬ ‫اﻟﺠﺎﻧﺒﻲ‬ ‫اﻟﻀﻐﻂ‬‫ﺠﺬع‬Stem‫ﺣﺮﻛﺔ‬(‫)اﻧﺰﻻق‬ ‫ﺟﺎﻧﺒﻴﺔ‬‫اﻟﻘﻄﺎع‬ ‫ﻋﲆ‬BB’
‫ﻋﲆ‬ (‫)اﻧﺰﻻق‬ ‫ﺟﺎﻧﺒﻴﺔ‬ ‫ﺣﺮﻛﺔ‬ ‫ﻛﻠﻪ‬ ‫اﻟﺤﺎﺋﻂ‬ ‫ﺗﺤﺮك‬ ‫وﻳﺴﺒﺐ‬‫اﻟﻘﻄﺎع‬AA’.
‫ﻗﻮ‬ ‫اﻻﻧﺰﻻق‬ ‫ﻫﺬا‬ ‫وﻳﻘﺎوم‬‫ى‬‫ﻋﲆ‬ ‫واﻟﻘﺎﻋﺪة‬ ‫اﻟﺠﺬع‬ ‫ﺑني‬ ‫اﻻﺣﺘﻜﺎك‬‫اﻟﻘﻄﺎع‬BB’‫وﻗﻮ‬ ،‫ى‬‫اﻟﻘﺎﻋﺪة‬ ‫ﺑني‬ ‫اﻻﺣﺘﻜﺎك‬
‫اﻟﻘﻄﺎع‬ ‫ﻋﲇ‬ ‫ﻣﻨﻬﺎ‬ ‫اﺳﻔﻞ‬ ‫واﻟﱰﺑﺔ‬AA’.
Sliding forces ‫ܨ‬ௌ௟௜ௗ௜௡௚ = Active Lateral earth forces
Resisting forces ‫ܨ‬ோ௘௦௜௦௧௜௡௚ = Friction forces
‫اﻟﺮأﺳﻴﺔ‬ ‫اﻟﻘﻮي‬ ‫ﻣﺠﻤﻮع‬ ‫ﺗﺴﺎوي‬ ‫اﻻﺣﺘﻜﺎك‬ ‫ﻗﻮي‬ ‫و‬)(‫ﻓﻮﻗﻪ‬ ‫اﻟﱰﺑﺔ‬ ‫ووزن‬ ‫اﻟﺤﺎﺋﻂ‬ ‫وزن‬‫ﻣﻌﺎﻣﻞ‬ ‫ﰲ‬ ‫ﻣﴬوب‬
‫اﻻﺣﺘﻜﺎك‬Ɋ‫واﻟﺬي‬‫اﻻﺣﺘﻜﺎك‬ ‫ﻓﻴﻪ‬ ‫ﻳﺤﺪث‬ ‫اﻟﺬي‬ ‫اﻟﻮﺳﻂ‬ ‫ﻧﻮع‬ ‫ﻋﲇ‬ ‫ﻳﺘﻮﻗﻒ‬.
‫ܨ‬ோ௘௦௜௦௧௜௡௚= σ ‫ݏݐ݄݃݅݁ݓ‬ × ȝ in cohesionless soil
‫ܨ‬ோ௘௦௜௦௧௜௡௚= σ ‫ݏݐ݄݃݅݁ݓ‬ × ȝ + (0.8×‫ܥ‬௨)×B in cohesive soil
ȝ = 0.33 Clay
ȝ = 0.6 Sand
ȝ = 0.7 Friction between 2 concrete faces

4. *5;9*5;9*5;9*5;9 ͮ ϯƌĚ zĞĂƌ ʹ ŝǀŝů ŶŐŝŶĞĞƌŝŶŐ ĞƉ͘
ŽƵŶĚĂƚŝŽŶ ŶŐŝŶĞĞƌŝŶŐ ʹ ^ĞĐƚŝŽŶ EŽƚĞƐ
Ξ ŶŐ͘ ŚŵĂĚ DĂŚĞƌ ĚĂŵ
(‫)اﻻﺣﺘﻜﺎك‬ ‫اﳌﻘﺎوﻣﺔ‬ ‫وﻗﻮي‬ ‫اﻻﻧﺰﻻق‬ ‫ﻗﻮى‬ ‫ﺑني‬ ‫ﻣﻨﺎﺳﺐ‬ ‫اﻣﺎن‬ ‫ﻣﻌﺎﻣﻞ‬ ‫ﻫﻨﺎك‬ ‫ﻳﻜﻮن‬ ‫ان‬ ‫وﻻﺑﺪ‬
ࡲǤ ࡻǤ ࡿࢇࢍࢇ࢏࢔࢙࢚ ࢙࢒࢏ࢊ࢏࢔ࢍ =
ࡲࡾࢋ࢙࢏࢙࢚࢏࢔ࢍ
ࡲࡿ࢒࢏ࢊ࢏࢔ࢍ
൒ 2
‫اﻟـ‬ ‫ﻣﻦ‬ ‫ﺟﺰء‬ ‫أﺧﺬ‬ ‫اﳌﻤﻜﻦ‬ ‫ﻣﻦ‬ ‫اﻻﻧﺰﻻق‬ ‫ﳌﻘﺎوﻣﺔ‬ ‫ﻛﺎﻓﻴﺔ‬ ‫ﻏري‬ ‫اﻻﺣﺘﻜﺎك‬ ‫ﻗﻮى‬ ‫ﻛﺎﻧﺖ‬ ‫إذا‬Passive forces‫ﰲ‬
‫ﻣﻘﺎوﻣﺔ‬ ‫ﻛﻘﻮى‬ ‫اﻻﻋﺘﺒﺎر‬.
‫ܨ‬ோ௘௦௜௦௧௜௡௚= σ ‫ݏݐ݄݃݅݁ݓ‬ × ȝ + (0.8×‫ܥ‬௨)×B +
૚
૜
σ ࡱ࢖
‫اﻟـ‬ ‫و‬ ‫اﻻﺣﺘﻜﺎك‬ ‫ﻗﻮى‬ ‫ﻛﺎﻧﺖ‬ ‫إذا‬passive force‫ﻻﺳﺘﺨﺪام‬ ‫ﻧﻠﺠﺄ‬ ،‫ﻛﺎﻓﻴﺔ‬ ‫ﻏري‬ ‫اﳌﺄﺧﻮذة‬key

5. *5;9*5;9*5;9*5;9 ͮ ϯƌĚ zĞĂƌ ʹ ŝǀŝů ŶŐŝŶĞĞƌŝŶŐ ĞƉ͘
ŽƵŶĚĂƚŝŽŶ ŶŐŝŶĞĞƌŝŶŐ ʹ ^ĞĐƚŝŽŶ EŽƚĞƐ
Ξ ŶŐ͘ ŚŵĂĚ DĂŚĞƌ ĚĂŵ
3- Bearing capacity
‫ﻃﺮﻳﻖ‬ ‫ﻋﻦ‬ ‫وﻳﻨﺘﻘﻞ‬ .(‫ﻓﻮﻗﻪ‬ ‫اﻟﱰﺑﺔ‬ ‫ووزن‬ ‫اﻟﺤﺎﺋﻂ‬ ‫)وزن‬ ‫اﻻوزان‬ ‫ﻣﺤﺼﻠﺔ‬ ‫ﻋﻦ‬ ‫ﻧﺎﺗﺞ‬ ‫ﻳﻜﻮن‬ ‫ﻟﻠﱰﺑﺔ‬ ‫اﳌﻨﻘﻮل‬ ‫اﻻﺟﻬﺎد‬
.‫اﻟﺤﺎﺋﻂ‬ ‫ﻗﺎﻋﺪة‬
‫ﰲ‬ ‫ﺗﺆﺛﺮ‬ ‫ﻻ‬ ‫اﻻوزان‬ ‫ﻣﺤﺼﻠﺔ‬Centroid‫ﺑـ‬ ‫ﺗﺆﺛﺮ‬ ‫وﻟﻜﻦ‬ ً‫ﺎ‬‫متﺎﻣ‬ ‫اﻟﻘﺎﻋﺪة‬eccentricityً‫ﻻ‬‫او‬ ‫ﺣﺴﺎﺑﻬﺎ‬ ‫ﻳﺘﻢ‬ ‫ﻣﻌﻴﻨﺔ‬
‫ﻟﻠﱰﺑﺔ‬ ‫اﳌﻨﻘﻮﻟﺔ‬ ‫اﻻﺟﻬﺎدات‬ ‫ﻟﺤﺴﺎب‬.

6. *5;9*5;9*5;9*5;9 ͮ ϯƌĚ zĞĂƌ ʹ ŝǀŝů ŶŐŝŶĞĞƌŝŶŐ ĞƉ͘
ŽƵŶĚĂƚŝŽŶ ŶŐŝŶĞĞƌŝŶŐ ʹ ^ĞĐƚŝŽŶ EŽƚĞƐ
Ξ ŶŐ͘ ŚŵĂĚ DĂŚĞƌ ĚĂŵ
‫اﻟـ‬ ‫ﺣﺴﺎب‬eccentricity
‫ﺑني‬ ‫واﻟﻔﺮق‬ ،‫اﻻوزان‬ ‫ﻣﺤﺼﻠﺔ‬ ‫ﻋﻠﻴﻬﺎ‬ ‫ﻳﺆﺛﺮ‬ ‫اﻟﺤﺎﺋﻂ‬ ‫ﻗﺎﻋﺪة‬Overturning moment‫و‬Resisting moment
‫ﺣﻮل‬‫ﻧﻘﻄﺔ‬A
‫ܯ‬ோ௘௦௜௦௧௜௡௚ - ‫ܯ‬௢௩௘௥ ௧௨௥௡௜௡௚ = σ ‫ݏݐ݄݃݅݁ݓ‬ × ܺ
ܺ =
ெೃ೐ೞ೔ೞ೟೔೙೒ ି ெ೚ೡ೐ೝ ೟ೠೝ೙೔೙೒
σ ௪௘௜௚௛௧௦
e =
஻
ଶ
– ܺ
:‫ﻣﻠﺤﻮﻇﺔ‬‫اﻟـ‬Core‫اﻟﻨﻮع‬ ‫ﻧﻔﺲ‬ ‫ﻣﻦ‬ ‫ﻛﻠﻬﺎ‬ ‫اﻻﺟﻬﺎدات‬ ‫ﺗﻜﻮن‬ ،‫اﻟﻘﻮة‬ ‫ﻓﻴﻬﺎ‬ ‫أﺛﺮت‬ ‫إذا‬ ‫اﻟﺘﻲ‬ ‫اﳌﻨﻄﻘﺔ‬ ‫ﻫﻮ‬ ‫ﻗﻄﺎع‬ ‫ﻷي‬
)‫إذا‬(‫ﻟﻠﺸﺪ‬ ‫ﺑﺎﻟﻨﺴﺒﺔ‬ ‫ﺻﺤﻴﺢ‬ ‫واﻟﻌﻜﺲ‬ ‫ﺿﻐﻂ‬ ‫اﻻﺟﻬﺎدات‬ ‫ﺗﻜﻮن‬ ‫ﺿﻐﻂ‬ ‫اﻟﻘﻮة‬ ‫ﻛﺎﻧﺖ‬
‫اﻟـ‬ ‫ﺧﺎرج‬ ‫اﻟﻘﻮة‬ ‫اﺛﺮت‬ ‫وإذا‬Core‫اﻹﺟﻬﺎدا‬ ‫ﺗﻜﻮن‬‫ت‬‫ﺛﻢ‬ ‫اﻟﻘﻮة‬ ‫ﻣﻦ‬ ‫اﻟﻘﺮﻳﺒﺔ‬ ‫اﳌﻨﻄﻘﺔ‬ ‫ﰲ‬ ‫اﻟﻘﻮة‬ ‫ﻟﻨﻮع‬ ‫ﻣﺸﺎﺑﻬﺔ‬
‫ﻟﻠﺼﻔ‬ ‫ﺗﺼﻞ‬ ‫ﺣﺘﻰ‬ ‫ﺗﻘﻞ‬‫اﻷﺧﺮى‬ ‫اﻟﺠﻬﺔ‬ ‫ﰲ‬ ‫اﻟﻘﻮة‬ ‫ﻧﻮع‬ ‫ﻋﻜﺲ‬ ‫وﺗﺼﺒﺢ‬ ‫ﺮ‬
‫اﻟـ‬ ‫ﻳﻘﻊ‬ ،‫اﳌﺴﺘﻄﻴﻞ‬ ‫ﻟﻠﻘﻄﺎع‬ ‫ﺑﺎﻟﻨﺴﺒﺔ‬Core.‫ﺑﺎﻟﺸﻜﻞ‬ ‫ﻣﻮﺿﺢ‬ ‫ﻫﻮ‬ ‫ﻛام‬ ‫ﻟﻠﻘﻄﺎع‬ ‫اﻷوﺳﻂ‬ ‫اﻟﺜﻠﺚ‬ ‫ﰲ‬

7. *5;9*5;9*5;9*5;9 ͮ ϯƌĚ zĞĂƌ ʹ ŝǀŝů ŶŐŝŶĞĞƌŝŶŐ ĞƉ͘
ŽƵŶĚĂƚŝŽŶ ŶŐŝŶĞĞƌŝŶŐ ʹ ^ĞĐƚŝŽŶ EŽƚĞƐ
Ξ ŶŐ͘ ŚŵĂĚ DĂŚĞƌ ĚĂŵ
If e ൏
۰
૟
(Inside the core)
‫اﻟـ‬ ‫داﺧﻞ‬ ‫اﻟﻘﻮة‬ ‫ﺗﺆﺛﺮ‬Core‫ﺿﻐﻂ‬ ‫ﻛﻠﻬﺎ‬ ‫اﻻﺟﻬﺎدات‬ ‫ﺗﺼﺒﺢ‬ ‫وﺑﺎﻟﺘﺎﱄ‬.
࣌૚ǡ૛ =
ࡺ
࡭
േ
ࡹǤࢅ
ࡵ
ൌ σ ‫ݏݐ݄݃݅݁ݓ‬
ൌ σ ‫×ݏݐ݄݃݅݁ݓ‬‡

8. ൌ
஻య
ଵଶ
ൌ
࣌૚ǡ૛ ൌൌൌൌ
σ ௪௘௜௚௛௧௦
࡮
േ
σ ௪௘௜௚௛௧௦ൈ௘ ൈ଴Ǥହ஻
ಳయ
భమ
࣌૚ǡ૛ ൌൌൌൌ
σ ࢝ࢋ࢏ࢍࢎ࢚࢙
࡮
ሺͳሺͳሺͳሺͳ േ
૟Ǥࢋ
࡮
ሻሻሻሻ
‫ﻣﻦ‬ ‫اﻗﻞ‬ ‫اﻻﺟﻬﺎدات‬ ‫ﺗﻜﻮن‬ ‫ان‬ ‫وﻻﺑﺪ‬allowable bearing capacity.
‫ﺣﺪوث‬ ‫وﻟﺘﻼﳾ‬Differential settlement‫ﺗﻜﻮن‬ ‫ان‬ ‫ﻻﺑﺪ‬ ‫ﻛﺒري‬

9. *5;9*5;9*5;9*5;9 ͮ ϯƌĚ zĞĂƌ ʹ ŝǀŝů ŶŐŝŶĞĞƌŝŶŐ ĞƉ͘
ŽƵŶĚĂƚŝŽŶ ŶŐŝŶĞĞƌŝŶŐ ʹ ^ĞĐƚŝŽŶ EŽƚĞƐ
Ξ ŶŐ͘ ŚŵĂĚ DĂŚĞƌ ĚĂŵ
If e ൐
۰
૟
(Outside the core)
‫اﻟﻘﻮة‬ ‫ﺗﺆﺛﺮ‬‫ﺧﺎرج‬‫اﻟـ‬Core‫ﺗ‬ ‫وﺑﺎﻟﺘﺎﱄ‬.‫ﺷﺪ‬ ‫اﺟﻬﺎدات‬ ‫ﻈﻬﺮ‬
‫اﻹﺟﻬﺎدا‬ ‫ﻓﺈن‬ ‫ﺷﺪ‬ ‫اﺟﻬﺎدات‬ ‫ﺗﺘﺤﻤﻞ‬ ‫ﻻ‬ ‫اﻟﱰﺑﺔ‬ ‫وﻷن‬‫ت‬‫اﻟﻘﻮة‬ ‫ﺗﺆﺛﺮ‬ ‫ﻣﺜﻠﺚ‬ ‫ﺷﻜﻞ‬ ‫ﻋﲇ‬ ‫ﻟﺘﺼﺒﺢ‬ ‫ﻧﻔﺴﻬﺎ‬ ‫ﺗﻮزﻳﻊ‬ ‫ﺗﻌﻴﺪ‬
‫اﻟـ‬ ‫ﰲ‬Centroid.
ͲǤͷߪଵ ൈ ‫ܮ‬ =σ ‫ݏݐ݄݃݅݁ݓ‬
ͲǤͷߪଵ ൈ ͵ܺ = σ ‫ݏݐ݄݃݅݁ݓ‬
࣌૚ =
૛ σ ࢝ࢋ࢏ࢍࢎ࢚࢙
૜ሺ૙Ǥ૞࡮ିࢋሻ
࣌૛ = zero

10. *5;9*5;9*5;9*5;9 ͮ ϯƌĚ zĞĂƌ ʹ ŝǀŝů ŶŐŝŶĞĞƌŝŶŐ ĞƉ͘
ŽƵŶĚĂƚŝŽŶ ŶŐŝŶĞĞƌŝŶŐ ʹ ^ĞĐƚŝŽŶ EŽƚĞƐ
Ξ ŶŐ͘ ŚŵĂĚ DĂŚĞƌ ĚĂŵ
4- Excessive settlement
‫اﻟﻬﺒﻮط‬ ‫ﺣﺴﺎب‬ ‫ﻳﺠﺐ‬Settlement‫اﻟﻬﺒﻮط‬ ‫وﻓﺮق‬ ‫ﻟﻠﺤﺎﺋﻂ‬Differential settlement‫ﰲ‬ ‫اﻧﻬﻢ‬ ‫واﻟﺘﺄﻛﺪ‬
‫اﳌﺴﻤﻮح‬ ‫ﺣﺪود‬.
5- Rotational sliding (Global slope failure)
‫اﻻﻧﺰﻻق‬ ‫ﻫﺬا‬ ‫وﻳﻘﺎوم‬ ،‫ﻧﻔﺴﻪ‬ ‫اﻟﱰﺑﺔ‬ ‫ﻟـﻮزن‬ ‫ﻧﺘﻴﺠﺔ‬ ‫ﻣﻌني‬ ‫ﻣﺴﺘﻮي‬ ‫ﻋﲆ‬ ‫واﺣﺪة‬ ‫ﻛـﻜﺘﻠﺔ‬ ‫ﻟﻼﻧﺰﻻق‬ ‫ﺗﺘﻌﺮض‬ ‫اﻟﱰﺑﺔ‬
‫اﻟﱰﺑﺔ‬ ‫متﺎﺳﻚ‬Cohesion‫ﻛﺎﻧﺖ‬ ‫إذا‬Cohesive soil‫اﻟﺪاﺧﲇ‬ ‫اﻻﺣﺘﻜﺎك‬ ‫زاوﻳﺔ‬ ‫أو‬Angle of friction‫إذا‬
‫ﻛﺎﻧﺖ‬Cohesionless soil.‫اﻻﻧﺰﻻق‬ ‫ﻣﺴﺘﻮي‬ ‫ﻋﲆ‬
‫ا‬ ‫ﻟـﻬﺬا‬ ‫أﻛرث‬ ‫ﺗﻔﺎﺻﻴﻞ‬‫اﳌﻴﻮل‬ ‫ان‬‫ﺰ‬‫واﺗ‬ ‫ﺛﺒﺎت‬ ‫دراﺳﺔ‬ ‫ﰲ‬ ‫ﺗﻜﻮن‬ ‫ﳌﻮﺿﻮع‬Slope stability.

11. *5;9*5;9*5;9*5;9 ͮ ϯƌĚ zĞĂƌ ʹ ŝǀŝů ŶŐŝŶĞĞƌŝŶŐ ĞƉ͘
ŽƵŶĚĂƚŝŽŶ ŶŐŝŶĞĞƌŝŶŐ ʹ ^ĞĐƚŝŽŶ EŽƚĞƐ
Ξ ŶŐ͘ ŚŵĂĚ DĂŚĞƌ ĚĂŵ
Design steps of Cantilever Gravity wall
‫وﺿﻊ‬ ‫اﻋﻲ‬‫ﺮ‬ُ‫ﻳ‬Surcharge loadmin‫اﻟـ‬ ‫ﻋﲆ‬Back fill‫ﻗﻴﻤﺘﻪ‬1‫ݐ‬ ݉ଶΤ‫اﻟﺤﻴﺔ‬ ‫اﻻﺣامل‬ ‫ﺗﺄﺛري‬ ‫ﻻﻋﺘﺒﺎر‬ .
‫مل‬ ‫ﻟﻮ‬ ‫ﺣﺘﻰ‬ ‫اﻟﺘﻨﻔﻴﺬ‬ ‫اﺛﻨﺎء‬ ‫اﻟﺤﻔﺮ‬ ‫وأدوات‬ ‫اﻟﺘﺸﻮﻳﻨﺎت‬ ‫ﻣﻦ‬ ‫اﻟﻨﺎﺗﺠﺔ‬.‫ﻌﻄﻲ‬ُ‫ﻣ‬ ‫ﻳﻜﻦ‬
1- Soil properties
Calcukate ‫ܭ‬௔ , ‫ܭ‬௣ for soil layers
2- Acting forces and moments
‫ﻧﻘﻄﺔ‬ ‫ﺣﻮل‬ ‫ﺗﺴﺒﺒﻬﺎ‬ ‫اﻟﺘﻲ‬ ‫واﻟﻌﺰوم‬ ،‫اﻟﺠﺎﻧﺒﻴﺔ‬ ‫واﻟﻘﻮي‬ ،‫ﻟﻠﱰﺑﺔ‬ ‫اﻟﺠﺎﻧﺒﻲ‬ ‫اﻟﻀﻐﻂ‬ ‫ﺣﺴﺎب‬ ‫ﻳﺘﻢ‬A
No e
ሺ‫ݐ‬ ݉ଶ
ሻΤ
E ሺ‫ݐ‬ ݉ᇱΤ ሻ Y ሺ݉ሻ M ሺ‫ݐ‬Ǥ ݉ ݉ᇱΤ )
1 Active forces only ‫اﻟﺮأﺳﻴﺔ‬ ‫اﳌﺴﺎﻓﺔ‬
‫اﻟﻘﻮة‬ ‫ﺑني‬
‫وﻧﻘﻄﺔ‬A
M = E×Y
2
3
4
….
σ ࡱ = ࡲ࢙࢒࢏ࢊ࢏࢔ࢍ σ ࡹ = ࡹ࢕࢜ࢋ࢚࢛࢘࢘࢔࢏࢔ࢍ

12. *5;9*5;9*5;9*5;9 ͮ ϯƌĚ zĞĂƌ ʹ ŝǀŝů ŶŐŝŶĞĞƌŝŶŐ ĞƉ͘
ŽƵŶĚĂƚŝŽŶ ŶŐŝŶĞĞƌŝŶŐ ʹ ^ĞĐƚŝŽŶ EŽƚĞƐ
Ξ ŶŐ͘ ŚŵĂĚ DĂŚĞƌ ĚĂŵ
3- Resisting forces and moments
‫ﺑﺎﻟﺮﺳﻢ‬ ‫ﻣﻮﺿﺢ‬ ‫ﻫﻮ‬ ‫ﻛام‬ ‫وزﻧﻬﺎ‬ ‫ﺣﺴﺎب‬ ‫ﻞ‬ُ‫ﻬ‬‫ﻳﺴ‬ ‫اء‬‫ﺰ‬‫أﺟ‬ ‫اﱄ‬ ‫ﻓﻮﻗﻪ‬ ‫واﻟﱰﺑﺔ‬ ‫اﻟﺤﺎﺋﻂ‬ ‫ﺗﻘﺴﻴﻢ‬ ‫ﻳﺘﻢ‬‫اﻟﺴﺎﺑﻖ‬،‫ﺣﺴﺎب‬ ‫ﺛﻢ‬
‫ﺗﺴﺒﺒﻬﺎ‬ ‫اﻟﺘﻲ‬ ‫اﻟﻌﺰوم‬‫ﻧﻘﻄﺔ‬ ‫ﺣﻮل‬A.
No W ሺ‫ݐ‬ ݉ᇱ
ሻΤ X ሺ݉ሻ M ሺ‫ݐ‬Ǥ ݉ ݉ᇱΤ )
1 ‫اﳌﺴﺎﻓﺔ‬
‫اﻻﻓﻘﻴﺔ‬‫ﺑني‬
‫وﻧﻘﻄﺔ‬ ‫اﻟﻘﻮة‬
A
M = W×X
2
3
4
….
σ ࢃ =σ ࢝ࢋ࢏ࢍࢎ࢚࢙ σ ࡹ = ࡹࡾࢋ࢙࢏࢙࢚࢏࢔ࢍ
4- Check against Overturning
ࡲǤ ࡻǤ ࡿࢇࢍࢇ࢏࢔࢙࢚ ࢕࢜ࢋ࢚࢛࢘࢘࢔࢏࢔ࢍ =
ࡹࡾࢋ࢙࢏࢙࢚࢏࢔ࢍ
ࡹ࢕࢜ࢋ࢘ ࢚࢛࢘࢔࢏࢔ࢍ
൒ 1.5
If not safe Increase dimensions
5- Check against sliding
‫ܨ‬ோ௘௦௜௦௧௜௡௚= σ ‫ݏݐ݄݃݅݁ݓ‬ × ȝ in cohesionless soil
‫ܨ‬ோ௘௦௜௦௧௜௡௚= σ ‫ݏݐ݄݃݅݁ݓ‬ × ȝ + (0.8×‫ܥ‬௨)×B in cohesive soil
ȝ = 0.33 Clay
ȝ = 0.6 Sand
ȝ = 0.7 Friction between 2 concrete faces
ࡲǤ ࡻǤ ࡿࢇࢍࢇ࢏࢔࢙࢚ ࢙࢒࢏ࢊ࢏࢔ࢍ =
ࡲࡾࢋ࢙࢏࢙࢚࢏࢔ࢍ
ࡲ࢙࢒࢏ࢊ࢏࢔ࢍ
൒ 2
If not safe, Egyptian code permits to take a part of passive forces as a resisting
force
‫ܨ‬ோ௘௦௜௦௧௜௡௚= σ ‫ݏݐ݄݃݅݁ݓ‬ × ȝ + (0.8×‫ܥ‬௨)×B +
૚
૜
σ ࡱ࢖
If not safe, use key

13. *5;9*5;9*5;9*5;9 ͮ ϯƌĚ zĞĂƌ ʹ ŝǀŝů ŶŐŝŶĞĞƌŝŶŐ ĞƉ͘
ŽƵŶĚĂƚŝŽŶ ŶŐŝŶĞĞƌŝŶŐ ʹ ^ĞĐƚŝŽŶ EŽƚĞƐ
Ξ ŶŐ͘ ŚŵĂĚ DĂŚĞƌ ĚĂŵ
6- Check soil stress
‫ܯ‬ோ௘௦௜௦௧௜௡௚ - ‫ܯ‬௢௩௘௥ ௧௨௥௡௜௡௚ = σ ‫ݏݐ݄݃݅݁ݓ‬ × ܺ
ܺ =
ெೃ೐ೞ೔ೞ೟೔೙೒ ି ெ೚ೡ೐ೝ ೟ೠೝ೙೔೙೒
σ ௪௘௜௚௛௧௦
e =
஻
ଶ
– ܺ
If e ൏
୆
଺
(Inside the core)
࣌૚ǡ૛ ൌൌൌൌ
σ ࢝ࢋ࢏ࢍࢎ࢚࢙
࡮
ሺͳሺͳሺͳሺͳ േ
૟Ǥࢋ
࡮
ሻሻሻሻ
If e ൐
୆
଺
(Outside the core)
࣌૚ =
૛ σ ࢝ࢋ࢏ࢍࢎ࢚࢙
૜ሺ૙Ǥ૞࡮ିࢋሻ
࣌૛ = zero
If ࣌૚ǡ૛ ൑ allowable B.C Ok safe
If ࣌૚ǡ૛ ൐ allowable B.C Not safe Increase B

14. *5;9*5;9*5;9*5;9 ͮ ϯƌĚ zĞĂƌ ʹ ŝǀŝů ŶŐŝŶĞĞƌŝŶŐ ĞƉ͘
ŽƵŶĚĂƚŝŽŶ ŶŐŝŶĞĞƌŝŶŐ ʹ ^ĞĐƚŝŽŶ EŽƚĞƐ
Ξ ŶŐ͘ ŚŵĂĚ DĂŚĞƌ ĚĂŵ
7- Design of concrete critical section
‫ﻋﺮﺿﻬﺎ‬ ‫ﴍﻳﺤﺔ‬ ‫ﻧﺼﻤﻢ‬ ،‫اﻟﻘﻄﺎﻋﺎت‬ ‫ﻟﺠﻤﻴﻊ‬1‫ﻳﻜﻮن‬ ‫ان‬ ‫اﻋﻲ‬‫ﺮ‬ُ‫ﻳ‬‫و‬ ،‫ﻣﱰ‬Concrete cover‫ﻳﺴﺎوي‬7‫ﺳﻢ‬
a- Stem
‫ﻳﺘﻢ‬‫ﺣﺴﺎب‬‫ܯ‬௥௘௦௜௦௧௜௡௚‫و‬‫ܯ‬௔௖௧௜௡௚‫اﻟـ‬ ‫ﻗﻄﺎع‬ ‫ﻓﻮق‬ ‫اﳌﻮﺟﻮدة‬ ‫واﻻوزان‬ ‫ﺑﺎﻟﻘﻮي‬ ‫وﻟﻜﻦ‬ ‫اﻟﻄﺮﻳﻘﺔ‬ ‫ﺑﻨﻔﺲ‬
Stem(‫ﻣﻮﺟﻮدة‬ ‫ﻏري‬ ‫اﻟﺤﺎﺋﻂ‬ ‫ﻗﺎﻋﺪة‬ ‫ﻧﻌﺘﱪ‬ ‫)أي‬ .‫ﻓﻘﻂ‬.
‫ܯ‬஽௘௦௜௚௡ =1.5 (‫ܯ‬௔௖௧௜௡௚ - ‫ܯ‬௥௘௦௜௦௧௜௡௚)
.(‫اﻟﺨﻠﻔﻲ‬ ‫اﻟﺮدم‬ ‫)ﺟﻬﺔ‬ ‫اﻟﺸﺪ‬ ‫ﺟﻬﺔ‬ ‫اﻟﺘﺴﻠﻴﺢ‬ ‫ﺣﺪﻳﺪ‬ ‫ﻮﺿﻊ‬ُ‫ﻳ‬‫و‬ ‫اﻟﻌﺰم‬ ‫ﻫﺬا‬ ‫ﻋﲆ‬ ‫اﻟﻘﻄﺎع‬ ‫ﻳﺼﻤﻢ‬

15. *5;9*5;9*5;9*5;9 ͮ ϯƌĚ zĞĂƌ ʹ ŝǀŝů ŶŐŝŶĞĞƌŝŶŐ ĞƉ͘
ŽƵŶĚĂƚŝŽŶ ŶŐŝŶĞĞƌŝŶŐ ʹ ^ĞĐƚŝŽŶ EŽƚĞƐ
Ξ ŶŐ͘ ŚŵĂĚ DĂŚĞƌ ĚĂŵ
b- Heel
‫اﻟـ‬ ‫ﻗﻄﺎع‬ ‫ﻋﲆ‬ ‫اﳌﺆﺛﺮة‬ ‫اﻟﻌﺰوم‬Heel‫ﻫﻲ‬:
1-‫اﻟـ‬ ‫ﻓﻮق‬ ‫اﳌﻮﺟﻮدة‬ ‫ان‬‫ز‬‫اﻻو‬ ‫ﻋﻦ‬ ‫ﻧﺎﺗﺠﺔ‬ ‫ﻋﺰوم‬Heel.‫ﻓﻘﻂ‬‫ܯ‬௪
2-‫اﳌﺘﻮﻟﺪة‬ ‫اﻟﱰﺑﺔ‬ ‫اﺟﻬﺎدات‬ ‫ﻋﻦ‬ ‫ﻧﺎﺗﺠﺔ‬ ‫ﻋﺰوم‬‫أﺳﻔﻞ‬‫اﻟـ‬Heel.‫ﻓﻘﻂ‬‫ܯ‬௦
‫ﺣﺴﺎب‬ࡹ࢙
‫ﻗﻴﻤﺔ‬ ‫ﻧﺴﺘﻨﺘﺞ‬ ‫اﳌﺜﻠﺜﺎت‬ ‫ﺗﺸﺎﺑﻪ‬ ‫ﻣﻦ‬࣌ᇱ
‫اﻟـ‬ ‫اﺳﻔﻞ‬ ‫اﻻﺟﻬﺎدات‬ ‫ﻣﺴﺎﺣﺔ‬ ‫ﻧﺮﻛﺰﻫﺎ‬ ‫ﺛﻢ‬Heel‫اﻟﻘﻮة‬ ‫ﰲ‬ࢌᇱ
݂ᇱ
= ሺߪᇱ
െ ߪଶሻ ൈ ͲǤͷܾ + ߪଶ ൈ ܾ
ࡹ࢙ = ࢌᇱ
× moment arm
‫ܯ‬஽௘௦௜௚௡ =1.5 (‫ܯ‬௪ - ‫ܯ‬௦)
) ‫اﻟﺸﺪ‬ ‫ﺟﻬﺔ‬ ‫اﻟﺘﺴﻠﻴﺢ‬ ‫ﺣﺪﻳﺪ‬ ‫ﻮﺿﻊ‬ُ‫ﻳ‬‫و‬ ‫اﻟﻌﺰم‬ ‫ﻫﺬا‬ ‫ﻋﲆ‬ ‫اﻟﻘﻄﺎع‬ ‫ﻳﺼﻤﻢ‬‫اﻟﻘﻄﺎع‬ ‫اﻋﲇ‬.(

16. *5;9*5;9*5;9*5;9 ͮ ϯƌĚ zĞĂƌ ʹ ŝǀŝů ŶŐŝŶĞĞƌŝŶŐ ĞƉ͘
ŽƵŶĚĂƚŝŽŶ ŶŐŝŶĞĞƌŝŶŐ ʹ ^ĞĐƚŝŽŶ EŽƚĞƐ
Ξ ŶŐ͘ ŚŵĂĚ DĂŚĞƌ ĚĂŵ
c- Toe
‫اﻟـ‬ ‫ﻗﻄﺎع‬ ‫ﻋﲆ‬ ‫اﳌﺆﺛﺮة‬ ‫اﻟﻌﺰوم‬Toe‫ﻫﻲ‬:
1-‫اﻟـ‬ ‫ﻓﻮق‬ ‫اﳌﻮﺟﻮدة‬ ‫ان‬‫ز‬‫اﻻو‬ ‫ﻋﻦ‬ ‫ﻧﺎﺗﺠﺔ‬ ‫ﻋﺰوم‬Toe.‫ﻓﻘﻂ‬‫ܯ‬௪
2-‫اﻟـ‬ ‫أﺳﻔﻞ‬ ‫اﳌﺘﻮﻟﺪة‬ ‫اﻟﱰﺑﺔ‬ ‫اﺟﻬﺎدات‬ ‫ﻋﻦ‬ ‫ﻧﺎﺗﺠﺔ‬ ‫ﻋﺰوم‬Toe.‫ﻓﻘﻂ‬‫ܯ‬௦
‫ﺣﺴﺎب‬ࡹ࢙
‫ﻗﻴﻤﺔ‬ ‫ﻧﺴﺘﻨﺘﺞ‬ ‫اﳌﺜﻠﺜﺎت‬ ‫ﺗﺸﺎﺑﻪ‬ ‫ﻣﻦ‬࣌ᇱ
‫اﻟـ‬ ‫اﺳﻔﻞ‬ ‫اﻻﺟﻬﺎدات‬ ‫ﻣﺴﺎﺣﺔ‬ ‫ﻧﺮﻛﺰﻫﺎ‬ ‫ﺛﻢ‬Toe‫اﻟﻘﻮة‬ ‫ﰲ‬ࢌᇱ
݂ᇱ
= ሺߪଵ െ ߪᇱሻ ൈ ͲǤͷܾ + ߪᇱ
ൈ ܾ
ࡹ࢙ = ࢌᇱ
× moment arm
‫ܯ‬஽௘௦௜௚௡ =1.5 (‫ܯ‬௦ - ‫ܯ‬௪)
‫ﻳﺼﻤﻢ‬) ‫اﻟﺸﺪ‬ ‫ﺟﻬﺔ‬ ‫اﻟﺘﺴﻠﻴﺢ‬ ‫ﺣﺪﻳﺪ‬ ‫ﻮﺿﻊ‬ُ‫ﻳ‬‫و‬ ‫اﻟﻌﺰم‬ ‫ﻫﺬا‬ ‫ﻋﲆ‬ ‫اﻟﻘﻄﺎع‬‫اﻟﻘﻄﺎع‬ ‫أﺳﻔﻞ‬.(

17. *5;9*5;9*5;9*5;9 ͮ ϯƌĚ zĞĂƌ ʹ ŝǀŝů ŶŐŝŶĞĞƌŝŶŐ ĞƉ͘
ŽƵŶĚĂƚŝŽŶ ŶŐŝŶĞĞƌŝŶŐ ʹ ^ĞĐƚŝŽŶ EŽƚĞƐ
Ξ ŶŐ͘ ŚŵĂĚ DĂŚĞƌ ĚĂŵ
8- Detailing